Download GATE GATE CE Civil Question Paper With Solution Part 1

Download GATE (Graduate Aptitude Test in Engineering) GATE CE Civil Question Paper With Solution Part 1

2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D
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2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :
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2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.
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2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00

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2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status
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2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :
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2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance
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2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2

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2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
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2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth
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2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :
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2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.

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2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is
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2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.
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2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :
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2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.
FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.
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2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion
FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :
FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :



FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)
FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :
FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km
FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.
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2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C
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2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C



27

and 1 atm pressure as 22.4 litres per mole. The equivalent NO2 concentration (in microgram
per cubic meter, round off to 2 decimal places) would be _______
Answer :
Solution :
0.02 ppm of NO2 means


41.Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number
of vehicles arriving on this highway follows Poisson distribution, the probability (round off to
2 decimal places) that the headway between successive vehicles lies between 6 and 10
seconds is _________
Answer :
Solution :
? = 360 veh/hr


FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C



27

and 1 atm pressure as 22.4 litres per mole. The equivalent NO2 concentration (in microgram
per cubic meter, round off to 2 decimal places) would be _______
Answer :
Solution :
0.02 ppm of NO2 means


41.Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number
of vehicles arriving on this highway follows Poisson distribution, the probability (round off to
2 decimal places) that the headway between successive vehicles lies between 6 and 10
seconds is _________
Answer :
Solution :
? = 360 veh/hr





28

42.Consider the ordinary differential equation Given the values of y(1)
= 0 and y(2) = 2, the value of y(3) (round off to 1 decimal place), is ______
Answer :
Solution :

y(1) = 0 & y(2) = 2
Assume x = e
t


Then

Putting this into ordinary differential equation
D(D ? 1)y ? 2Dy + 2y = 0
[D
2
? 3D + 2] = 0
Auxillary equation is
m
2
? 3m + 2 = 0
(m ? 1) (m ? 2) = 0
i.e. m = 1 & m = 2
? solution of equation
y = c1e
t
+ c2e
2t

? Putting et as x
? y = c1x + c2X
2

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2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C



27

and 1 atm pressure as 22.4 litres per mole. The equivalent NO2 concentration (in microgram
per cubic meter, round off to 2 decimal places) would be _______
Answer :
Solution :
0.02 ppm of NO2 means


41.Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number
of vehicles arriving on this highway follows Poisson distribution, the probability (round off to
2 decimal places) that the headway between successive vehicles lies between 6 and 10
seconds is _________
Answer :
Solution :
? = 360 veh/hr





28

42.Consider the ordinary differential equation Given the values of y(1)
= 0 and y(2) = 2, the value of y(3) (round off to 1 decimal place), is ______
Answer :
Solution :

y(1) = 0 & y(2) = 2
Assume x = e
t


Then

Putting this into ordinary differential equation
D(D ? 1)y ? 2Dy + 2y = 0
[D
2
? 3D + 2] = 0
Auxillary equation is
m
2
? 3m + 2 = 0
(m ? 1) (m ? 2) = 0
i.e. m = 1 & m = 2
? solution of equation
y = c1e
t
+ c2e
2t

? Putting et as x
? y = c1x + c2X
2




29

? y(1)= 0
? c1 + c2 = 0 ...(i)
& y(2) = 2
? 2c1 + 4c2 = 2
? c1 + 2c2 = 1 ?(ii)
(ii) ? (i)
? c2 = 1
c1 = ?1
? y = ?x + x
2

Then y(3) = ?3 + 3
2
= 6

43.A 3 m ? 3 m square precast reinforced concrete segments to be installed by pushing them
through an existing railway embankment for making an underpass as shown in the figure. A
reaction arrangement using precast PCC blocks placed on the ground is to be made for the
jacks.

At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The
jacks will react against the rigid steel plate placed against the reaction arrangement. The
footprint area of reaction arrangement on natural ground are: c = 17 kPa; ? = 25
o
and ? = 18
kN/m
3
. Assuming that the reaction arrangement has rough interface and has the same
properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure
is __________.
Answer :
Solution :
FOS against shear failure
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2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C



27

and 1 atm pressure as 22.4 litres per mole. The equivalent NO2 concentration (in microgram
per cubic meter, round off to 2 decimal places) would be _______
Answer :
Solution :
0.02 ppm of NO2 means


41.Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number
of vehicles arriving on this highway follows Poisson distribution, the probability (round off to
2 decimal places) that the headway between successive vehicles lies between 6 and 10
seconds is _________
Answer :
Solution :
? = 360 veh/hr





28

42.Consider the ordinary differential equation Given the values of y(1)
= 0 and y(2) = 2, the value of y(3) (round off to 1 decimal place), is ______
Answer :
Solution :

y(1) = 0 & y(2) = 2
Assume x = e
t


Then

Putting this into ordinary differential equation
D(D ? 1)y ? 2Dy + 2y = 0
[D
2
? 3D + 2] = 0
Auxillary equation is
m
2
? 3m + 2 = 0
(m ? 1) (m ? 2) = 0
i.e. m = 1 & m = 2
? solution of equation
y = c1e
t
+ c2e
2t

? Putting et as x
? y = c1x + c2X
2




29

? y(1)= 0
? c1 + c2 = 0 ...(i)
& y(2) = 2
? 2c1 + 4c2 = 2
? c1 + 2c2 = 1 ?(ii)
(ii) ? (i)
? c2 = 1
c1 = ?1
? y = ?x + x
2

Then y(3) = ?3 + 3
2
= 6

43.A 3 m ? 3 m square precast reinforced concrete segments to be installed by pushing them
through an existing railway embankment for making an underpass as shown in the figure. A
reaction arrangement using precast PCC blocks placed on the ground is to be made for the
jacks.

At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The
jacks will react against the rigid steel plate placed against the reaction arrangement. The
footprint area of reaction arrangement on natural ground are: c = 17 kPa; ? = 25
o
and ? = 18
kN/m
3
. Assuming that the reaction arrangement has rough interface and has the same
properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure
is __________.
Answer :
Solution :
FOS against shear failure



30





44.A parabolic vertical curve is being designed to join a road of grade + 5% with a road of
grade ?3%. The length of the vertical curve is 400 m measured along the horizontal. The
vertical point of curvature (VPC) is located on the road of grade
+5%. The difference in height between VPC and vertical point of intersection (VPI) (in m,
round off to the nearest integer) is ______________
Answer :
Solution :

Height difference between
VPI & VPC = 5% of 200 m = 10 m

FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C



27

and 1 atm pressure as 22.4 litres per mole. The equivalent NO2 concentration (in microgram
per cubic meter, round off to 2 decimal places) would be _______
Answer :
Solution :
0.02 ppm of NO2 means


41.Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number
of vehicles arriving on this highway follows Poisson distribution, the probability (round off to
2 decimal places) that the headway between successive vehicles lies between 6 and 10
seconds is _________
Answer :
Solution :
? = 360 veh/hr





28

42.Consider the ordinary differential equation Given the values of y(1)
= 0 and y(2) = 2, the value of y(3) (round off to 1 decimal place), is ______
Answer :
Solution :

y(1) = 0 & y(2) = 2
Assume x = e
t


Then

Putting this into ordinary differential equation
D(D ? 1)y ? 2Dy + 2y = 0
[D
2
? 3D + 2] = 0
Auxillary equation is
m
2
? 3m + 2 = 0
(m ? 1) (m ? 2) = 0
i.e. m = 1 & m = 2
? solution of equation
y = c1e
t
+ c2e
2t

? Putting et as x
? y = c1x + c2X
2




29

? y(1)= 0
? c1 + c2 = 0 ...(i)
& y(2) = 2
? 2c1 + 4c2 = 2
? c1 + 2c2 = 1 ?(ii)
(ii) ? (i)
? c2 = 1
c1 = ?1
? y = ?x + x
2

Then y(3) = ?3 + 3
2
= 6

43.A 3 m ? 3 m square precast reinforced concrete segments to be installed by pushing them
through an existing railway embankment for making an underpass as shown in the figure. A
reaction arrangement using precast PCC blocks placed on the ground is to be made for the
jacks.

At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The
jacks will react against the rigid steel plate placed against the reaction arrangement. The
footprint area of reaction arrangement on natural ground are: c = 17 kPa; ? = 25
o
and ? = 18
kN/m
3
. Assuming that the reaction arrangement has rough interface and has the same
properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure
is __________.
Answer :
Solution :
FOS against shear failure



30





44.A parabolic vertical curve is being designed to join a road of grade + 5% with a road of
grade ?3%. The length of the vertical curve is 400 m measured along the horizontal. The
vertical point of curvature (VPC) is located on the road of grade
+5%. The difference in height between VPC and vertical point of intersection (VPI) (in m,
round off to the nearest integer) is ______________
Answer :
Solution :

Height difference between
VPI & VPC = 5% of 200 m = 10 m




31

45.If the section shown in the figure turns from fully-elastic to fully-plastic, the depth of
neutral axis (N.A.), decreases by

All dimensions are in mm
A.
13.75 mm

B. 10.75 mm
C. 15.25 mm
D. 12.25 mm

Answer :A
Solution :

For fully elastic case,

For fully plastic case,
FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C



27

and 1 atm pressure as 22.4 litres per mole. The equivalent NO2 concentration (in microgram
per cubic meter, round off to 2 decimal places) would be _______
Answer :
Solution :
0.02 ppm of NO2 means


41.Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number
of vehicles arriving on this highway follows Poisson distribution, the probability (round off to
2 decimal places) that the headway between successive vehicles lies between 6 and 10
seconds is _________
Answer :
Solution :
? = 360 veh/hr





28

42.Consider the ordinary differential equation Given the values of y(1)
= 0 and y(2) = 2, the value of y(3) (round off to 1 decimal place), is ______
Answer :
Solution :

y(1) = 0 & y(2) = 2
Assume x = e
t


Then

Putting this into ordinary differential equation
D(D ? 1)y ? 2Dy + 2y = 0
[D
2
? 3D + 2] = 0
Auxillary equation is
m
2
? 3m + 2 = 0
(m ? 1) (m ? 2) = 0
i.e. m = 1 & m = 2
? solution of equation
y = c1e
t
+ c2e
2t

? Putting et as x
? y = c1x + c2X
2




29

? y(1)= 0
? c1 + c2 = 0 ...(i)
& y(2) = 2
? 2c1 + 4c2 = 2
? c1 + 2c2 = 1 ?(ii)
(ii) ? (i)
? c2 = 1
c1 = ?1
? y = ?x + x
2

Then y(3) = ?3 + 3
2
= 6

43.A 3 m ? 3 m square precast reinforced concrete segments to be installed by pushing them
through an existing railway embankment for making an underpass as shown in the figure. A
reaction arrangement using precast PCC blocks placed on the ground is to be made for the
jacks.

At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The
jacks will react against the rigid steel plate placed against the reaction arrangement. The
footprint area of reaction arrangement on natural ground are: c = 17 kPa; ? = 25
o
and ? = 18
kN/m
3
. Assuming that the reaction arrangement has rough interface and has the same
properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure
is __________.
Answer :
Solution :
FOS against shear failure



30





44.A parabolic vertical curve is being designed to join a road of grade + 5% with a road of
grade ?3%. The length of the vertical curve is 400 m measured along the horizontal. The
vertical point of curvature (VPC) is located on the road of grade
+5%. The difference in height between VPC and vertical point of intersection (VPI) (in m,
round off to the nearest integer) is ______________
Answer :
Solution :

Height difference between
VPI & VPC = 5% of 200 m = 10 m




31

45.If the section shown in the figure turns from fully-elastic to fully-plastic, the depth of
neutral axis (N.A.), decreases by

All dimensions are in mm
A.
13.75 mm

B. 10.75 mm
C. 15.25 mm
D. 12.25 mm

Answer :A
Solution :

For fully elastic case,

For fully plastic case,



32

y = Equal area axis = 5
N.A reduces by = 18.75 ? 5 = 13.75 mm

46.A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a
roller support at joint R. A point load of 50 kN is acting at joint R in the horizontal direction.
The flexural rigidity. EI, of each member is 10
6
kNm
2
. Under the applied load, the horizontal
displacement (in mm, round off to 1 decimal place) of joint R would be __________

Answer :
Solution :

For reaction
?Mp = 0
?W ? 5 + 50 ? 10 = 0

When unit load at R is acting in the direction of 50kN load, then reaction at
R = 2 (downward)
FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C



27

and 1 atm pressure as 22.4 litres per mole. The equivalent NO2 concentration (in microgram
per cubic meter, round off to 2 decimal places) would be _______
Answer :
Solution :
0.02 ppm of NO2 means


41.Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number
of vehicles arriving on this highway follows Poisson distribution, the probability (round off to
2 decimal places) that the headway between successive vehicles lies between 6 and 10
seconds is _________
Answer :
Solution :
? = 360 veh/hr





28

42.Consider the ordinary differential equation Given the values of y(1)
= 0 and y(2) = 2, the value of y(3) (round off to 1 decimal place), is ______
Answer :
Solution :

y(1) = 0 & y(2) = 2
Assume x = e
t


Then

Putting this into ordinary differential equation
D(D ? 1)y ? 2Dy + 2y = 0
[D
2
? 3D + 2] = 0
Auxillary equation is
m
2
? 3m + 2 = 0
(m ? 1) (m ? 2) = 0
i.e. m = 1 & m = 2
? solution of equation
y = c1e
t
+ c2e
2t

? Putting et as x
? y = c1x + c2X
2




29

? y(1)= 0
? c1 + c2 = 0 ...(i)
& y(2) = 2
? 2c1 + 4c2 = 2
? c1 + 2c2 = 1 ?(ii)
(ii) ? (i)
? c2 = 1
c1 = ?1
? y = ?x + x
2

Then y(3) = ?3 + 3
2
= 6

43.A 3 m ? 3 m square precast reinforced concrete segments to be installed by pushing them
through an existing railway embankment for making an underpass as shown in the figure. A
reaction arrangement using precast PCC blocks placed on the ground is to be made for the
jacks.

At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The
jacks will react against the rigid steel plate placed against the reaction arrangement. The
footprint area of reaction arrangement on natural ground are: c = 17 kPa; ? = 25
o
and ? = 18
kN/m
3
. Assuming that the reaction arrangement has rough interface and has the same
properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure
is __________.
Answer :
Solution :
FOS against shear failure



30





44.A parabolic vertical curve is being designed to join a road of grade + 5% with a road of
grade ?3%. The length of the vertical curve is 400 m measured along the horizontal. The
vertical point of curvature (VPC) is located on the road of grade
+5%. The difference in height between VPC and vertical point of intersection (VPI) (in m,
round off to the nearest integer) is ______________
Answer :
Solution :

Height difference between
VPI & VPC = 5% of 200 m = 10 m




31

45.If the section shown in the figure turns from fully-elastic to fully-plastic, the depth of
neutral axis (N.A.), decreases by

All dimensions are in mm
A.
13.75 mm

B. 10.75 mm
C. 15.25 mm
D. 12.25 mm

Answer :A
Solution :

For fully elastic case,

For fully plastic case,



32

y = Equal area axis = 5
N.A reduces by = 18.75 ? 5 = 13.75 mm

46.A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a
roller support at joint R. A point load of 50 kN is acting at joint R in the horizontal direction.
The flexural rigidity. EI, of each member is 10
6
kNm
2
. Under the applied load, the horizontal
displacement (in mm, round off to 1 decimal place) of joint R would be __________

Answer :
Solution :

For reaction
?Mp = 0
?W ? 5 + 50 ? 10 = 0

When unit load at R is acting in the direction of 50kN load, then reaction at
R = 2 (downward)



33




Alternatively:


FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C



27

and 1 atm pressure as 22.4 litres per mole. The equivalent NO2 concentration (in microgram
per cubic meter, round off to 2 decimal places) would be _______
Answer :
Solution :
0.02 ppm of NO2 means


41.Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number
of vehicles arriving on this highway follows Poisson distribution, the probability (round off to
2 decimal places) that the headway between successive vehicles lies between 6 and 10
seconds is _________
Answer :
Solution :
? = 360 veh/hr





28

42.Consider the ordinary differential equation Given the values of y(1)
= 0 and y(2) = 2, the value of y(3) (round off to 1 decimal place), is ______
Answer :
Solution :

y(1) = 0 & y(2) = 2
Assume x = e
t


Then

Putting this into ordinary differential equation
D(D ? 1)y ? 2Dy + 2y = 0
[D
2
? 3D + 2] = 0
Auxillary equation is
m
2
? 3m + 2 = 0
(m ? 1) (m ? 2) = 0
i.e. m = 1 & m = 2
? solution of equation
y = c1e
t
+ c2e
2t

? Putting et as x
? y = c1x + c2X
2




29

? y(1)= 0
? c1 + c2 = 0 ...(i)
& y(2) = 2
? 2c1 + 4c2 = 2
? c1 + 2c2 = 1 ?(ii)
(ii) ? (i)
? c2 = 1
c1 = ?1
? y = ?x + x
2

Then y(3) = ?3 + 3
2
= 6

43.A 3 m ? 3 m square precast reinforced concrete segments to be installed by pushing them
through an existing railway embankment for making an underpass as shown in the figure. A
reaction arrangement using precast PCC blocks placed on the ground is to be made for the
jacks.

At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The
jacks will react against the rigid steel plate placed against the reaction arrangement. The
footprint area of reaction arrangement on natural ground are: c = 17 kPa; ? = 25
o
and ? = 18
kN/m
3
. Assuming that the reaction arrangement has rough interface and has the same
properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure
is __________.
Answer :
Solution :
FOS against shear failure



30





44.A parabolic vertical curve is being designed to join a road of grade + 5% with a road of
grade ?3%. The length of the vertical curve is 400 m measured along the horizontal. The
vertical point of curvature (VPC) is located on the road of grade
+5%. The difference in height between VPC and vertical point of intersection (VPI) (in m,
round off to the nearest integer) is ______________
Answer :
Solution :

Height difference between
VPI & VPC = 5% of 200 m = 10 m




31

45.If the section shown in the figure turns from fully-elastic to fully-plastic, the depth of
neutral axis (N.A.), decreases by

All dimensions are in mm
A.
13.75 mm

B. 10.75 mm
C. 15.25 mm
D. 12.25 mm

Answer :A
Solution :

For fully elastic case,

For fully plastic case,



32

y = Equal area axis = 5
N.A reduces by = 18.75 ? 5 = 13.75 mm

46.A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a
roller support at joint R. A point load of 50 kN is acting at joint R in the horizontal direction.
The flexural rigidity. EI, of each member is 10
6
kNm
2
. Under the applied load, the horizontal
displacement (in mm, round off to 1 decimal place) of joint R would be __________

Answer :
Solution :

For reaction
?Mp = 0
?W ? 5 + 50 ? 10 = 0

When unit load at R is acting in the direction of 50kN load, then reaction at
R = 2 (downward)



33




Alternatively:





34





47.A box measuring 50 cm ? 50 cm ? 50 cm is filled to the top with dry coarse aggregate of
mass 187.5 kg. The water absorption and specific gravity of the aggregate are 0.5% and 2.5,
respectively. The maximum quantity of water (in kg, round off to 2 decimal places) required
to fill the box completely is _________
Answer :
Solution :
Volume of the box = 0.5 ? 0.5 ? 0.5
= 0.125 m
3

Mass of aggregate = 187.5 kg
Gagg = 2.5
Volume of aggregate
Volume of empty space = 0.125 ? 0.075
= 0.05 m
3

Water absorption = 0.5%
Volume of water absorbed
FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C



27

and 1 atm pressure as 22.4 litres per mole. The equivalent NO2 concentration (in microgram
per cubic meter, round off to 2 decimal places) would be _______
Answer :
Solution :
0.02 ppm of NO2 means


41.Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number
of vehicles arriving on this highway follows Poisson distribution, the probability (round off to
2 decimal places) that the headway between successive vehicles lies between 6 and 10
seconds is _________
Answer :
Solution :
? = 360 veh/hr





28

42.Consider the ordinary differential equation Given the values of y(1)
= 0 and y(2) = 2, the value of y(3) (round off to 1 decimal place), is ______
Answer :
Solution :

y(1) = 0 & y(2) = 2
Assume x = e
t


Then

Putting this into ordinary differential equation
D(D ? 1)y ? 2Dy + 2y = 0
[D
2
? 3D + 2] = 0
Auxillary equation is
m
2
? 3m + 2 = 0
(m ? 1) (m ? 2) = 0
i.e. m = 1 & m = 2
? solution of equation
y = c1e
t
+ c2e
2t

? Putting et as x
? y = c1x + c2X
2




29

? y(1)= 0
? c1 + c2 = 0 ...(i)
& y(2) = 2
? 2c1 + 4c2 = 2
? c1 + 2c2 = 1 ?(ii)
(ii) ? (i)
? c2 = 1
c1 = ?1
? y = ?x + x
2

Then y(3) = ?3 + 3
2
= 6

43.A 3 m ? 3 m square precast reinforced concrete segments to be installed by pushing them
through an existing railway embankment for making an underpass as shown in the figure. A
reaction arrangement using precast PCC blocks placed on the ground is to be made for the
jacks.

At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The
jacks will react against the rigid steel plate placed against the reaction arrangement. The
footprint area of reaction arrangement on natural ground are: c = 17 kPa; ? = 25
o
and ? = 18
kN/m
3
. Assuming that the reaction arrangement has rough interface and has the same
properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure
is __________.
Answer :
Solution :
FOS against shear failure



30





44.A parabolic vertical curve is being designed to join a road of grade + 5% with a road of
grade ?3%. The length of the vertical curve is 400 m measured along the horizontal. The
vertical point of curvature (VPC) is located on the road of grade
+5%. The difference in height between VPC and vertical point of intersection (VPI) (in m,
round off to the nearest integer) is ______________
Answer :
Solution :

Height difference between
VPI & VPC = 5% of 200 m = 10 m




31

45.If the section shown in the figure turns from fully-elastic to fully-plastic, the depth of
neutral axis (N.A.), decreases by

All dimensions are in mm
A.
13.75 mm

B. 10.75 mm
C. 15.25 mm
D. 12.25 mm

Answer :A
Solution :

For fully elastic case,

For fully plastic case,



32

y = Equal area axis = 5
N.A reduces by = 18.75 ? 5 = 13.75 mm

46.A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a
roller support at joint R. A point load of 50 kN is acting at joint R in the horizontal direction.
The flexural rigidity. EI, of each member is 10
6
kNm
2
. Under the applied load, the horizontal
displacement (in mm, round off to 1 decimal place) of joint R would be __________

Answer :
Solution :

For reaction
?Mp = 0
?W ? 5 + 50 ? 10 = 0

When unit load at R is acting in the direction of 50kN load, then reaction at
R = 2 (downward)



33




Alternatively:





34





47.A box measuring 50 cm ? 50 cm ? 50 cm is filled to the top with dry coarse aggregate of
mass 187.5 kg. The water absorption and specific gravity of the aggregate are 0.5% and 2.5,
respectively. The maximum quantity of water (in kg, round off to 2 decimal places) required
to fill the box completely is _________
Answer :
Solution :
Volume of the box = 0.5 ? 0.5 ? 0.5
= 0.125 m
3

Mass of aggregate = 187.5 kg
Gagg = 2.5
Volume of aggregate
Volume of empty space = 0.125 ? 0.075
= 0.05 m
3

Water absorption = 0.5%
Volume of water absorbed



35


Total volume of water that can be filled
= 9.375 ? 10
?4
+ 0.05
= 0.0509 m
3

Mass of water = 50.94 kg

48.A wastewater is to be disinfected with 35mg/L of chlorine to obtain 99% kill of
microorganisms. The number of micro-organisms remaining alive (Nt) at time t, is modelled
by Nt = N0e
?kt
, where N0 is number of microorganisms at t = 0, and k is the rate of kill. The
wastewater flow rate is 36m
3
/h, and k = 0.23 min-If the depth and width of the chlorination
tank are 1.5 m and 1.0m, respectively, the length of the tank (in m, round off to 2 decimal
places) is _________
Answer :
Solution :
For 99% kill of mircoorganision

?0.23t = ?4.605
t = 20.022 min
Volume of tank req. = Q.t


FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C



27

and 1 atm pressure as 22.4 litres per mole. The equivalent NO2 concentration (in microgram
per cubic meter, round off to 2 decimal places) would be _______
Answer :
Solution :
0.02 ppm of NO2 means


41.Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number
of vehicles arriving on this highway follows Poisson distribution, the probability (round off to
2 decimal places) that the headway between successive vehicles lies between 6 and 10
seconds is _________
Answer :
Solution :
? = 360 veh/hr





28

42.Consider the ordinary differential equation Given the values of y(1)
= 0 and y(2) = 2, the value of y(3) (round off to 1 decimal place), is ______
Answer :
Solution :

y(1) = 0 & y(2) = 2
Assume x = e
t


Then

Putting this into ordinary differential equation
D(D ? 1)y ? 2Dy + 2y = 0
[D
2
? 3D + 2] = 0
Auxillary equation is
m
2
? 3m + 2 = 0
(m ? 1) (m ? 2) = 0
i.e. m = 1 & m = 2
? solution of equation
y = c1e
t
+ c2e
2t

? Putting et as x
? y = c1x + c2X
2




29

? y(1)= 0
? c1 + c2 = 0 ...(i)
& y(2) = 2
? 2c1 + 4c2 = 2
? c1 + 2c2 = 1 ?(ii)
(ii) ? (i)
? c2 = 1
c1 = ?1
? y = ?x + x
2

Then y(3) = ?3 + 3
2
= 6

43.A 3 m ? 3 m square precast reinforced concrete segments to be installed by pushing them
through an existing railway embankment for making an underpass as shown in the figure. A
reaction arrangement using precast PCC blocks placed on the ground is to be made for the
jacks.

At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The
jacks will react against the rigid steel plate placed against the reaction arrangement. The
footprint area of reaction arrangement on natural ground are: c = 17 kPa; ? = 25
o
and ? = 18
kN/m
3
. Assuming that the reaction arrangement has rough interface and has the same
properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure
is __________.
Answer :
Solution :
FOS against shear failure



30





44.A parabolic vertical curve is being designed to join a road of grade + 5% with a road of
grade ?3%. The length of the vertical curve is 400 m measured along the horizontal. The
vertical point of curvature (VPC) is located on the road of grade
+5%. The difference in height between VPC and vertical point of intersection (VPI) (in m,
round off to the nearest integer) is ______________
Answer :
Solution :

Height difference between
VPI & VPC = 5% of 200 m = 10 m




31

45.If the section shown in the figure turns from fully-elastic to fully-plastic, the depth of
neutral axis (N.A.), decreases by

All dimensions are in mm
A.
13.75 mm

B. 10.75 mm
C. 15.25 mm
D. 12.25 mm

Answer :A
Solution :

For fully elastic case,

For fully plastic case,



32

y = Equal area axis = 5
N.A reduces by = 18.75 ? 5 = 13.75 mm

46.A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a
roller support at joint R. A point load of 50 kN is acting at joint R in the horizontal direction.
The flexural rigidity. EI, of each member is 10
6
kNm
2
. Under the applied load, the horizontal
displacement (in mm, round off to 1 decimal place) of joint R would be __________

Answer :
Solution :

For reaction
?Mp = 0
?W ? 5 + 50 ? 10 = 0

When unit load at R is acting in the direction of 50kN load, then reaction at
R = 2 (downward)



33




Alternatively:





34





47.A box measuring 50 cm ? 50 cm ? 50 cm is filled to the top with dry coarse aggregate of
mass 187.5 kg. The water absorption and specific gravity of the aggregate are 0.5% and 2.5,
respectively. The maximum quantity of water (in kg, round off to 2 decimal places) required
to fill the box completely is _________
Answer :
Solution :
Volume of the box = 0.5 ? 0.5 ? 0.5
= 0.125 m
3

Mass of aggregate = 187.5 kg
Gagg = 2.5
Volume of aggregate
Volume of empty space = 0.125 ? 0.075
= 0.05 m
3

Water absorption = 0.5%
Volume of water absorbed



35


Total volume of water that can be filled
= 9.375 ? 10
?4
+ 0.05
= 0.0509 m
3

Mass of water = 50.94 kg

48.A wastewater is to be disinfected with 35mg/L of chlorine to obtain 99% kill of
microorganisms. The number of micro-organisms remaining alive (Nt) at time t, is modelled
by Nt = N0e
?kt
, where N0 is number of microorganisms at t = 0, and k is the rate of kill. The
wastewater flow rate is 36m
3
/h, and k = 0.23 min-If the depth and width of the chlorination
tank are 1.5 m and 1.0m, respectively, the length of the tank (in m, round off to 2 decimal
places) is _________
Answer :
Solution :
For 99% kill of mircoorganision

?0.23t = ?4.605
t = 20.022 min
Volume of tank req. = Q.t





36



49.The cross-section of a built-up wooden beam as shown in the figure (not drawn to scale) is
subjected to a vertical shear force of 8kN. The beam is symmetrical about the neutral axis
(N.A.) shown, and the moment of inertia about N.A. is 1.5 ? 10
9
mm
4
. Considering that the
nails at the location P are spaced longitudinally (along the length of the beam) at 60 mm, each
of the nails at P will be subjected to the shear force of

All dimensions are in mm
A.
60 N

B. 120 N
C. 240 N
D. 480 N

Answer :C
Solution :

FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C



27

and 1 atm pressure as 22.4 litres per mole. The equivalent NO2 concentration (in microgram
per cubic meter, round off to 2 decimal places) would be _______
Answer :
Solution :
0.02 ppm of NO2 means


41.Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number
of vehicles arriving on this highway follows Poisson distribution, the probability (round off to
2 decimal places) that the headway between successive vehicles lies between 6 and 10
seconds is _________
Answer :
Solution :
? = 360 veh/hr





28

42.Consider the ordinary differential equation Given the values of y(1)
= 0 and y(2) = 2, the value of y(3) (round off to 1 decimal place), is ______
Answer :
Solution :

y(1) = 0 & y(2) = 2
Assume x = e
t


Then

Putting this into ordinary differential equation
D(D ? 1)y ? 2Dy + 2y = 0
[D
2
? 3D + 2] = 0
Auxillary equation is
m
2
? 3m + 2 = 0
(m ? 1) (m ? 2) = 0
i.e. m = 1 & m = 2
? solution of equation
y = c1e
t
+ c2e
2t

? Putting et as x
? y = c1x + c2X
2




29

? y(1)= 0
? c1 + c2 = 0 ...(i)
& y(2) = 2
? 2c1 + 4c2 = 2
? c1 + 2c2 = 1 ?(ii)
(ii) ? (i)
? c2 = 1
c1 = ?1
? y = ?x + x
2

Then y(3) = ?3 + 3
2
= 6

43.A 3 m ? 3 m square precast reinforced concrete segments to be installed by pushing them
through an existing railway embankment for making an underpass as shown in the figure. A
reaction arrangement using precast PCC blocks placed on the ground is to be made for the
jacks.

At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The
jacks will react against the rigid steel plate placed against the reaction arrangement. The
footprint area of reaction arrangement on natural ground are: c = 17 kPa; ? = 25
o
and ? = 18
kN/m
3
. Assuming that the reaction arrangement has rough interface and has the same
properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure
is __________.
Answer :
Solution :
FOS against shear failure



30





44.A parabolic vertical curve is being designed to join a road of grade + 5% with a road of
grade ?3%. The length of the vertical curve is 400 m measured along the horizontal. The
vertical point of curvature (VPC) is located on the road of grade
+5%. The difference in height between VPC and vertical point of intersection (VPI) (in m,
round off to the nearest integer) is ______________
Answer :
Solution :

Height difference between
VPI & VPC = 5% of 200 m = 10 m




31

45.If the section shown in the figure turns from fully-elastic to fully-plastic, the depth of
neutral axis (N.A.), decreases by

All dimensions are in mm
A.
13.75 mm

B. 10.75 mm
C. 15.25 mm
D. 12.25 mm

Answer :A
Solution :

For fully elastic case,

For fully plastic case,



32

y = Equal area axis = 5
N.A reduces by = 18.75 ? 5 = 13.75 mm

46.A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a
roller support at joint R. A point load of 50 kN is acting at joint R in the horizontal direction.
The flexural rigidity. EI, of each member is 10
6
kNm
2
. Under the applied load, the horizontal
displacement (in mm, round off to 1 decimal place) of joint R would be __________

Answer :
Solution :

For reaction
?Mp = 0
?W ? 5 + 50 ? 10 = 0

When unit load at R is acting in the direction of 50kN load, then reaction at
R = 2 (downward)



33




Alternatively:





34





47.A box measuring 50 cm ? 50 cm ? 50 cm is filled to the top with dry coarse aggregate of
mass 187.5 kg. The water absorption and specific gravity of the aggregate are 0.5% and 2.5,
respectively. The maximum quantity of water (in kg, round off to 2 decimal places) required
to fill the box completely is _________
Answer :
Solution :
Volume of the box = 0.5 ? 0.5 ? 0.5
= 0.125 m
3

Mass of aggregate = 187.5 kg
Gagg = 2.5
Volume of aggregate
Volume of empty space = 0.125 ? 0.075
= 0.05 m
3

Water absorption = 0.5%
Volume of water absorbed



35


Total volume of water that can be filled
= 9.375 ? 10
?4
+ 0.05
= 0.0509 m
3

Mass of water = 50.94 kg

48.A wastewater is to be disinfected with 35mg/L of chlorine to obtain 99% kill of
microorganisms. The number of micro-organisms remaining alive (Nt) at time t, is modelled
by Nt = N0e
?kt
, where N0 is number of microorganisms at t = 0, and k is the rate of kill. The
wastewater flow rate is 36m
3
/h, and k = 0.23 min-If the depth and width of the chlorination
tank are 1.5 m and 1.0m, respectively, the length of the tank (in m, round off to 2 decimal
places) is _________
Answer :
Solution :
For 99% kill of mircoorganision

?0.23t = ?4.605
t = 20.022 min
Volume of tank req. = Q.t





36



49.The cross-section of a built-up wooden beam as shown in the figure (not drawn to scale) is
subjected to a vertical shear force of 8kN. The beam is symmetrical about the neutral axis
(N.A.) shown, and the moment of inertia about N.A. is 1.5 ? 10
9
mm
4
. Considering that the
nails at the location P are spaced longitudinally (along the length of the beam) at 60 mm, each
of the nails at P will be subjected to the shear force of

All dimensions are in mm
A.
60 N

B. 120 N
C. 240 N
D. 480 N

Answer :C
Solution :




37

Shear force in nail at

So shear force in nail = 22 ? 60 = 1320 N

50.A staff is placed on a benchmark (BM) of reduced level (RL) 100.000 m and a theodolite
is placed at a horizontal distance of 50m from the BM to measure the vertical angles. The
measured vertical angles from the horizontal at the staff readings of 0.400m and 2.400 m are
found to be the same. Taking the height of the instrument as 1.400 m, the RL (in m) of the
theodolite station is _________
Answer :
Solution :


2x = 2.8
x = 1.4m
H.O.I = 100 + 1.4
= 101.4m
RL of theodelite station = 101.4 ? theodolite hight
= 101.4 ? 1.4
= 100m

FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C



27

and 1 atm pressure as 22.4 litres per mole. The equivalent NO2 concentration (in microgram
per cubic meter, round off to 2 decimal places) would be _______
Answer :
Solution :
0.02 ppm of NO2 means


41.Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number
of vehicles arriving on this highway follows Poisson distribution, the probability (round off to
2 decimal places) that the headway between successive vehicles lies between 6 and 10
seconds is _________
Answer :
Solution :
? = 360 veh/hr





28

42.Consider the ordinary differential equation Given the values of y(1)
= 0 and y(2) = 2, the value of y(3) (round off to 1 decimal place), is ______
Answer :
Solution :

y(1) = 0 & y(2) = 2
Assume x = e
t


Then

Putting this into ordinary differential equation
D(D ? 1)y ? 2Dy + 2y = 0
[D
2
? 3D + 2] = 0
Auxillary equation is
m
2
? 3m + 2 = 0
(m ? 1) (m ? 2) = 0
i.e. m = 1 & m = 2
? solution of equation
y = c1e
t
+ c2e
2t

? Putting et as x
? y = c1x + c2X
2




29

? y(1)= 0
? c1 + c2 = 0 ...(i)
& y(2) = 2
? 2c1 + 4c2 = 2
? c1 + 2c2 = 1 ?(ii)
(ii) ? (i)
? c2 = 1
c1 = ?1
? y = ?x + x
2

Then y(3) = ?3 + 3
2
= 6

43.A 3 m ? 3 m square precast reinforced concrete segments to be installed by pushing them
through an existing railway embankment for making an underpass as shown in the figure. A
reaction arrangement using precast PCC blocks placed on the ground is to be made for the
jacks.

At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The
jacks will react against the rigid steel plate placed against the reaction arrangement. The
footprint area of reaction arrangement on natural ground are: c = 17 kPa; ? = 25
o
and ? = 18
kN/m
3
. Assuming that the reaction arrangement has rough interface and has the same
properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure
is __________.
Answer :
Solution :
FOS against shear failure



30





44.A parabolic vertical curve is being designed to join a road of grade + 5% with a road of
grade ?3%. The length of the vertical curve is 400 m measured along the horizontal. The
vertical point of curvature (VPC) is located on the road of grade
+5%. The difference in height between VPC and vertical point of intersection (VPI) (in m,
round off to the nearest integer) is ______________
Answer :
Solution :

Height difference between
VPI & VPC = 5% of 200 m = 10 m




31

45.If the section shown in the figure turns from fully-elastic to fully-plastic, the depth of
neutral axis (N.A.), decreases by

All dimensions are in mm
A.
13.75 mm

B. 10.75 mm
C. 15.25 mm
D. 12.25 mm

Answer :A
Solution :

For fully elastic case,

For fully plastic case,



32

y = Equal area axis = 5
N.A reduces by = 18.75 ? 5 = 13.75 mm

46.A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a
roller support at joint R. A point load of 50 kN is acting at joint R in the horizontal direction.
The flexural rigidity. EI, of each member is 10
6
kNm
2
. Under the applied load, the horizontal
displacement (in mm, round off to 1 decimal place) of joint R would be __________

Answer :
Solution :

For reaction
?Mp = 0
?W ? 5 + 50 ? 10 = 0

When unit load at R is acting in the direction of 50kN load, then reaction at
R = 2 (downward)



33




Alternatively:





34





47.A box measuring 50 cm ? 50 cm ? 50 cm is filled to the top with dry coarse aggregate of
mass 187.5 kg. The water absorption and specific gravity of the aggregate are 0.5% and 2.5,
respectively. The maximum quantity of water (in kg, round off to 2 decimal places) required
to fill the box completely is _________
Answer :
Solution :
Volume of the box = 0.5 ? 0.5 ? 0.5
= 0.125 m
3

Mass of aggregate = 187.5 kg
Gagg = 2.5
Volume of aggregate
Volume of empty space = 0.125 ? 0.075
= 0.05 m
3

Water absorption = 0.5%
Volume of water absorbed



35


Total volume of water that can be filled
= 9.375 ? 10
?4
+ 0.05
= 0.0509 m
3

Mass of water = 50.94 kg

48.A wastewater is to be disinfected with 35mg/L of chlorine to obtain 99% kill of
microorganisms. The number of micro-organisms remaining alive (Nt) at time t, is modelled
by Nt = N0e
?kt
, where N0 is number of microorganisms at t = 0, and k is the rate of kill. The
wastewater flow rate is 36m
3
/h, and k = 0.23 min-If the depth and width of the chlorination
tank are 1.5 m and 1.0m, respectively, the length of the tank (in m, round off to 2 decimal
places) is _________
Answer :
Solution :
For 99% kill of mircoorganision

?0.23t = ?4.605
t = 20.022 min
Volume of tank req. = Q.t





36



49.The cross-section of a built-up wooden beam as shown in the figure (not drawn to scale) is
subjected to a vertical shear force of 8kN. The beam is symmetrical about the neutral axis
(N.A.) shown, and the moment of inertia about N.A. is 1.5 ? 10
9
mm
4
. Considering that the
nails at the location P are spaced longitudinally (along the length of the beam) at 60 mm, each
of the nails at P will be subjected to the shear force of

All dimensions are in mm
A.
60 N

B. 120 N
C. 240 N
D. 480 N

Answer :C
Solution :




37

Shear force in nail at

So shear force in nail = 22 ? 60 = 1320 N

50.A staff is placed on a benchmark (BM) of reduced level (RL) 100.000 m and a theodolite
is placed at a horizontal distance of 50m from the BM to measure the vertical angles. The
measured vertical angles from the horizontal at the staff readings of 0.400m and 2.400 m are
found to be the same. Taking the height of the instrument as 1.400 m, the RL (in m) of the
theodolite station is _________
Answer :
Solution :


2x = 2.8
x = 1.4m
H.O.I = 100 + 1.4
= 101.4m
RL of theodelite station = 101.4 ? theodolite hight
= 101.4 ? 1.4
= 100m




38

51.A 0.80 m deep bed of sand filter (length 4m and width 3m) is made of uniform particles
(diameter = 0.40 mm, specific gravity = 2.65, shape factor = 0.85) with bed porosity of 0.the
bed has to be backwashed at a flow rate of 3.60 m
3
/min. During backwashing, if the terminal
settling velocity of sand particles is 0.05 m/s, the expanded bed depth (in m, round off to 2
decimal places) is ______
Answer :
Solution :


then L ex (1 ? nex) = L(1 ? n)
? Lex (1 ? 0.6025) = 0.8 ? (1 ? 0.4)


52.A reinforced concrete circular pile of 12m length and 0.6 m diameter is embedded in stiff
clay which has an undrained unit cohesion of 110 kN/m
2
. The adhesion factor is 0.The Net
Ultimate Pullout (Uplift) Load for the pile (in kN, round off to 1 decimal place is) is
_________
Answer :
Solution :
Pull out load
p = perimeter
? = length
= 0.5 ? 110 ? 12 ? ?(0.6)
= 1244.07 kN
FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C



27

and 1 atm pressure as 22.4 litres per mole. The equivalent NO2 concentration (in microgram
per cubic meter, round off to 2 decimal places) would be _______
Answer :
Solution :
0.02 ppm of NO2 means


41.Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number
of vehicles arriving on this highway follows Poisson distribution, the probability (round off to
2 decimal places) that the headway between successive vehicles lies between 6 and 10
seconds is _________
Answer :
Solution :
? = 360 veh/hr





28

42.Consider the ordinary differential equation Given the values of y(1)
= 0 and y(2) = 2, the value of y(3) (round off to 1 decimal place), is ______
Answer :
Solution :

y(1) = 0 & y(2) = 2
Assume x = e
t


Then

Putting this into ordinary differential equation
D(D ? 1)y ? 2Dy + 2y = 0
[D
2
? 3D + 2] = 0
Auxillary equation is
m
2
? 3m + 2 = 0
(m ? 1) (m ? 2) = 0
i.e. m = 1 & m = 2
? solution of equation
y = c1e
t
+ c2e
2t

? Putting et as x
? y = c1x + c2X
2




29

? y(1)= 0
? c1 + c2 = 0 ...(i)
& y(2) = 2
? 2c1 + 4c2 = 2
? c1 + 2c2 = 1 ?(ii)
(ii) ? (i)
? c2 = 1
c1 = ?1
? y = ?x + x
2

Then y(3) = ?3 + 3
2
= 6

43.A 3 m ? 3 m square precast reinforced concrete segments to be installed by pushing them
through an existing railway embankment for making an underpass as shown in the figure. A
reaction arrangement using precast PCC blocks placed on the ground is to be made for the
jacks.

At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The
jacks will react against the rigid steel plate placed against the reaction arrangement. The
footprint area of reaction arrangement on natural ground are: c = 17 kPa; ? = 25
o
and ? = 18
kN/m
3
. Assuming that the reaction arrangement has rough interface and has the same
properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure
is __________.
Answer :
Solution :
FOS against shear failure



30





44.A parabolic vertical curve is being designed to join a road of grade + 5% with a road of
grade ?3%. The length of the vertical curve is 400 m measured along the horizontal. The
vertical point of curvature (VPC) is located on the road of grade
+5%. The difference in height between VPC and vertical point of intersection (VPI) (in m,
round off to the nearest integer) is ______________
Answer :
Solution :

Height difference between
VPI & VPC = 5% of 200 m = 10 m




31

45.If the section shown in the figure turns from fully-elastic to fully-plastic, the depth of
neutral axis (N.A.), decreases by

All dimensions are in mm
A.
13.75 mm

B. 10.75 mm
C. 15.25 mm
D. 12.25 mm

Answer :A
Solution :

For fully elastic case,

For fully plastic case,



32

y = Equal area axis = 5
N.A reduces by = 18.75 ? 5 = 13.75 mm

46.A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a
roller support at joint R. A point load of 50 kN is acting at joint R in the horizontal direction.
The flexural rigidity. EI, of each member is 10
6
kNm
2
. Under the applied load, the horizontal
displacement (in mm, round off to 1 decimal place) of joint R would be __________

Answer :
Solution :

For reaction
?Mp = 0
?W ? 5 + 50 ? 10 = 0

When unit load at R is acting in the direction of 50kN load, then reaction at
R = 2 (downward)



33




Alternatively:





34





47.A box measuring 50 cm ? 50 cm ? 50 cm is filled to the top with dry coarse aggregate of
mass 187.5 kg. The water absorption and specific gravity of the aggregate are 0.5% and 2.5,
respectively. The maximum quantity of water (in kg, round off to 2 decimal places) required
to fill the box completely is _________
Answer :
Solution :
Volume of the box = 0.5 ? 0.5 ? 0.5
= 0.125 m
3

Mass of aggregate = 187.5 kg
Gagg = 2.5
Volume of aggregate
Volume of empty space = 0.125 ? 0.075
= 0.05 m
3

Water absorption = 0.5%
Volume of water absorbed



35


Total volume of water that can be filled
= 9.375 ? 10
?4
+ 0.05
= 0.0509 m
3

Mass of water = 50.94 kg

48.A wastewater is to be disinfected with 35mg/L of chlorine to obtain 99% kill of
microorganisms. The number of micro-organisms remaining alive (Nt) at time t, is modelled
by Nt = N0e
?kt
, where N0 is number of microorganisms at t = 0, and k is the rate of kill. The
wastewater flow rate is 36m
3
/h, and k = 0.23 min-If the depth and width of the chlorination
tank are 1.5 m and 1.0m, respectively, the length of the tank (in m, round off to 2 decimal
places) is _________
Answer :
Solution :
For 99% kill of mircoorganision

?0.23t = ?4.605
t = 20.022 min
Volume of tank req. = Q.t





36



49.The cross-section of a built-up wooden beam as shown in the figure (not drawn to scale) is
subjected to a vertical shear force of 8kN. The beam is symmetrical about the neutral axis
(N.A.) shown, and the moment of inertia about N.A. is 1.5 ? 10
9
mm
4
. Considering that the
nails at the location P are spaced longitudinally (along the length of the beam) at 60 mm, each
of the nails at P will be subjected to the shear force of

All dimensions are in mm
A.
60 N

B. 120 N
C. 240 N
D. 480 N

Answer :C
Solution :




37

Shear force in nail at

So shear force in nail = 22 ? 60 = 1320 N

50.A staff is placed on a benchmark (BM) of reduced level (RL) 100.000 m and a theodolite
is placed at a horizontal distance of 50m from the BM to measure the vertical angles. The
measured vertical angles from the horizontal at the staff readings of 0.400m and 2.400 m are
found to be the same. Taking the height of the instrument as 1.400 m, the RL (in m) of the
theodolite station is _________
Answer :
Solution :


2x = 2.8
x = 1.4m
H.O.I = 100 + 1.4
= 101.4m
RL of theodelite station = 101.4 ? theodolite hight
= 101.4 ? 1.4
= 100m




38

51.A 0.80 m deep bed of sand filter (length 4m and width 3m) is made of uniform particles
(diameter = 0.40 mm, specific gravity = 2.65, shape factor = 0.85) with bed porosity of 0.the
bed has to be backwashed at a flow rate of 3.60 m
3
/min. During backwashing, if the terminal
settling velocity of sand particles is 0.05 m/s, the expanded bed depth (in m, round off to 2
decimal places) is ______
Answer :
Solution :


then L ex (1 ? nex) = L(1 ? n)
? Lex (1 ? 0.6025) = 0.8 ? (1 ? 0.4)


52.A reinforced concrete circular pile of 12m length and 0.6 m diameter is embedded in stiff
clay which has an undrained unit cohesion of 110 kN/m
2
. The adhesion factor is 0.The Net
Ultimate Pullout (Uplift) Load for the pile (in kN, round off to 1 decimal place is) is
_________
Answer :
Solution :
Pull out load
p = perimeter
? = length
= 0.5 ? 110 ? 12 ? ?(0.6)
= 1244.07 kN



39


53.A survey line was measured to be 285.5m with a tape having a nominal length of 30m. On
checking, the true length of the tape was found to be 0.05 m too short. If the line lay on a
slope of 1 in 10, the reduced length (horizontal length) of the line for plotting of survey work
would be
A. 285.0 m
B. 284.5 m
C. 285.6 m
D. 283.6 m

Answer :D
Solution :
Measured length = 285.5 m
Nominal length of tape = 30 m
Slope = 1 in 10
The tape is 0.05 m too short
Actual length of tape = 30 ? 0.05 = 29.95 m
Actual length measured
Measured length

Now slope correction
? Slope = 1 in 10

FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C



27

and 1 atm pressure as 22.4 litres per mole. The equivalent NO2 concentration (in microgram
per cubic meter, round off to 2 decimal places) would be _______
Answer :
Solution :
0.02 ppm of NO2 means


41.Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number
of vehicles arriving on this highway follows Poisson distribution, the probability (round off to
2 decimal places) that the headway between successive vehicles lies between 6 and 10
seconds is _________
Answer :
Solution :
? = 360 veh/hr





28

42.Consider the ordinary differential equation Given the values of y(1)
= 0 and y(2) = 2, the value of y(3) (round off to 1 decimal place), is ______
Answer :
Solution :

y(1) = 0 & y(2) = 2
Assume x = e
t


Then

Putting this into ordinary differential equation
D(D ? 1)y ? 2Dy + 2y = 0
[D
2
? 3D + 2] = 0
Auxillary equation is
m
2
? 3m + 2 = 0
(m ? 1) (m ? 2) = 0
i.e. m = 1 & m = 2
? solution of equation
y = c1e
t
+ c2e
2t

? Putting et as x
? y = c1x + c2X
2




29

? y(1)= 0
? c1 + c2 = 0 ...(i)
& y(2) = 2
? 2c1 + 4c2 = 2
? c1 + 2c2 = 1 ?(ii)
(ii) ? (i)
? c2 = 1
c1 = ?1
? y = ?x + x
2

Then y(3) = ?3 + 3
2
= 6

43.A 3 m ? 3 m square precast reinforced concrete segments to be installed by pushing them
through an existing railway embankment for making an underpass as shown in the figure. A
reaction arrangement using precast PCC blocks placed on the ground is to be made for the
jacks.

At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The
jacks will react against the rigid steel plate placed against the reaction arrangement. The
footprint area of reaction arrangement on natural ground are: c = 17 kPa; ? = 25
o
and ? = 18
kN/m
3
. Assuming that the reaction arrangement has rough interface and has the same
properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure
is __________.
Answer :
Solution :
FOS against shear failure



30





44.A parabolic vertical curve is being designed to join a road of grade + 5% with a road of
grade ?3%. The length of the vertical curve is 400 m measured along the horizontal. The
vertical point of curvature (VPC) is located on the road of grade
+5%. The difference in height between VPC and vertical point of intersection (VPI) (in m,
round off to the nearest integer) is ______________
Answer :
Solution :

Height difference between
VPI & VPC = 5% of 200 m = 10 m




31

45.If the section shown in the figure turns from fully-elastic to fully-plastic, the depth of
neutral axis (N.A.), decreases by

All dimensions are in mm
A.
13.75 mm

B. 10.75 mm
C. 15.25 mm
D. 12.25 mm

Answer :A
Solution :

For fully elastic case,

For fully plastic case,



32

y = Equal area axis = 5
N.A reduces by = 18.75 ? 5 = 13.75 mm

46.A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a
roller support at joint R. A point load of 50 kN is acting at joint R in the horizontal direction.
The flexural rigidity. EI, of each member is 10
6
kNm
2
. Under the applied load, the horizontal
displacement (in mm, round off to 1 decimal place) of joint R would be __________

Answer :
Solution :

For reaction
?Mp = 0
?W ? 5 + 50 ? 10 = 0

When unit load at R is acting in the direction of 50kN load, then reaction at
R = 2 (downward)



33




Alternatively:





34





47.A box measuring 50 cm ? 50 cm ? 50 cm is filled to the top with dry coarse aggregate of
mass 187.5 kg. The water absorption and specific gravity of the aggregate are 0.5% and 2.5,
respectively. The maximum quantity of water (in kg, round off to 2 decimal places) required
to fill the box completely is _________
Answer :
Solution :
Volume of the box = 0.5 ? 0.5 ? 0.5
= 0.125 m
3

Mass of aggregate = 187.5 kg
Gagg = 2.5
Volume of aggregate
Volume of empty space = 0.125 ? 0.075
= 0.05 m
3

Water absorption = 0.5%
Volume of water absorbed



35


Total volume of water that can be filled
= 9.375 ? 10
?4
+ 0.05
= 0.0509 m
3

Mass of water = 50.94 kg

48.A wastewater is to be disinfected with 35mg/L of chlorine to obtain 99% kill of
microorganisms. The number of micro-organisms remaining alive (Nt) at time t, is modelled
by Nt = N0e
?kt
, where N0 is number of microorganisms at t = 0, and k is the rate of kill. The
wastewater flow rate is 36m
3
/h, and k = 0.23 min-If the depth and width of the chlorination
tank are 1.5 m and 1.0m, respectively, the length of the tank (in m, round off to 2 decimal
places) is _________
Answer :
Solution :
For 99% kill of mircoorganision

?0.23t = ?4.605
t = 20.022 min
Volume of tank req. = Q.t





36



49.The cross-section of a built-up wooden beam as shown in the figure (not drawn to scale) is
subjected to a vertical shear force of 8kN. The beam is symmetrical about the neutral axis
(N.A.) shown, and the moment of inertia about N.A. is 1.5 ? 10
9
mm
4
. Considering that the
nails at the location P are spaced longitudinally (along the length of the beam) at 60 mm, each
of the nails at P will be subjected to the shear force of

All dimensions are in mm
A.
60 N

B. 120 N
C. 240 N
D. 480 N

Answer :C
Solution :




37

Shear force in nail at

So shear force in nail = 22 ? 60 = 1320 N

50.A staff is placed on a benchmark (BM) of reduced level (RL) 100.000 m and a theodolite
is placed at a horizontal distance of 50m from the BM to measure the vertical angles. The
measured vertical angles from the horizontal at the staff readings of 0.400m and 2.400 m are
found to be the same. Taking the height of the instrument as 1.400 m, the RL (in m) of the
theodolite station is _________
Answer :
Solution :


2x = 2.8
x = 1.4m
H.O.I = 100 + 1.4
= 101.4m
RL of theodelite station = 101.4 ? theodolite hight
= 101.4 ? 1.4
= 100m




38

51.A 0.80 m deep bed of sand filter (length 4m and width 3m) is made of uniform particles
(diameter = 0.40 mm, specific gravity = 2.65, shape factor = 0.85) with bed porosity of 0.the
bed has to be backwashed at a flow rate of 3.60 m
3
/min. During backwashing, if the terminal
settling velocity of sand particles is 0.05 m/s, the expanded bed depth (in m, round off to 2
decimal places) is ______
Answer :
Solution :


then L ex (1 ? nex) = L(1 ? n)
? Lex (1 ? 0.6025) = 0.8 ? (1 ? 0.4)


52.A reinforced concrete circular pile of 12m length and 0.6 m diameter is embedded in stiff
clay which has an undrained unit cohesion of 110 kN/m
2
. The adhesion factor is 0.The Net
Ultimate Pullout (Uplift) Load for the pile (in kN, round off to 1 decimal place is) is
_________
Answer :
Solution :
Pull out load
p = perimeter
? = length
= 0.5 ? 110 ? 12 ? ?(0.6)
= 1244.07 kN



39


53.A survey line was measured to be 285.5m with a tape having a nominal length of 30m. On
checking, the true length of the tape was found to be 0.05 m too short. If the line lay on a
slope of 1 in 10, the reduced length (horizontal length) of the line for plotting of survey work
would be
A. 285.0 m
B. 284.5 m
C. 285.6 m
D. 283.6 m

Answer :D
Solution :
Measured length = 285.5 m
Nominal length of tape = 30 m
Slope = 1 in 10
The tape is 0.05 m too short
Actual length of tape = 30 ? 0.05 = 29.95 m
Actual length measured
Measured length

Now slope correction
? Slope = 1 in 10




40


? Length to be plotted
= Actual length measured + correction
= 285.024 + (-1.42512)
= 283.599 m
Hence, option (d) is correct.

54.The rigid-joined plane frame QRS shown in the figure is subjected to a load P at the joint
R. Let the axial deformation in the frame be neglected. If the support S undergoes a
settlement of the vertical reaction at the support S will become zero when ? is equal
to

A. 3.0
B. 7.5
C. 0.1
D. 48.0

Answer :B
Solution :
FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C



27

and 1 atm pressure as 22.4 litres per mole. The equivalent NO2 concentration (in microgram
per cubic meter, round off to 2 decimal places) would be _______
Answer :
Solution :
0.02 ppm of NO2 means


41.Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number
of vehicles arriving on this highway follows Poisson distribution, the probability (round off to
2 decimal places) that the headway between successive vehicles lies between 6 and 10
seconds is _________
Answer :
Solution :
? = 360 veh/hr





28

42.Consider the ordinary differential equation Given the values of y(1)
= 0 and y(2) = 2, the value of y(3) (round off to 1 decimal place), is ______
Answer :
Solution :

y(1) = 0 & y(2) = 2
Assume x = e
t


Then

Putting this into ordinary differential equation
D(D ? 1)y ? 2Dy + 2y = 0
[D
2
? 3D + 2] = 0
Auxillary equation is
m
2
? 3m + 2 = 0
(m ? 1) (m ? 2) = 0
i.e. m = 1 & m = 2
? solution of equation
y = c1e
t
+ c2e
2t

? Putting et as x
? y = c1x + c2X
2




29

? y(1)= 0
? c1 + c2 = 0 ...(i)
& y(2) = 2
? 2c1 + 4c2 = 2
? c1 + 2c2 = 1 ?(ii)
(ii) ? (i)
? c2 = 1
c1 = ?1
? y = ?x + x
2

Then y(3) = ?3 + 3
2
= 6

43.A 3 m ? 3 m square precast reinforced concrete segments to be installed by pushing them
through an existing railway embankment for making an underpass as shown in the figure. A
reaction arrangement using precast PCC blocks placed on the ground is to be made for the
jacks.

At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The
jacks will react against the rigid steel plate placed against the reaction arrangement. The
footprint area of reaction arrangement on natural ground are: c = 17 kPa; ? = 25
o
and ? = 18
kN/m
3
. Assuming that the reaction arrangement has rough interface and has the same
properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure
is __________.
Answer :
Solution :
FOS against shear failure



30





44.A parabolic vertical curve is being designed to join a road of grade + 5% with a road of
grade ?3%. The length of the vertical curve is 400 m measured along the horizontal. The
vertical point of curvature (VPC) is located on the road of grade
+5%. The difference in height between VPC and vertical point of intersection (VPI) (in m,
round off to the nearest integer) is ______________
Answer :
Solution :

Height difference between
VPI & VPC = 5% of 200 m = 10 m




31

45.If the section shown in the figure turns from fully-elastic to fully-plastic, the depth of
neutral axis (N.A.), decreases by

All dimensions are in mm
A.
13.75 mm

B. 10.75 mm
C. 15.25 mm
D. 12.25 mm

Answer :A
Solution :

For fully elastic case,

For fully plastic case,



32

y = Equal area axis = 5
N.A reduces by = 18.75 ? 5 = 13.75 mm

46.A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a
roller support at joint R. A point load of 50 kN is acting at joint R in the horizontal direction.
The flexural rigidity. EI, of each member is 10
6
kNm
2
. Under the applied load, the horizontal
displacement (in mm, round off to 1 decimal place) of joint R would be __________

Answer :
Solution :

For reaction
?Mp = 0
?W ? 5 + 50 ? 10 = 0

When unit load at R is acting in the direction of 50kN load, then reaction at
R = 2 (downward)



33




Alternatively:





34





47.A box measuring 50 cm ? 50 cm ? 50 cm is filled to the top with dry coarse aggregate of
mass 187.5 kg. The water absorption and specific gravity of the aggregate are 0.5% and 2.5,
respectively. The maximum quantity of water (in kg, round off to 2 decimal places) required
to fill the box completely is _________
Answer :
Solution :
Volume of the box = 0.5 ? 0.5 ? 0.5
= 0.125 m
3

Mass of aggregate = 187.5 kg
Gagg = 2.5
Volume of aggregate
Volume of empty space = 0.125 ? 0.075
= 0.05 m
3

Water absorption = 0.5%
Volume of water absorbed



35


Total volume of water that can be filled
= 9.375 ? 10
?4
+ 0.05
= 0.0509 m
3

Mass of water = 50.94 kg

48.A wastewater is to be disinfected with 35mg/L of chlorine to obtain 99% kill of
microorganisms. The number of micro-organisms remaining alive (Nt) at time t, is modelled
by Nt = N0e
?kt
, where N0 is number of microorganisms at t = 0, and k is the rate of kill. The
wastewater flow rate is 36m
3
/h, and k = 0.23 min-If the depth and width of the chlorination
tank are 1.5 m and 1.0m, respectively, the length of the tank (in m, round off to 2 decimal
places) is _________
Answer :
Solution :
For 99% kill of mircoorganision

?0.23t = ?4.605
t = 20.022 min
Volume of tank req. = Q.t





36



49.The cross-section of a built-up wooden beam as shown in the figure (not drawn to scale) is
subjected to a vertical shear force of 8kN. The beam is symmetrical about the neutral axis
(N.A.) shown, and the moment of inertia about N.A. is 1.5 ? 10
9
mm
4
. Considering that the
nails at the location P are spaced longitudinally (along the length of the beam) at 60 mm, each
of the nails at P will be subjected to the shear force of

All dimensions are in mm
A.
60 N

B. 120 N
C. 240 N
D. 480 N

Answer :C
Solution :




37

Shear force in nail at

So shear force in nail = 22 ? 60 = 1320 N

50.A staff is placed on a benchmark (BM) of reduced level (RL) 100.000 m and a theodolite
is placed at a horizontal distance of 50m from the BM to measure the vertical angles. The
measured vertical angles from the horizontal at the staff readings of 0.400m and 2.400 m are
found to be the same. Taking the height of the instrument as 1.400 m, the RL (in m) of the
theodolite station is _________
Answer :
Solution :


2x = 2.8
x = 1.4m
H.O.I = 100 + 1.4
= 101.4m
RL of theodelite station = 101.4 ? theodolite hight
= 101.4 ? 1.4
= 100m




38

51.A 0.80 m deep bed of sand filter (length 4m and width 3m) is made of uniform particles
(diameter = 0.40 mm, specific gravity = 2.65, shape factor = 0.85) with bed porosity of 0.the
bed has to be backwashed at a flow rate of 3.60 m
3
/min. During backwashing, if the terminal
settling velocity of sand particles is 0.05 m/s, the expanded bed depth (in m, round off to 2
decimal places) is ______
Answer :
Solution :


then L ex (1 ? nex) = L(1 ? n)
? Lex (1 ? 0.6025) = 0.8 ? (1 ? 0.4)


52.A reinforced concrete circular pile of 12m length and 0.6 m diameter is embedded in stiff
clay which has an undrained unit cohesion of 110 kN/m
2
. The adhesion factor is 0.The Net
Ultimate Pullout (Uplift) Load for the pile (in kN, round off to 1 decimal place is) is
_________
Answer :
Solution :
Pull out load
p = perimeter
? = length
= 0.5 ? 110 ? 12 ? ?(0.6)
= 1244.07 kN



39


53.A survey line was measured to be 285.5m with a tape having a nominal length of 30m. On
checking, the true length of the tape was found to be 0.05 m too short. If the line lay on a
slope of 1 in 10, the reduced length (horizontal length) of the line for plotting of survey work
would be
A. 285.0 m
B. 284.5 m
C. 285.6 m
D. 283.6 m

Answer :D
Solution :
Measured length = 285.5 m
Nominal length of tape = 30 m
Slope = 1 in 10
The tape is 0.05 m too short
Actual length of tape = 30 ? 0.05 = 29.95 m
Actual length measured
Measured length

Now slope correction
? Slope = 1 in 10




40


? Length to be plotted
= Actual length measured + correction
= 285.024 + (-1.42512)
= 283.599 m
Hence, option (d) is correct.

54.The rigid-joined plane frame QRS shown in the figure is subjected to a load P at the joint
R. Let the axial deformation in the frame be neglected. If the support S undergoes a
settlement of the vertical reaction at the support S will become zero when ? is equal
to

A. 3.0
B. 7.5
C. 0.1
D. 48.0

Answer :B
Solution :



41


Using slope deflection method,

If reaction at S is equal to zero


From equilibrium of joint

FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C



27

and 1 atm pressure as 22.4 litres per mole. The equivalent NO2 concentration (in microgram
per cubic meter, round off to 2 decimal places) would be _______
Answer :
Solution :
0.02 ppm of NO2 means


41.Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number
of vehicles arriving on this highway follows Poisson distribution, the probability (round off to
2 decimal places) that the headway between successive vehicles lies between 6 and 10
seconds is _________
Answer :
Solution :
? = 360 veh/hr





28

42.Consider the ordinary differential equation Given the values of y(1)
= 0 and y(2) = 2, the value of y(3) (round off to 1 decimal place), is ______
Answer :
Solution :

y(1) = 0 & y(2) = 2
Assume x = e
t


Then

Putting this into ordinary differential equation
D(D ? 1)y ? 2Dy + 2y = 0
[D
2
? 3D + 2] = 0
Auxillary equation is
m
2
? 3m + 2 = 0
(m ? 1) (m ? 2) = 0
i.e. m = 1 & m = 2
? solution of equation
y = c1e
t
+ c2e
2t

? Putting et as x
? y = c1x + c2X
2




29

? y(1)= 0
? c1 + c2 = 0 ...(i)
& y(2) = 2
? 2c1 + 4c2 = 2
? c1 + 2c2 = 1 ?(ii)
(ii) ? (i)
? c2 = 1
c1 = ?1
? y = ?x + x
2

Then y(3) = ?3 + 3
2
= 6

43.A 3 m ? 3 m square precast reinforced concrete segments to be installed by pushing them
through an existing railway embankment for making an underpass as shown in the figure. A
reaction arrangement using precast PCC blocks placed on the ground is to be made for the
jacks.

At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The
jacks will react against the rigid steel plate placed against the reaction arrangement. The
footprint area of reaction arrangement on natural ground are: c = 17 kPa; ? = 25
o
and ? = 18
kN/m
3
. Assuming that the reaction arrangement has rough interface and has the same
properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure
is __________.
Answer :
Solution :
FOS against shear failure



30





44.A parabolic vertical curve is being designed to join a road of grade + 5% with a road of
grade ?3%. The length of the vertical curve is 400 m measured along the horizontal. The
vertical point of curvature (VPC) is located on the road of grade
+5%. The difference in height between VPC and vertical point of intersection (VPI) (in m,
round off to the nearest integer) is ______________
Answer :
Solution :

Height difference between
VPI & VPC = 5% of 200 m = 10 m




31

45.If the section shown in the figure turns from fully-elastic to fully-plastic, the depth of
neutral axis (N.A.), decreases by

All dimensions are in mm
A.
13.75 mm

B. 10.75 mm
C. 15.25 mm
D. 12.25 mm

Answer :A
Solution :

For fully elastic case,

For fully plastic case,



32

y = Equal area axis = 5
N.A reduces by = 18.75 ? 5 = 13.75 mm

46.A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a
roller support at joint R. A point load of 50 kN is acting at joint R in the horizontal direction.
The flexural rigidity. EI, of each member is 10
6
kNm
2
. Under the applied load, the horizontal
displacement (in mm, round off to 1 decimal place) of joint R would be __________

Answer :
Solution :

For reaction
?Mp = 0
?W ? 5 + 50 ? 10 = 0

When unit load at R is acting in the direction of 50kN load, then reaction at
R = 2 (downward)



33




Alternatively:





34





47.A box measuring 50 cm ? 50 cm ? 50 cm is filled to the top with dry coarse aggregate of
mass 187.5 kg. The water absorption and specific gravity of the aggregate are 0.5% and 2.5,
respectively. The maximum quantity of water (in kg, round off to 2 decimal places) required
to fill the box completely is _________
Answer :
Solution :
Volume of the box = 0.5 ? 0.5 ? 0.5
= 0.125 m
3

Mass of aggregate = 187.5 kg
Gagg = 2.5
Volume of aggregate
Volume of empty space = 0.125 ? 0.075
= 0.05 m
3

Water absorption = 0.5%
Volume of water absorbed



35


Total volume of water that can be filled
= 9.375 ? 10
?4
+ 0.05
= 0.0509 m
3

Mass of water = 50.94 kg

48.A wastewater is to be disinfected with 35mg/L of chlorine to obtain 99% kill of
microorganisms. The number of micro-organisms remaining alive (Nt) at time t, is modelled
by Nt = N0e
?kt
, where N0 is number of microorganisms at t = 0, and k is the rate of kill. The
wastewater flow rate is 36m
3
/h, and k = 0.23 min-If the depth and width of the chlorination
tank are 1.5 m and 1.0m, respectively, the length of the tank (in m, round off to 2 decimal
places) is _________
Answer :
Solution :
For 99% kill of mircoorganision

?0.23t = ?4.605
t = 20.022 min
Volume of tank req. = Q.t





36



49.The cross-section of a built-up wooden beam as shown in the figure (not drawn to scale) is
subjected to a vertical shear force of 8kN. The beam is symmetrical about the neutral axis
(N.A.) shown, and the moment of inertia about N.A. is 1.5 ? 10
9
mm
4
. Considering that the
nails at the location P are spaced longitudinally (along the length of the beam) at 60 mm, each
of the nails at P will be subjected to the shear force of

All dimensions are in mm
A.
60 N

B. 120 N
C. 240 N
D. 480 N

Answer :C
Solution :




37

Shear force in nail at

So shear force in nail = 22 ? 60 = 1320 N

50.A staff is placed on a benchmark (BM) of reduced level (RL) 100.000 m and a theodolite
is placed at a horizontal distance of 50m from the BM to measure the vertical angles. The
measured vertical angles from the horizontal at the staff readings of 0.400m and 2.400 m are
found to be the same. Taking the height of the instrument as 1.400 m, the RL (in m) of the
theodolite station is _________
Answer :
Solution :


2x = 2.8
x = 1.4m
H.O.I = 100 + 1.4
= 101.4m
RL of theodelite station = 101.4 ? theodolite hight
= 101.4 ? 1.4
= 100m




38

51.A 0.80 m deep bed of sand filter (length 4m and width 3m) is made of uniform particles
(diameter = 0.40 mm, specific gravity = 2.65, shape factor = 0.85) with bed porosity of 0.the
bed has to be backwashed at a flow rate of 3.60 m
3
/min. During backwashing, if the terminal
settling velocity of sand particles is 0.05 m/s, the expanded bed depth (in m, round off to 2
decimal places) is ______
Answer :
Solution :


then L ex (1 ? nex) = L(1 ? n)
? Lex (1 ? 0.6025) = 0.8 ? (1 ? 0.4)


52.A reinforced concrete circular pile of 12m length and 0.6 m diameter is embedded in stiff
clay which has an undrained unit cohesion of 110 kN/m
2
. The adhesion factor is 0.The Net
Ultimate Pullout (Uplift) Load for the pile (in kN, round off to 1 decimal place is) is
_________
Answer :
Solution :
Pull out load
p = perimeter
? = length
= 0.5 ? 110 ? 12 ? ?(0.6)
= 1244.07 kN



39


53.A survey line was measured to be 285.5m with a tape having a nominal length of 30m. On
checking, the true length of the tape was found to be 0.05 m too short. If the line lay on a
slope of 1 in 10, the reduced length (horizontal length) of the line for plotting of survey work
would be
A. 285.0 m
B. 284.5 m
C. 285.6 m
D. 283.6 m

Answer :D
Solution :
Measured length = 285.5 m
Nominal length of tape = 30 m
Slope = 1 in 10
The tape is 0.05 m too short
Actual length of tape = 30 ? 0.05 = 29.95 m
Actual length measured
Measured length

Now slope correction
? Slope = 1 in 10




40


? Length to be plotted
= Actual length measured + correction
= 285.024 + (-1.42512)
= 283.599 m
Hence, option (d) is correct.

54.The rigid-joined plane frame QRS shown in the figure is subjected to a load P at the joint
R. Let the axial deformation in the frame be neglected. If the support S undergoes a
settlement of the vertical reaction at the support S will become zero when ? is equal
to

A. 3.0
B. 7.5
C. 0.1
D. 48.0

Answer :B
Solution :



41


Using slope deflection method,

If reaction at S is equal to zero


From equilibrium of joint




42

? From (i) & (ii)



55.Which one of the following is NOT a correct statement?
A. The function x?x, (x > 0), has the global minima at x = e
B. The function x?x, (x > 0), has the global maxima at x = e
C. The function x
3
has neither global minima nor global maxima
D. The function |x| has the global minima at x = 0

Answer :A
Solution :
y = x
1/x


For
? x = e
Thus point x = e is the critical point for
y = x
1/x

Now at x = e, dy/dx changes its sign from (+ve) to (-ve). Thus point (x = e) is point of global
maxima.
y = x
3
has neither global minima nor global maxima, it only have saddle point at x = 0
y | x |; attains its minimum value at x = 0; so x = 0 is the global minima for y = f(x)
FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C



27

and 1 atm pressure as 22.4 litres per mole. The equivalent NO2 concentration (in microgram
per cubic meter, round off to 2 decimal places) would be _______
Answer :
Solution :
0.02 ppm of NO2 means


41.Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number
of vehicles arriving on this highway follows Poisson distribution, the probability (round off to
2 decimal places) that the headway between successive vehicles lies between 6 and 10
seconds is _________
Answer :
Solution :
? = 360 veh/hr





28

42.Consider the ordinary differential equation Given the values of y(1)
= 0 and y(2) = 2, the value of y(3) (round off to 1 decimal place), is ______
Answer :
Solution :

y(1) = 0 & y(2) = 2
Assume x = e
t


Then

Putting this into ordinary differential equation
D(D ? 1)y ? 2Dy + 2y = 0
[D
2
? 3D + 2] = 0
Auxillary equation is
m
2
? 3m + 2 = 0
(m ? 1) (m ? 2) = 0
i.e. m = 1 & m = 2
? solution of equation
y = c1e
t
+ c2e
2t

? Putting et as x
? y = c1x + c2X
2




29

? y(1)= 0
? c1 + c2 = 0 ...(i)
& y(2) = 2
? 2c1 + 4c2 = 2
? c1 + 2c2 = 1 ?(ii)
(ii) ? (i)
? c2 = 1
c1 = ?1
? y = ?x + x
2

Then y(3) = ?3 + 3
2
= 6

43.A 3 m ? 3 m square precast reinforced concrete segments to be installed by pushing them
through an existing railway embankment for making an underpass as shown in the figure. A
reaction arrangement using precast PCC blocks placed on the ground is to be made for the
jacks.

At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The
jacks will react against the rigid steel plate placed against the reaction arrangement. The
footprint area of reaction arrangement on natural ground are: c = 17 kPa; ? = 25
o
and ? = 18
kN/m
3
. Assuming that the reaction arrangement has rough interface and has the same
properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure
is __________.
Answer :
Solution :
FOS against shear failure



30





44.A parabolic vertical curve is being designed to join a road of grade + 5% with a road of
grade ?3%. The length of the vertical curve is 400 m measured along the horizontal. The
vertical point of curvature (VPC) is located on the road of grade
+5%. The difference in height between VPC and vertical point of intersection (VPI) (in m,
round off to the nearest integer) is ______________
Answer :
Solution :

Height difference between
VPI & VPC = 5% of 200 m = 10 m




31

45.If the section shown in the figure turns from fully-elastic to fully-plastic, the depth of
neutral axis (N.A.), decreases by

All dimensions are in mm
A.
13.75 mm

B. 10.75 mm
C. 15.25 mm
D. 12.25 mm

Answer :A
Solution :

For fully elastic case,

For fully plastic case,



32

y = Equal area axis = 5
N.A reduces by = 18.75 ? 5 = 13.75 mm

46.A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a
roller support at joint R. A point load of 50 kN is acting at joint R in the horizontal direction.
The flexural rigidity. EI, of each member is 10
6
kNm
2
. Under the applied load, the horizontal
displacement (in mm, round off to 1 decimal place) of joint R would be __________

Answer :
Solution :

For reaction
?Mp = 0
?W ? 5 + 50 ? 10 = 0

When unit load at R is acting in the direction of 50kN load, then reaction at
R = 2 (downward)



33




Alternatively:





34





47.A box measuring 50 cm ? 50 cm ? 50 cm is filled to the top with dry coarse aggregate of
mass 187.5 kg. The water absorption and specific gravity of the aggregate are 0.5% and 2.5,
respectively. The maximum quantity of water (in kg, round off to 2 decimal places) required
to fill the box completely is _________
Answer :
Solution :
Volume of the box = 0.5 ? 0.5 ? 0.5
= 0.125 m
3

Mass of aggregate = 187.5 kg
Gagg = 2.5
Volume of aggregate
Volume of empty space = 0.125 ? 0.075
= 0.05 m
3

Water absorption = 0.5%
Volume of water absorbed



35


Total volume of water that can be filled
= 9.375 ? 10
?4
+ 0.05
= 0.0509 m
3

Mass of water = 50.94 kg

48.A wastewater is to be disinfected with 35mg/L of chlorine to obtain 99% kill of
microorganisms. The number of micro-organisms remaining alive (Nt) at time t, is modelled
by Nt = N0e
?kt
, where N0 is number of microorganisms at t = 0, and k is the rate of kill. The
wastewater flow rate is 36m
3
/h, and k = 0.23 min-If the depth and width of the chlorination
tank are 1.5 m and 1.0m, respectively, the length of the tank (in m, round off to 2 decimal
places) is _________
Answer :
Solution :
For 99% kill of mircoorganision

?0.23t = ?4.605
t = 20.022 min
Volume of tank req. = Q.t





36



49.The cross-section of a built-up wooden beam as shown in the figure (not drawn to scale) is
subjected to a vertical shear force of 8kN. The beam is symmetrical about the neutral axis
(N.A.) shown, and the moment of inertia about N.A. is 1.5 ? 10
9
mm
4
. Considering that the
nails at the location P are spaced longitudinally (along the length of the beam) at 60 mm, each
of the nails at P will be subjected to the shear force of

All dimensions are in mm
A.
60 N

B. 120 N
C. 240 N
D. 480 N

Answer :C
Solution :




37

Shear force in nail at

So shear force in nail = 22 ? 60 = 1320 N

50.A staff is placed on a benchmark (BM) of reduced level (RL) 100.000 m and a theodolite
is placed at a horizontal distance of 50m from the BM to measure the vertical angles. The
measured vertical angles from the horizontal at the staff readings of 0.400m and 2.400 m are
found to be the same. Taking the height of the instrument as 1.400 m, the RL (in m) of the
theodolite station is _________
Answer :
Solution :


2x = 2.8
x = 1.4m
H.O.I = 100 + 1.4
= 101.4m
RL of theodelite station = 101.4 ? theodolite hight
= 101.4 ? 1.4
= 100m




38

51.A 0.80 m deep bed of sand filter (length 4m and width 3m) is made of uniform particles
(diameter = 0.40 mm, specific gravity = 2.65, shape factor = 0.85) with bed porosity of 0.the
bed has to be backwashed at a flow rate of 3.60 m
3
/min. During backwashing, if the terminal
settling velocity of sand particles is 0.05 m/s, the expanded bed depth (in m, round off to 2
decimal places) is ______
Answer :
Solution :


then L ex (1 ? nex) = L(1 ? n)
? Lex (1 ? 0.6025) = 0.8 ? (1 ? 0.4)


52.A reinforced concrete circular pile of 12m length and 0.6 m diameter is embedded in stiff
clay which has an undrained unit cohesion of 110 kN/m
2
. The adhesion factor is 0.The Net
Ultimate Pullout (Uplift) Load for the pile (in kN, round off to 1 decimal place is) is
_________
Answer :
Solution :
Pull out load
p = perimeter
? = length
= 0.5 ? 110 ? 12 ? ?(0.6)
= 1244.07 kN



39


53.A survey line was measured to be 285.5m with a tape having a nominal length of 30m. On
checking, the true length of the tape was found to be 0.05 m too short. If the line lay on a
slope of 1 in 10, the reduced length (horizontal length) of the line for plotting of survey work
would be
A. 285.0 m
B. 284.5 m
C. 285.6 m
D. 283.6 m

Answer :D
Solution :
Measured length = 285.5 m
Nominal length of tape = 30 m
Slope = 1 in 10
The tape is 0.05 m too short
Actual length of tape = 30 ? 0.05 = 29.95 m
Actual length measured
Measured length

Now slope correction
? Slope = 1 in 10




40


? Length to be plotted
= Actual length measured + correction
= 285.024 + (-1.42512)
= 283.599 m
Hence, option (d) is correct.

54.The rigid-joined plane frame QRS shown in the figure is subjected to a load P at the joint
R. Let the axial deformation in the frame be neglected. If the support S undergoes a
settlement of the vertical reaction at the support S will become zero when ? is equal
to

A. 3.0
B. 7.5
C. 0.1
D. 48.0

Answer :B
Solution :



41


Using slope deflection method,

If reaction at S is equal to zero


From equilibrium of joint




42

? From (i) & (ii)



55.Which one of the following is NOT a correct statement?
A. The function x?x, (x > 0), has the global minima at x = e
B. The function x?x, (x > 0), has the global maxima at x = e
C. The function x
3
has neither global minima nor global maxima
D. The function |x| has the global minima at x = 0

Answer :A
Solution :
y = x
1/x


For
? x = e
Thus point x = e is the critical point for
y = x
1/x

Now at x = e, dy/dx changes its sign from (+ve) to (-ve). Thus point (x = e) is point of global
maxima.
y = x
3
has neither global minima nor global maxima, it only have saddle point at x = 0
y | x |; attains its minimum value at x = 0; so x = 0 is the global minima for y = f(x)



43


56.A rectangular open channel has a width of 5m and a bed slope of 0.001. For a uniform
flow of depth 2m, the velocity is 2m/s. The Manning?s roughness coefficient for the channel
is
A. 0.033
B. 0.050
C. 0.002
D. 0.017

Answer :D
Solution :
For a rectangular channel
Width of channel = 5 m
Depth of flow = 2 m
Bed slope = 0.001
Velocity V = 2 m/sec.
From manning?s

Where


57.The hyetograph of a storm event of duration 140 minutes is shown in the figure.
FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C



27

and 1 atm pressure as 22.4 litres per mole. The equivalent NO2 concentration (in microgram
per cubic meter, round off to 2 decimal places) would be _______
Answer :
Solution :
0.02 ppm of NO2 means


41.Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number
of vehicles arriving on this highway follows Poisson distribution, the probability (round off to
2 decimal places) that the headway between successive vehicles lies between 6 and 10
seconds is _________
Answer :
Solution :
? = 360 veh/hr





28

42.Consider the ordinary differential equation Given the values of y(1)
= 0 and y(2) = 2, the value of y(3) (round off to 1 decimal place), is ______
Answer :
Solution :

y(1) = 0 & y(2) = 2
Assume x = e
t


Then

Putting this into ordinary differential equation
D(D ? 1)y ? 2Dy + 2y = 0
[D
2
? 3D + 2] = 0
Auxillary equation is
m
2
? 3m + 2 = 0
(m ? 1) (m ? 2) = 0
i.e. m = 1 & m = 2
? solution of equation
y = c1e
t
+ c2e
2t

? Putting et as x
? y = c1x + c2X
2




29

? y(1)= 0
? c1 + c2 = 0 ...(i)
& y(2) = 2
? 2c1 + 4c2 = 2
? c1 + 2c2 = 1 ?(ii)
(ii) ? (i)
? c2 = 1
c1 = ?1
? y = ?x + x
2

Then y(3) = ?3 + 3
2
= 6

43.A 3 m ? 3 m square precast reinforced concrete segments to be installed by pushing them
through an existing railway embankment for making an underpass as shown in the figure. A
reaction arrangement using precast PCC blocks placed on the ground is to be made for the
jacks.

At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The
jacks will react against the rigid steel plate placed against the reaction arrangement. The
footprint area of reaction arrangement on natural ground are: c = 17 kPa; ? = 25
o
and ? = 18
kN/m
3
. Assuming that the reaction arrangement has rough interface and has the same
properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure
is __________.
Answer :
Solution :
FOS against shear failure



30





44.A parabolic vertical curve is being designed to join a road of grade + 5% with a road of
grade ?3%. The length of the vertical curve is 400 m measured along the horizontal. The
vertical point of curvature (VPC) is located on the road of grade
+5%. The difference in height between VPC and vertical point of intersection (VPI) (in m,
round off to the nearest integer) is ______________
Answer :
Solution :

Height difference between
VPI & VPC = 5% of 200 m = 10 m




31

45.If the section shown in the figure turns from fully-elastic to fully-plastic, the depth of
neutral axis (N.A.), decreases by

All dimensions are in mm
A.
13.75 mm

B. 10.75 mm
C. 15.25 mm
D. 12.25 mm

Answer :A
Solution :

For fully elastic case,

For fully plastic case,



32

y = Equal area axis = 5
N.A reduces by = 18.75 ? 5 = 13.75 mm

46.A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a
roller support at joint R. A point load of 50 kN is acting at joint R in the horizontal direction.
The flexural rigidity. EI, of each member is 10
6
kNm
2
. Under the applied load, the horizontal
displacement (in mm, round off to 1 decimal place) of joint R would be __________

Answer :
Solution :

For reaction
?Mp = 0
?W ? 5 + 50 ? 10 = 0

When unit load at R is acting in the direction of 50kN load, then reaction at
R = 2 (downward)



33




Alternatively:





34





47.A box measuring 50 cm ? 50 cm ? 50 cm is filled to the top with dry coarse aggregate of
mass 187.5 kg. The water absorption and specific gravity of the aggregate are 0.5% and 2.5,
respectively. The maximum quantity of water (in kg, round off to 2 decimal places) required
to fill the box completely is _________
Answer :
Solution :
Volume of the box = 0.5 ? 0.5 ? 0.5
= 0.125 m
3

Mass of aggregate = 187.5 kg
Gagg = 2.5
Volume of aggregate
Volume of empty space = 0.125 ? 0.075
= 0.05 m
3

Water absorption = 0.5%
Volume of water absorbed



35


Total volume of water that can be filled
= 9.375 ? 10
?4
+ 0.05
= 0.0509 m
3

Mass of water = 50.94 kg

48.A wastewater is to be disinfected with 35mg/L of chlorine to obtain 99% kill of
microorganisms. The number of micro-organisms remaining alive (Nt) at time t, is modelled
by Nt = N0e
?kt
, where N0 is number of microorganisms at t = 0, and k is the rate of kill. The
wastewater flow rate is 36m
3
/h, and k = 0.23 min-If the depth and width of the chlorination
tank are 1.5 m and 1.0m, respectively, the length of the tank (in m, round off to 2 decimal
places) is _________
Answer :
Solution :
For 99% kill of mircoorganision

?0.23t = ?4.605
t = 20.022 min
Volume of tank req. = Q.t





36



49.The cross-section of a built-up wooden beam as shown in the figure (not drawn to scale) is
subjected to a vertical shear force of 8kN. The beam is symmetrical about the neutral axis
(N.A.) shown, and the moment of inertia about N.A. is 1.5 ? 10
9
mm
4
. Considering that the
nails at the location P are spaced longitudinally (along the length of the beam) at 60 mm, each
of the nails at P will be subjected to the shear force of

All dimensions are in mm
A.
60 N

B. 120 N
C. 240 N
D. 480 N

Answer :C
Solution :




37

Shear force in nail at

So shear force in nail = 22 ? 60 = 1320 N

50.A staff is placed on a benchmark (BM) of reduced level (RL) 100.000 m and a theodolite
is placed at a horizontal distance of 50m from the BM to measure the vertical angles. The
measured vertical angles from the horizontal at the staff readings of 0.400m and 2.400 m are
found to be the same. Taking the height of the instrument as 1.400 m, the RL (in m) of the
theodolite station is _________
Answer :
Solution :


2x = 2.8
x = 1.4m
H.O.I = 100 + 1.4
= 101.4m
RL of theodelite station = 101.4 ? theodolite hight
= 101.4 ? 1.4
= 100m




38

51.A 0.80 m deep bed of sand filter (length 4m and width 3m) is made of uniform particles
(diameter = 0.40 mm, specific gravity = 2.65, shape factor = 0.85) with bed porosity of 0.the
bed has to be backwashed at a flow rate of 3.60 m
3
/min. During backwashing, if the terminal
settling velocity of sand particles is 0.05 m/s, the expanded bed depth (in m, round off to 2
decimal places) is ______
Answer :
Solution :


then L ex (1 ? nex) = L(1 ? n)
? Lex (1 ? 0.6025) = 0.8 ? (1 ? 0.4)


52.A reinforced concrete circular pile of 12m length and 0.6 m diameter is embedded in stiff
clay which has an undrained unit cohesion of 110 kN/m
2
. The adhesion factor is 0.The Net
Ultimate Pullout (Uplift) Load for the pile (in kN, round off to 1 decimal place is) is
_________
Answer :
Solution :
Pull out load
p = perimeter
? = length
= 0.5 ? 110 ? 12 ? ?(0.6)
= 1244.07 kN



39


53.A survey line was measured to be 285.5m with a tape having a nominal length of 30m. On
checking, the true length of the tape was found to be 0.05 m too short. If the line lay on a
slope of 1 in 10, the reduced length (horizontal length) of the line for plotting of survey work
would be
A. 285.0 m
B. 284.5 m
C. 285.6 m
D. 283.6 m

Answer :D
Solution :
Measured length = 285.5 m
Nominal length of tape = 30 m
Slope = 1 in 10
The tape is 0.05 m too short
Actual length of tape = 30 ? 0.05 = 29.95 m
Actual length measured
Measured length

Now slope correction
? Slope = 1 in 10




40


? Length to be plotted
= Actual length measured + correction
= 285.024 + (-1.42512)
= 283.599 m
Hence, option (d) is correct.

54.The rigid-joined plane frame QRS shown in the figure is subjected to a load P at the joint
R. Let the axial deformation in the frame be neglected. If the support S undergoes a
settlement of the vertical reaction at the support S will become zero when ? is equal
to

A. 3.0
B. 7.5
C. 0.1
D. 48.0

Answer :B
Solution :



41


Using slope deflection method,

If reaction at S is equal to zero


From equilibrium of joint




42

? From (i) & (ii)



55.Which one of the following is NOT a correct statement?
A. The function x?x, (x > 0), has the global minima at x = e
B. The function x?x, (x > 0), has the global maxima at x = e
C. The function x
3
has neither global minima nor global maxima
D. The function |x| has the global minima at x = 0

Answer :A
Solution :
y = x
1/x


For
? x = e
Thus point x = e is the critical point for
y = x
1/x

Now at x = e, dy/dx changes its sign from (+ve) to (-ve). Thus point (x = e) is point of global
maxima.
y = x
3
has neither global minima nor global maxima, it only have saddle point at x = 0
y | x |; attains its minimum value at x = 0; so x = 0 is the global minima for y = f(x)



43


56.A rectangular open channel has a width of 5m and a bed slope of 0.001. For a uniform
flow of depth 2m, the velocity is 2m/s. The Manning?s roughness coefficient for the channel
is
A. 0.033
B. 0.050
C. 0.002
D. 0.017

Answer :D
Solution :
For a rectangular channel
Width of channel = 5 m
Depth of flow = 2 m
Bed slope = 0.001
Velocity V = 2 m/sec.
From manning?s

Where


57.The hyetograph of a storm event of duration 140 minutes is shown in the figure.



44


The infiltration capacity at the start of this event (t = 0) is 17mm/hour, which linearly
decreases to 10 mm/hour after 40 minutes duration. As the event progresses, the infiltration
rate further drops down linearly to attain a value of 4mm/ hour at t = 100 minutes and
remains constant thereafter till the end of the storm event. The value of the infiltration
index, ? (in mm/hour, round off to 2 decimal places), is _______
Answer :
Solution :

Depth of infiltration = Area of hyetograph above Horton?s curve

Now, assuming
FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C



27

and 1 atm pressure as 22.4 litres per mole. The equivalent NO2 concentration (in microgram
per cubic meter, round off to 2 decimal places) would be _______
Answer :
Solution :
0.02 ppm of NO2 means


41.Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number
of vehicles arriving on this highway follows Poisson distribution, the probability (round off to
2 decimal places) that the headway between successive vehicles lies between 6 and 10
seconds is _________
Answer :
Solution :
? = 360 veh/hr





28

42.Consider the ordinary differential equation Given the values of y(1)
= 0 and y(2) = 2, the value of y(3) (round off to 1 decimal place), is ______
Answer :
Solution :

y(1) = 0 & y(2) = 2
Assume x = e
t


Then

Putting this into ordinary differential equation
D(D ? 1)y ? 2Dy + 2y = 0
[D
2
? 3D + 2] = 0
Auxillary equation is
m
2
? 3m + 2 = 0
(m ? 1) (m ? 2) = 0
i.e. m = 1 & m = 2
? solution of equation
y = c1e
t
+ c2e
2t

? Putting et as x
? y = c1x + c2X
2




29

? y(1)= 0
? c1 + c2 = 0 ...(i)
& y(2) = 2
? 2c1 + 4c2 = 2
? c1 + 2c2 = 1 ?(ii)
(ii) ? (i)
? c2 = 1
c1 = ?1
? y = ?x + x
2

Then y(3) = ?3 + 3
2
= 6

43.A 3 m ? 3 m square precast reinforced concrete segments to be installed by pushing them
through an existing railway embankment for making an underpass as shown in the figure. A
reaction arrangement using precast PCC blocks placed on the ground is to be made for the
jacks.

At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The
jacks will react against the rigid steel plate placed against the reaction arrangement. The
footprint area of reaction arrangement on natural ground are: c = 17 kPa; ? = 25
o
and ? = 18
kN/m
3
. Assuming that the reaction arrangement has rough interface and has the same
properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure
is __________.
Answer :
Solution :
FOS against shear failure



30





44.A parabolic vertical curve is being designed to join a road of grade + 5% with a road of
grade ?3%. The length of the vertical curve is 400 m measured along the horizontal. The
vertical point of curvature (VPC) is located on the road of grade
+5%. The difference in height between VPC and vertical point of intersection (VPI) (in m,
round off to the nearest integer) is ______________
Answer :
Solution :

Height difference between
VPI & VPC = 5% of 200 m = 10 m




31

45.If the section shown in the figure turns from fully-elastic to fully-plastic, the depth of
neutral axis (N.A.), decreases by

All dimensions are in mm
A.
13.75 mm

B. 10.75 mm
C. 15.25 mm
D. 12.25 mm

Answer :A
Solution :

For fully elastic case,

For fully plastic case,



32

y = Equal area axis = 5
N.A reduces by = 18.75 ? 5 = 13.75 mm

46.A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a
roller support at joint R. A point load of 50 kN is acting at joint R in the horizontal direction.
The flexural rigidity. EI, of each member is 10
6
kNm
2
. Under the applied load, the horizontal
displacement (in mm, round off to 1 decimal place) of joint R would be __________

Answer :
Solution :

For reaction
?Mp = 0
?W ? 5 + 50 ? 10 = 0

When unit load at R is acting in the direction of 50kN load, then reaction at
R = 2 (downward)



33




Alternatively:





34





47.A box measuring 50 cm ? 50 cm ? 50 cm is filled to the top with dry coarse aggregate of
mass 187.5 kg. The water absorption and specific gravity of the aggregate are 0.5% and 2.5,
respectively. The maximum quantity of water (in kg, round off to 2 decimal places) required
to fill the box completely is _________
Answer :
Solution :
Volume of the box = 0.5 ? 0.5 ? 0.5
= 0.125 m
3

Mass of aggregate = 187.5 kg
Gagg = 2.5
Volume of aggregate
Volume of empty space = 0.125 ? 0.075
= 0.05 m
3

Water absorption = 0.5%
Volume of water absorbed



35


Total volume of water that can be filled
= 9.375 ? 10
?4
+ 0.05
= 0.0509 m
3

Mass of water = 50.94 kg

48.A wastewater is to be disinfected with 35mg/L of chlorine to obtain 99% kill of
microorganisms. The number of micro-organisms remaining alive (Nt) at time t, is modelled
by Nt = N0e
?kt
, where N0 is number of microorganisms at t = 0, and k is the rate of kill. The
wastewater flow rate is 36m
3
/h, and k = 0.23 min-If the depth and width of the chlorination
tank are 1.5 m and 1.0m, respectively, the length of the tank (in m, round off to 2 decimal
places) is _________
Answer :
Solution :
For 99% kill of mircoorganision

?0.23t = ?4.605
t = 20.022 min
Volume of tank req. = Q.t





36



49.The cross-section of a built-up wooden beam as shown in the figure (not drawn to scale) is
subjected to a vertical shear force of 8kN. The beam is symmetrical about the neutral axis
(N.A.) shown, and the moment of inertia about N.A. is 1.5 ? 10
9
mm
4
. Considering that the
nails at the location P are spaced longitudinally (along the length of the beam) at 60 mm, each
of the nails at P will be subjected to the shear force of

All dimensions are in mm
A.
60 N

B. 120 N
C. 240 N
D. 480 N

Answer :C
Solution :




37

Shear force in nail at

So shear force in nail = 22 ? 60 = 1320 N

50.A staff is placed on a benchmark (BM) of reduced level (RL) 100.000 m and a theodolite
is placed at a horizontal distance of 50m from the BM to measure the vertical angles. The
measured vertical angles from the horizontal at the staff readings of 0.400m and 2.400 m are
found to be the same. Taking the height of the instrument as 1.400 m, the RL (in m) of the
theodolite station is _________
Answer :
Solution :


2x = 2.8
x = 1.4m
H.O.I = 100 + 1.4
= 101.4m
RL of theodelite station = 101.4 ? theodolite hight
= 101.4 ? 1.4
= 100m




38

51.A 0.80 m deep bed of sand filter (length 4m and width 3m) is made of uniform particles
(diameter = 0.40 mm, specific gravity = 2.65, shape factor = 0.85) with bed porosity of 0.the
bed has to be backwashed at a flow rate of 3.60 m
3
/min. During backwashing, if the terminal
settling velocity of sand particles is 0.05 m/s, the expanded bed depth (in m, round off to 2
decimal places) is ______
Answer :
Solution :


then L ex (1 ? nex) = L(1 ? n)
? Lex (1 ? 0.6025) = 0.8 ? (1 ? 0.4)


52.A reinforced concrete circular pile of 12m length and 0.6 m diameter is embedded in stiff
clay which has an undrained unit cohesion of 110 kN/m
2
. The adhesion factor is 0.The Net
Ultimate Pullout (Uplift) Load for the pile (in kN, round off to 1 decimal place is) is
_________
Answer :
Solution :
Pull out load
p = perimeter
? = length
= 0.5 ? 110 ? 12 ? ?(0.6)
= 1244.07 kN



39


53.A survey line was measured to be 285.5m with a tape having a nominal length of 30m. On
checking, the true length of the tape was found to be 0.05 m too short. If the line lay on a
slope of 1 in 10, the reduced length (horizontal length) of the line for plotting of survey work
would be
A. 285.0 m
B. 284.5 m
C. 285.6 m
D. 283.6 m

Answer :D
Solution :
Measured length = 285.5 m
Nominal length of tape = 30 m
Slope = 1 in 10
The tape is 0.05 m too short
Actual length of tape = 30 ? 0.05 = 29.95 m
Actual length measured
Measured length

Now slope correction
? Slope = 1 in 10




40


? Length to be plotted
= Actual length measured + correction
= 285.024 + (-1.42512)
= 283.599 m
Hence, option (d) is correct.

54.The rigid-joined plane frame QRS shown in the figure is subjected to a load P at the joint
R. Let the axial deformation in the frame be neglected. If the support S undergoes a
settlement of the vertical reaction at the support S will become zero when ? is equal
to

A. 3.0
B. 7.5
C. 0.1
D. 48.0

Answer :B
Solution :



41


Using slope deflection method,

If reaction at S is equal to zero


From equilibrium of joint




42

? From (i) & (ii)



55.Which one of the following is NOT a correct statement?
A. The function x?x, (x > 0), has the global minima at x = e
B. The function x?x, (x > 0), has the global maxima at x = e
C. The function x
3
has neither global minima nor global maxima
D. The function |x| has the global minima at x = 0

Answer :A
Solution :
y = x
1/x


For
? x = e
Thus point x = e is the critical point for
y = x
1/x

Now at x = e, dy/dx changes its sign from (+ve) to (-ve). Thus point (x = e) is point of global
maxima.
y = x
3
has neither global minima nor global maxima, it only have saddle point at x = 0
y | x |; attains its minimum value at x = 0; so x = 0 is the global minima for y = f(x)



43


56.A rectangular open channel has a width of 5m and a bed slope of 0.001. For a uniform
flow of depth 2m, the velocity is 2m/s. The Manning?s roughness coefficient for the channel
is
A. 0.033
B. 0.050
C. 0.002
D. 0.017

Answer :D
Solution :
For a rectangular channel
Width of channel = 5 m
Depth of flow = 2 m
Bed slope = 0.001
Velocity V = 2 m/sec.
From manning?s

Where


57.The hyetograph of a storm event of duration 140 minutes is shown in the figure.



44


The infiltration capacity at the start of this event (t = 0) is 17mm/hour, which linearly
decreases to 10 mm/hour after 40 minutes duration. As the event progresses, the infiltration
rate further drops down linearly to attain a value of 4mm/ hour at t = 100 minutes and
remains constant thereafter till the end of the storm event. The value of the infiltration
index, ? (in mm/hour, round off to 2 decimal places), is _______
Answer :
Solution :

Depth of infiltration = Area of hyetograph above Horton?s curve

Now, assuming



45




58.Consider a laminar flow in the x-direction between two infinite parallel plates (Couette
flow). The lower plate is stationary and the upper plate is moving with a velocity of 1 cm/ s in
the x-direction. The distance between the plates is 5mm and the dynamic viscosity of the
fluid is 0.01 N-s/mIf the shear stress on the lower plate is zero, the pressure gradient, (in
N/m
2
per m, round off to 1 decimal place) is______
Answer :
Solution :
Given data ;
Velocity of plate, V = 1 cm/sec
Distance between the late = 5 mm
Dynamic viscosity of fluid = 0.01 N-S/m
2

Shear stress at lower plate = 0
Pressure gradient
We know that, in case of couette flow, shear stress ( ? ) is given by

FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C



27

and 1 atm pressure as 22.4 litres per mole. The equivalent NO2 concentration (in microgram
per cubic meter, round off to 2 decimal places) would be _______
Answer :
Solution :
0.02 ppm of NO2 means


41.Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number
of vehicles arriving on this highway follows Poisson distribution, the probability (round off to
2 decimal places) that the headway between successive vehicles lies between 6 and 10
seconds is _________
Answer :
Solution :
? = 360 veh/hr





28

42.Consider the ordinary differential equation Given the values of y(1)
= 0 and y(2) = 2, the value of y(3) (round off to 1 decimal place), is ______
Answer :
Solution :

y(1) = 0 & y(2) = 2
Assume x = e
t


Then

Putting this into ordinary differential equation
D(D ? 1)y ? 2Dy + 2y = 0
[D
2
? 3D + 2] = 0
Auxillary equation is
m
2
? 3m + 2 = 0
(m ? 1) (m ? 2) = 0
i.e. m = 1 & m = 2
? solution of equation
y = c1e
t
+ c2e
2t

? Putting et as x
? y = c1x + c2X
2




29

? y(1)= 0
? c1 + c2 = 0 ...(i)
& y(2) = 2
? 2c1 + 4c2 = 2
? c1 + 2c2 = 1 ?(ii)
(ii) ? (i)
? c2 = 1
c1 = ?1
? y = ?x + x
2

Then y(3) = ?3 + 3
2
= 6

43.A 3 m ? 3 m square precast reinforced concrete segments to be installed by pushing them
through an existing railway embankment for making an underpass as shown in the figure. A
reaction arrangement using precast PCC blocks placed on the ground is to be made for the
jacks.

At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The
jacks will react against the rigid steel plate placed against the reaction arrangement. The
footprint area of reaction arrangement on natural ground are: c = 17 kPa; ? = 25
o
and ? = 18
kN/m
3
. Assuming that the reaction arrangement has rough interface and has the same
properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure
is __________.
Answer :
Solution :
FOS against shear failure



30





44.A parabolic vertical curve is being designed to join a road of grade + 5% with a road of
grade ?3%. The length of the vertical curve is 400 m measured along the horizontal. The
vertical point of curvature (VPC) is located on the road of grade
+5%. The difference in height between VPC and vertical point of intersection (VPI) (in m,
round off to the nearest integer) is ______________
Answer :
Solution :

Height difference between
VPI & VPC = 5% of 200 m = 10 m




31

45.If the section shown in the figure turns from fully-elastic to fully-plastic, the depth of
neutral axis (N.A.), decreases by

All dimensions are in mm
A.
13.75 mm

B. 10.75 mm
C. 15.25 mm
D. 12.25 mm

Answer :A
Solution :

For fully elastic case,

For fully plastic case,



32

y = Equal area axis = 5
N.A reduces by = 18.75 ? 5 = 13.75 mm

46.A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a
roller support at joint R. A point load of 50 kN is acting at joint R in the horizontal direction.
The flexural rigidity. EI, of each member is 10
6
kNm
2
. Under the applied load, the horizontal
displacement (in mm, round off to 1 decimal place) of joint R would be __________

Answer :
Solution :

For reaction
?Mp = 0
?W ? 5 + 50 ? 10 = 0

When unit load at R is acting in the direction of 50kN load, then reaction at
R = 2 (downward)



33




Alternatively:





34





47.A box measuring 50 cm ? 50 cm ? 50 cm is filled to the top with dry coarse aggregate of
mass 187.5 kg. The water absorption and specific gravity of the aggregate are 0.5% and 2.5,
respectively. The maximum quantity of water (in kg, round off to 2 decimal places) required
to fill the box completely is _________
Answer :
Solution :
Volume of the box = 0.5 ? 0.5 ? 0.5
= 0.125 m
3

Mass of aggregate = 187.5 kg
Gagg = 2.5
Volume of aggregate
Volume of empty space = 0.125 ? 0.075
= 0.05 m
3

Water absorption = 0.5%
Volume of water absorbed



35


Total volume of water that can be filled
= 9.375 ? 10
?4
+ 0.05
= 0.0509 m
3

Mass of water = 50.94 kg

48.A wastewater is to be disinfected with 35mg/L of chlorine to obtain 99% kill of
microorganisms. The number of micro-organisms remaining alive (Nt) at time t, is modelled
by Nt = N0e
?kt
, where N0 is number of microorganisms at t = 0, and k is the rate of kill. The
wastewater flow rate is 36m
3
/h, and k = 0.23 min-If the depth and width of the chlorination
tank are 1.5 m and 1.0m, respectively, the length of the tank (in m, round off to 2 decimal
places) is _________
Answer :
Solution :
For 99% kill of mircoorganision

?0.23t = ?4.605
t = 20.022 min
Volume of tank req. = Q.t





36



49.The cross-section of a built-up wooden beam as shown in the figure (not drawn to scale) is
subjected to a vertical shear force of 8kN. The beam is symmetrical about the neutral axis
(N.A.) shown, and the moment of inertia about N.A. is 1.5 ? 10
9
mm
4
. Considering that the
nails at the location P are spaced longitudinally (along the length of the beam) at 60 mm, each
of the nails at P will be subjected to the shear force of

All dimensions are in mm
A.
60 N

B. 120 N
C. 240 N
D. 480 N

Answer :C
Solution :




37

Shear force in nail at

So shear force in nail = 22 ? 60 = 1320 N

50.A staff is placed on a benchmark (BM) of reduced level (RL) 100.000 m and a theodolite
is placed at a horizontal distance of 50m from the BM to measure the vertical angles. The
measured vertical angles from the horizontal at the staff readings of 0.400m and 2.400 m are
found to be the same. Taking the height of the instrument as 1.400 m, the RL (in m) of the
theodolite station is _________
Answer :
Solution :


2x = 2.8
x = 1.4m
H.O.I = 100 + 1.4
= 101.4m
RL of theodelite station = 101.4 ? theodolite hight
= 101.4 ? 1.4
= 100m




38

51.A 0.80 m deep bed of sand filter (length 4m and width 3m) is made of uniform particles
(diameter = 0.40 mm, specific gravity = 2.65, shape factor = 0.85) with bed porosity of 0.the
bed has to be backwashed at a flow rate of 3.60 m
3
/min. During backwashing, if the terminal
settling velocity of sand particles is 0.05 m/s, the expanded bed depth (in m, round off to 2
decimal places) is ______
Answer :
Solution :


then L ex (1 ? nex) = L(1 ? n)
? Lex (1 ? 0.6025) = 0.8 ? (1 ? 0.4)


52.A reinforced concrete circular pile of 12m length and 0.6 m diameter is embedded in stiff
clay which has an undrained unit cohesion of 110 kN/m
2
. The adhesion factor is 0.The Net
Ultimate Pullout (Uplift) Load for the pile (in kN, round off to 1 decimal place is) is
_________
Answer :
Solution :
Pull out load
p = perimeter
? = length
= 0.5 ? 110 ? 12 ? ?(0.6)
= 1244.07 kN



39


53.A survey line was measured to be 285.5m with a tape having a nominal length of 30m. On
checking, the true length of the tape was found to be 0.05 m too short. If the line lay on a
slope of 1 in 10, the reduced length (horizontal length) of the line for plotting of survey work
would be
A. 285.0 m
B. 284.5 m
C. 285.6 m
D. 283.6 m

Answer :D
Solution :
Measured length = 285.5 m
Nominal length of tape = 30 m
Slope = 1 in 10
The tape is 0.05 m too short
Actual length of tape = 30 ? 0.05 = 29.95 m
Actual length measured
Measured length

Now slope correction
? Slope = 1 in 10




40


? Length to be plotted
= Actual length measured + correction
= 285.024 + (-1.42512)
= 283.599 m
Hence, option (d) is correct.

54.The rigid-joined plane frame QRS shown in the figure is subjected to a load P at the joint
R. Let the axial deformation in the frame be neglected. If the support S undergoes a
settlement of the vertical reaction at the support S will become zero when ? is equal
to

A. 3.0
B. 7.5
C. 0.1
D. 48.0

Answer :B
Solution :



41


Using slope deflection method,

If reaction at S is equal to zero


From equilibrium of joint




42

? From (i) & (ii)



55.Which one of the following is NOT a correct statement?
A. The function x?x, (x > 0), has the global minima at x = e
B. The function x?x, (x > 0), has the global maxima at x = e
C. The function x
3
has neither global minima nor global maxima
D. The function |x| has the global minima at x = 0

Answer :A
Solution :
y = x
1/x


For
? x = e
Thus point x = e is the critical point for
y = x
1/x

Now at x = e, dy/dx changes its sign from (+ve) to (-ve). Thus point (x = e) is point of global
maxima.
y = x
3
has neither global minima nor global maxima, it only have saddle point at x = 0
y | x |; attains its minimum value at x = 0; so x = 0 is the global minima for y = f(x)



43


56.A rectangular open channel has a width of 5m and a bed slope of 0.001. For a uniform
flow of depth 2m, the velocity is 2m/s. The Manning?s roughness coefficient for the channel
is
A. 0.033
B. 0.050
C. 0.002
D. 0.017

Answer :D
Solution :
For a rectangular channel
Width of channel = 5 m
Depth of flow = 2 m
Bed slope = 0.001
Velocity V = 2 m/sec.
From manning?s

Where


57.The hyetograph of a storm event of duration 140 minutes is shown in the figure.



44


The infiltration capacity at the start of this event (t = 0) is 17mm/hour, which linearly
decreases to 10 mm/hour after 40 minutes duration. As the event progresses, the infiltration
rate further drops down linearly to attain a value of 4mm/ hour at t = 100 minutes and
remains constant thereafter till the end of the storm event. The value of the infiltration
index, ? (in mm/hour, round off to 2 decimal places), is _______
Answer :
Solution :

Depth of infiltration = Area of hyetograph above Horton?s curve

Now, assuming



45




58.Consider a laminar flow in the x-direction between two infinite parallel plates (Couette
flow). The lower plate is stationary and the upper plate is moving with a velocity of 1 cm/ s in
the x-direction. The distance between the plates is 5mm and the dynamic viscosity of the
fluid is 0.01 N-s/mIf the shear stress on the lower plate is zero, the pressure gradient, (in
N/m
2
per m, round off to 1 decimal place) is______
Answer :
Solution :
Given data ;
Velocity of plate, V = 1 cm/sec
Distance between the late = 5 mm
Dynamic viscosity of fluid = 0.01 N-S/m
2

Shear stress at lower plate = 0
Pressure gradient
We know that, in case of couette flow, shear stress ( ? ) is given by




46

At lower plate, y = 0; ? = 0 [Given]


59.A granular soil has a saturated unit weight of 20 kN/m
3
and an effective angle of shearing
resistance of 30?. The unit weight of water is 9.81 kN/m
3
. A slope is to be made on this soil
deposit in which the seepage occurs parallel to the slope up to the free surface. Under this
seepage condition for a factor of safety of 1.5, the safe slope angle (in degree, round off to 1
decimal place) would be ____
Answer :
Solution :
?sat = 20KN/m
2

? = 30?
?w = 9.81 KN/m
2

FOS = 1.5
We know that

[i = safe slope angle]

? i = 11.0953

60.Two water reservoirs are connected by a siphon (running full) of total length 5000 m and
diameter of 0.10 m, as shown below (figure not drawn to scale).
FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C



27

and 1 atm pressure as 22.4 litres per mole. The equivalent NO2 concentration (in microgram
per cubic meter, round off to 2 decimal places) would be _______
Answer :
Solution :
0.02 ppm of NO2 means


41.Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number
of vehicles arriving on this highway follows Poisson distribution, the probability (round off to
2 decimal places) that the headway between successive vehicles lies between 6 and 10
seconds is _________
Answer :
Solution :
? = 360 veh/hr





28

42.Consider the ordinary differential equation Given the values of y(1)
= 0 and y(2) = 2, the value of y(3) (round off to 1 decimal place), is ______
Answer :
Solution :

y(1) = 0 & y(2) = 2
Assume x = e
t


Then

Putting this into ordinary differential equation
D(D ? 1)y ? 2Dy + 2y = 0
[D
2
? 3D + 2] = 0
Auxillary equation is
m
2
? 3m + 2 = 0
(m ? 1) (m ? 2) = 0
i.e. m = 1 & m = 2
? solution of equation
y = c1e
t
+ c2e
2t

? Putting et as x
? y = c1x + c2X
2




29

? y(1)= 0
? c1 + c2 = 0 ...(i)
& y(2) = 2
? 2c1 + 4c2 = 2
? c1 + 2c2 = 1 ?(ii)
(ii) ? (i)
? c2 = 1
c1 = ?1
? y = ?x + x
2

Then y(3) = ?3 + 3
2
= 6

43.A 3 m ? 3 m square precast reinforced concrete segments to be installed by pushing them
through an existing railway embankment for making an underpass as shown in the figure. A
reaction arrangement using precast PCC blocks placed on the ground is to be made for the
jacks.

At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The
jacks will react against the rigid steel plate placed against the reaction arrangement. The
footprint area of reaction arrangement on natural ground are: c = 17 kPa; ? = 25
o
and ? = 18
kN/m
3
. Assuming that the reaction arrangement has rough interface and has the same
properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure
is __________.
Answer :
Solution :
FOS against shear failure



30





44.A parabolic vertical curve is being designed to join a road of grade + 5% with a road of
grade ?3%. The length of the vertical curve is 400 m measured along the horizontal. The
vertical point of curvature (VPC) is located on the road of grade
+5%. The difference in height between VPC and vertical point of intersection (VPI) (in m,
round off to the nearest integer) is ______________
Answer :
Solution :

Height difference between
VPI & VPC = 5% of 200 m = 10 m




31

45.If the section shown in the figure turns from fully-elastic to fully-plastic, the depth of
neutral axis (N.A.), decreases by

All dimensions are in mm
A.
13.75 mm

B. 10.75 mm
C. 15.25 mm
D. 12.25 mm

Answer :A
Solution :

For fully elastic case,

For fully plastic case,



32

y = Equal area axis = 5
N.A reduces by = 18.75 ? 5 = 13.75 mm

46.A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a
roller support at joint R. A point load of 50 kN is acting at joint R in the horizontal direction.
The flexural rigidity. EI, of each member is 10
6
kNm
2
. Under the applied load, the horizontal
displacement (in mm, round off to 1 decimal place) of joint R would be __________

Answer :
Solution :

For reaction
?Mp = 0
?W ? 5 + 50 ? 10 = 0

When unit load at R is acting in the direction of 50kN load, then reaction at
R = 2 (downward)



33




Alternatively:





34





47.A box measuring 50 cm ? 50 cm ? 50 cm is filled to the top with dry coarse aggregate of
mass 187.5 kg. The water absorption and specific gravity of the aggregate are 0.5% and 2.5,
respectively. The maximum quantity of water (in kg, round off to 2 decimal places) required
to fill the box completely is _________
Answer :
Solution :
Volume of the box = 0.5 ? 0.5 ? 0.5
= 0.125 m
3

Mass of aggregate = 187.5 kg
Gagg = 2.5
Volume of aggregate
Volume of empty space = 0.125 ? 0.075
= 0.05 m
3

Water absorption = 0.5%
Volume of water absorbed



35


Total volume of water that can be filled
= 9.375 ? 10
?4
+ 0.05
= 0.0509 m
3

Mass of water = 50.94 kg

48.A wastewater is to be disinfected with 35mg/L of chlorine to obtain 99% kill of
microorganisms. The number of micro-organisms remaining alive (Nt) at time t, is modelled
by Nt = N0e
?kt
, where N0 is number of microorganisms at t = 0, and k is the rate of kill. The
wastewater flow rate is 36m
3
/h, and k = 0.23 min-If the depth and width of the chlorination
tank are 1.5 m and 1.0m, respectively, the length of the tank (in m, round off to 2 decimal
places) is _________
Answer :
Solution :
For 99% kill of mircoorganision

?0.23t = ?4.605
t = 20.022 min
Volume of tank req. = Q.t





36



49.The cross-section of a built-up wooden beam as shown in the figure (not drawn to scale) is
subjected to a vertical shear force of 8kN. The beam is symmetrical about the neutral axis
(N.A.) shown, and the moment of inertia about N.A. is 1.5 ? 10
9
mm
4
. Considering that the
nails at the location P are spaced longitudinally (along the length of the beam) at 60 mm, each
of the nails at P will be subjected to the shear force of

All dimensions are in mm
A.
60 N

B. 120 N
C. 240 N
D. 480 N

Answer :C
Solution :




37

Shear force in nail at

So shear force in nail = 22 ? 60 = 1320 N

50.A staff is placed on a benchmark (BM) of reduced level (RL) 100.000 m and a theodolite
is placed at a horizontal distance of 50m from the BM to measure the vertical angles. The
measured vertical angles from the horizontal at the staff readings of 0.400m and 2.400 m are
found to be the same. Taking the height of the instrument as 1.400 m, the RL (in m) of the
theodolite station is _________
Answer :
Solution :


2x = 2.8
x = 1.4m
H.O.I = 100 + 1.4
= 101.4m
RL of theodelite station = 101.4 ? theodolite hight
= 101.4 ? 1.4
= 100m




38

51.A 0.80 m deep bed of sand filter (length 4m and width 3m) is made of uniform particles
(diameter = 0.40 mm, specific gravity = 2.65, shape factor = 0.85) with bed porosity of 0.the
bed has to be backwashed at a flow rate of 3.60 m
3
/min. During backwashing, if the terminal
settling velocity of sand particles is 0.05 m/s, the expanded bed depth (in m, round off to 2
decimal places) is ______
Answer :
Solution :


then L ex (1 ? nex) = L(1 ? n)
? Lex (1 ? 0.6025) = 0.8 ? (1 ? 0.4)


52.A reinforced concrete circular pile of 12m length and 0.6 m diameter is embedded in stiff
clay which has an undrained unit cohesion of 110 kN/m
2
. The adhesion factor is 0.The Net
Ultimate Pullout (Uplift) Load for the pile (in kN, round off to 1 decimal place is) is
_________
Answer :
Solution :
Pull out load
p = perimeter
? = length
= 0.5 ? 110 ? 12 ? ?(0.6)
= 1244.07 kN



39


53.A survey line was measured to be 285.5m with a tape having a nominal length of 30m. On
checking, the true length of the tape was found to be 0.05 m too short. If the line lay on a
slope of 1 in 10, the reduced length (horizontal length) of the line for plotting of survey work
would be
A. 285.0 m
B. 284.5 m
C. 285.6 m
D. 283.6 m

Answer :D
Solution :
Measured length = 285.5 m
Nominal length of tape = 30 m
Slope = 1 in 10
The tape is 0.05 m too short
Actual length of tape = 30 ? 0.05 = 29.95 m
Actual length measured
Measured length

Now slope correction
? Slope = 1 in 10




40


? Length to be plotted
= Actual length measured + correction
= 285.024 + (-1.42512)
= 283.599 m
Hence, option (d) is correct.

54.The rigid-joined plane frame QRS shown in the figure is subjected to a load P at the joint
R. Let the axial deformation in the frame be neglected. If the support S undergoes a
settlement of the vertical reaction at the support S will become zero when ? is equal
to

A. 3.0
B. 7.5
C. 0.1
D. 48.0

Answer :B
Solution :



41


Using slope deflection method,

If reaction at S is equal to zero


From equilibrium of joint




42

? From (i) & (ii)



55.Which one of the following is NOT a correct statement?
A. The function x?x, (x > 0), has the global minima at x = e
B. The function x?x, (x > 0), has the global maxima at x = e
C. The function x
3
has neither global minima nor global maxima
D. The function |x| has the global minima at x = 0

Answer :A
Solution :
y = x
1/x


For
? x = e
Thus point x = e is the critical point for
y = x
1/x

Now at x = e, dy/dx changes its sign from (+ve) to (-ve). Thus point (x = e) is point of global
maxima.
y = x
3
has neither global minima nor global maxima, it only have saddle point at x = 0
y | x |; attains its minimum value at x = 0; so x = 0 is the global minima for y = f(x)



43


56.A rectangular open channel has a width of 5m and a bed slope of 0.001. For a uniform
flow of depth 2m, the velocity is 2m/s. The Manning?s roughness coefficient for the channel
is
A. 0.033
B. 0.050
C. 0.002
D. 0.017

Answer :D
Solution :
For a rectangular channel
Width of channel = 5 m
Depth of flow = 2 m
Bed slope = 0.001
Velocity V = 2 m/sec.
From manning?s

Where


57.The hyetograph of a storm event of duration 140 minutes is shown in the figure.



44


The infiltration capacity at the start of this event (t = 0) is 17mm/hour, which linearly
decreases to 10 mm/hour after 40 minutes duration. As the event progresses, the infiltration
rate further drops down linearly to attain a value of 4mm/ hour at t = 100 minutes and
remains constant thereafter till the end of the storm event. The value of the infiltration
index, ? (in mm/hour, round off to 2 decimal places), is _______
Answer :
Solution :

Depth of infiltration = Area of hyetograph above Horton?s curve

Now, assuming



45




58.Consider a laminar flow in the x-direction between two infinite parallel plates (Couette
flow). The lower plate is stationary and the upper plate is moving with a velocity of 1 cm/ s in
the x-direction. The distance between the plates is 5mm and the dynamic viscosity of the
fluid is 0.01 N-s/mIf the shear stress on the lower plate is zero, the pressure gradient, (in
N/m
2
per m, round off to 1 decimal place) is______
Answer :
Solution :
Given data ;
Velocity of plate, V = 1 cm/sec
Distance between the late = 5 mm
Dynamic viscosity of fluid = 0.01 N-S/m
2

Shear stress at lower plate = 0
Pressure gradient
We know that, in case of couette flow, shear stress ( ? ) is given by




46

At lower plate, y = 0; ? = 0 [Given]


59.A granular soil has a saturated unit weight of 20 kN/m
3
and an effective angle of shearing
resistance of 30?. The unit weight of water is 9.81 kN/m
3
. A slope is to be made on this soil
deposit in which the seepage occurs parallel to the slope up to the free surface. Under this
seepage condition for a factor of safety of 1.5, the safe slope angle (in degree, round off to 1
decimal place) would be ____
Answer :
Solution :
?sat = 20KN/m
2

? = 30?
?w = 9.81 KN/m
2

FOS = 1.5
We know that

[i = safe slope angle]

? i = 11.0953

60.Two water reservoirs are connected by a siphon (running full) of total length 5000 m and
diameter of 0.10 m, as shown below (figure not drawn to scale).



47


The inlet leg length of the siphon to its summit is 2000 m. The difference in the water surface
levels of the two reservoirs is 5m. Assume the permissible minimum absolute pressure at the
summit of siphon to be 2.5m of water when running full. Given: friction factor f = 0.02
throughout, atmospheric pressure = 10.3 m of water, and acceleration due to gravity g = 9.81
m/s
2
. Considering only major loss using Darcy- Weisbach equation the maximum height of
the summit of siphon from the water level of upper reservoir, h (in m round off to 1 decimal
place) is _____
Answer :
Solution :
Given data :

d = 0.1 m
Length of siphon = 5000 m
Length of siphon upto summit = 2000 m
Friction Factor, f = 0.02
Acceleration due to gravity, g = 9.81 m/sec
2

Applying Energy equation between point 1 and 3 to get

[From Darcy Weisback equation
FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C



27

and 1 atm pressure as 22.4 litres per mole. The equivalent NO2 concentration (in microgram
per cubic meter, round off to 2 decimal places) would be _______
Answer :
Solution :
0.02 ppm of NO2 means


41.Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number
of vehicles arriving on this highway follows Poisson distribution, the probability (round off to
2 decimal places) that the headway between successive vehicles lies between 6 and 10
seconds is _________
Answer :
Solution :
? = 360 veh/hr





28

42.Consider the ordinary differential equation Given the values of y(1)
= 0 and y(2) = 2, the value of y(3) (round off to 1 decimal place), is ______
Answer :
Solution :

y(1) = 0 & y(2) = 2
Assume x = e
t


Then

Putting this into ordinary differential equation
D(D ? 1)y ? 2Dy + 2y = 0
[D
2
? 3D + 2] = 0
Auxillary equation is
m
2
? 3m + 2 = 0
(m ? 1) (m ? 2) = 0
i.e. m = 1 & m = 2
? solution of equation
y = c1e
t
+ c2e
2t

? Putting et as x
? y = c1x + c2X
2




29

? y(1)= 0
? c1 + c2 = 0 ...(i)
& y(2) = 2
? 2c1 + 4c2 = 2
? c1 + 2c2 = 1 ?(ii)
(ii) ? (i)
? c2 = 1
c1 = ?1
? y = ?x + x
2

Then y(3) = ?3 + 3
2
= 6

43.A 3 m ? 3 m square precast reinforced concrete segments to be installed by pushing them
through an existing railway embankment for making an underpass as shown in the figure. A
reaction arrangement using precast PCC blocks placed on the ground is to be made for the
jacks.

At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The
jacks will react against the rigid steel plate placed against the reaction arrangement. The
footprint area of reaction arrangement on natural ground are: c = 17 kPa; ? = 25
o
and ? = 18
kN/m
3
. Assuming that the reaction arrangement has rough interface and has the same
properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure
is __________.
Answer :
Solution :
FOS against shear failure



30





44.A parabolic vertical curve is being designed to join a road of grade + 5% with a road of
grade ?3%. The length of the vertical curve is 400 m measured along the horizontal. The
vertical point of curvature (VPC) is located on the road of grade
+5%. The difference in height between VPC and vertical point of intersection (VPI) (in m,
round off to the nearest integer) is ______________
Answer :
Solution :

Height difference between
VPI & VPC = 5% of 200 m = 10 m




31

45.If the section shown in the figure turns from fully-elastic to fully-plastic, the depth of
neutral axis (N.A.), decreases by

All dimensions are in mm
A.
13.75 mm

B. 10.75 mm
C. 15.25 mm
D. 12.25 mm

Answer :A
Solution :

For fully elastic case,

For fully plastic case,



32

y = Equal area axis = 5
N.A reduces by = 18.75 ? 5 = 13.75 mm

46.A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a
roller support at joint R. A point load of 50 kN is acting at joint R in the horizontal direction.
The flexural rigidity. EI, of each member is 10
6
kNm
2
. Under the applied load, the horizontal
displacement (in mm, round off to 1 decimal place) of joint R would be __________

Answer :
Solution :

For reaction
?Mp = 0
?W ? 5 + 50 ? 10 = 0

When unit load at R is acting in the direction of 50kN load, then reaction at
R = 2 (downward)



33




Alternatively:





34





47.A box measuring 50 cm ? 50 cm ? 50 cm is filled to the top with dry coarse aggregate of
mass 187.5 kg. The water absorption and specific gravity of the aggregate are 0.5% and 2.5,
respectively. The maximum quantity of water (in kg, round off to 2 decimal places) required
to fill the box completely is _________
Answer :
Solution :
Volume of the box = 0.5 ? 0.5 ? 0.5
= 0.125 m
3

Mass of aggregate = 187.5 kg
Gagg = 2.5
Volume of aggregate
Volume of empty space = 0.125 ? 0.075
= 0.05 m
3

Water absorption = 0.5%
Volume of water absorbed



35


Total volume of water that can be filled
= 9.375 ? 10
?4
+ 0.05
= 0.0509 m
3

Mass of water = 50.94 kg

48.A wastewater is to be disinfected with 35mg/L of chlorine to obtain 99% kill of
microorganisms. The number of micro-organisms remaining alive (Nt) at time t, is modelled
by Nt = N0e
?kt
, where N0 is number of microorganisms at t = 0, and k is the rate of kill. The
wastewater flow rate is 36m
3
/h, and k = 0.23 min-If the depth and width of the chlorination
tank are 1.5 m and 1.0m, respectively, the length of the tank (in m, round off to 2 decimal
places) is _________
Answer :
Solution :
For 99% kill of mircoorganision

?0.23t = ?4.605
t = 20.022 min
Volume of tank req. = Q.t





36



49.The cross-section of a built-up wooden beam as shown in the figure (not drawn to scale) is
subjected to a vertical shear force of 8kN. The beam is symmetrical about the neutral axis
(N.A.) shown, and the moment of inertia about N.A. is 1.5 ? 10
9
mm
4
. Considering that the
nails at the location P are spaced longitudinally (along the length of the beam) at 60 mm, each
of the nails at P will be subjected to the shear force of

All dimensions are in mm
A.
60 N

B. 120 N
C. 240 N
D. 480 N

Answer :C
Solution :




37

Shear force in nail at

So shear force in nail = 22 ? 60 = 1320 N

50.A staff is placed on a benchmark (BM) of reduced level (RL) 100.000 m and a theodolite
is placed at a horizontal distance of 50m from the BM to measure the vertical angles. The
measured vertical angles from the horizontal at the staff readings of 0.400m and 2.400 m are
found to be the same. Taking the height of the instrument as 1.400 m, the RL (in m) of the
theodolite station is _________
Answer :
Solution :


2x = 2.8
x = 1.4m
H.O.I = 100 + 1.4
= 101.4m
RL of theodelite station = 101.4 ? theodolite hight
= 101.4 ? 1.4
= 100m




38

51.A 0.80 m deep bed of sand filter (length 4m and width 3m) is made of uniform particles
(diameter = 0.40 mm, specific gravity = 2.65, shape factor = 0.85) with bed porosity of 0.the
bed has to be backwashed at a flow rate of 3.60 m
3
/min. During backwashing, if the terminal
settling velocity of sand particles is 0.05 m/s, the expanded bed depth (in m, round off to 2
decimal places) is ______
Answer :
Solution :


then L ex (1 ? nex) = L(1 ? n)
? Lex (1 ? 0.6025) = 0.8 ? (1 ? 0.4)


52.A reinforced concrete circular pile of 12m length and 0.6 m diameter is embedded in stiff
clay which has an undrained unit cohesion of 110 kN/m
2
. The adhesion factor is 0.The Net
Ultimate Pullout (Uplift) Load for the pile (in kN, round off to 1 decimal place is) is
_________
Answer :
Solution :
Pull out load
p = perimeter
? = length
= 0.5 ? 110 ? 12 ? ?(0.6)
= 1244.07 kN



39


53.A survey line was measured to be 285.5m with a tape having a nominal length of 30m. On
checking, the true length of the tape was found to be 0.05 m too short. If the line lay on a
slope of 1 in 10, the reduced length (horizontal length) of the line for plotting of survey work
would be
A. 285.0 m
B. 284.5 m
C. 285.6 m
D. 283.6 m

Answer :D
Solution :
Measured length = 285.5 m
Nominal length of tape = 30 m
Slope = 1 in 10
The tape is 0.05 m too short
Actual length of tape = 30 ? 0.05 = 29.95 m
Actual length measured
Measured length

Now slope correction
? Slope = 1 in 10




40


? Length to be plotted
= Actual length measured + correction
= 285.024 + (-1.42512)
= 283.599 m
Hence, option (d) is correct.

54.The rigid-joined plane frame QRS shown in the figure is subjected to a load P at the joint
R. Let the axial deformation in the frame be neglected. If the support S undergoes a
settlement of the vertical reaction at the support S will become zero when ? is equal
to

A. 3.0
B. 7.5
C. 0.1
D. 48.0

Answer :B
Solution :



41


Using slope deflection method,

If reaction at S is equal to zero


From equilibrium of joint




42

? From (i) & (ii)



55.Which one of the following is NOT a correct statement?
A. The function x?x, (x > 0), has the global minima at x = e
B. The function x?x, (x > 0), has the global maxima at x = e
C. The function x
3
has neither global minima nor global maxima
D. The function |x| has the global minima at x = 0

Answer :A
Solution :
y = x
1/x


For
? x = e
Thus point x = e is the critical point for
y = x
1/x

Now at x = e, dy/dx changes its sign from (+ve) to (-ve). Thus point (x = e) is point of global
maxima.
y = x
3
has neither global minima nor global maxima, it only have saddle point at x = 0
y | x |; attains its minimum value at x = 0; so x = 0 is the global minima for y = f(x)



43


56.A rectangular open channel has a width of 5m and a bed slope of 0.001. For a uniform
flow of depth 2m, the velocity is 2m/s. The Manning?s roughness coefficient for the channel
is
A. 0.033
B. 0.050
C. 0.002
D. 0.017

Answer :D
Solution :
For a rectangular channel
Width of channel = 5 m
Depth of flow = 2 m
Bed slope = 0.001
Velocity V = 2 m/sec.
From manning?s

Where


57.The hyetograph of a storm event of duration 140 minutes is shown in the figure.



44


The infiltration capacity at the start of this event (t = 0) is 17mm/hour, which linearly
decreases to 10 mm/hour after 40 minutes duration. As the event progresses, the infiltration
rate further drops down linearly to attain a value of 4mm/ hour at t = 100 minutes and
remains constant thereafter till the end of the storm event. The value of the infiltration
index, ? (in mm/hour, round off to 2 decimal places), is _______
Answer :
Solution :

Depth of infiltration = Area of hyetograph above Horton?s curve

Now, assuming



45




58.Consider a laminar flow in the x-direction between two infinite parallel plates (Couette
flow). The lower plate is stationary and the upper plate is moving with a velocity of 1 cm/ s in
the x-direction. The distance between the plates is 5mm and the dynamic viscosity of the
fluid is 0.01 N-s/mIf the shear stress on the lower plate is zero, the pressure gradient, (in
N/m
2
per m, round off to 1 decimal place) is______
Answer :
Solution :
Given data ;
Velocity of plate, V = 1 cm/sec
Distance between the late = 5 mm
Dynamic viscosity of fluid = 0.01 N-S/m
2

Shear stress at lower plate = 0
Pressure gradient
We know that, in case of couette flow, shear stress ( ? ) is given by




46

At lower plate, y = 0; ? = 0 [Given]


59.A granular soil has a saturated unit weight of 20 kN/m
3
and an effective angle of shearing
resistance of 30?. The unit weight of water is 9.81 kN/m
3
. A slope is to be made on this soil
deposit in which the seepage occurs parallel to the slope up to the free surface. Under this
seepage condition for a factor of safety of 1.5, the safe slope angle (in degree, round off to 1
decimal place) would be ____
Answer :
Solution :
?sat = 20KN/m
2

? = 30?
?w = 9.81 KN/m
2

FOS = 1.5
We know that

[i = safe slope angle]

? i = 11.0953

60.Two water reservoirs are connected by a siphon (running full) of total length 5000 m and
diameter of 0.10 m, as shown below (figure not drawn to scale).



47


The inlet leg length of the siphon to its summit is 2000 m. The difference in the water surface
levels of the two reservoirs is 5m. Assume the permissible minimum absolute pressure at the
summit of siphon to be 2.5m of water when running full. Given: friction factor f = 0.02
throughout, atmospheric pressure = 10.3 m of water, and acceleration due to gravity g = 9.81
m/s
2
. Considering only major loss using Darcy- Weisbach equation the maximum height of
the summit of siphon from the water level of upper reservoir, h (in m round off to 1 decimal
place) is _____
Answer :
Solution :
Given data :

d = 0.1 m
Length of siphon = 5000 m
Length of siphon upto summit = 2000 m
Friction Factor, f = 0.02
Acceleration due to gravity, g = 9.81 m/sec
2

Applying Energy equation between point 1 and 3 to get

[From Darcy Weisback equation



48


[ ? Z1 - Z3 = 5m]
? Q = 2.4597 ? 10
-3
m
3
/sec
Now applying energy equation between 1 and 2 to get




61.Sedimentation basin in a water treatment plant is designed for a flow rate of 0.2 m
3
/s. The
basin is rectangular with a length of 32m, width of 8m and depth of 4m. Assume that the
settling velocity of these particles is governed by the Stokes? law. Given: density of the
particles = 2.5 g/cm
3
; density of water = 1 g/cm3; dynamic viscosity of water = 0.01 g/(cm.s);
gravitational acceleration = 980 cm/s
2
. If the incoming water contains particles of diameter 25
?m (spherical and uniform) the removal efficiency of these particles is
A. 100%
B. 65%
C. 78%
D. 51%

Answer :B
Solution :
Given :
Flow rate = 0.2 m
3
/sec
FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C



27

and 1 atm pressure as 22.4 litres per mole. The equivalent NO2 concentration (in microgram
per cubic meter, round off to 2 decimal places) would be _______
Answer :
Solution :
0.02 ppm of NO2 means


41.Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number
of vehicles arriving on this highway follows Poisson distribution, the probability (round off to
2 decimal places) that the headway between successive vehicles lies between 6 and 10
seconds is _________
Answer :
Solution :
? = 360 veh/hr





28

42.Consider the ordinary differential equation Given the values of y(1)
= 0 and y(2) = 2, the value of y(3) (round off to 1 decimal place), is ______
Answer :
Solution :

y(1) = 0 & y(2) = 2
Assume x = e
t


Then

Putting this into ordinary differential equation
D(D ? 1)y ? 2Dy + 2y = 0
[D
2
? 3D + 2] = 0
Auxillary equation is
m
2
? 3m + 2 = 0
(m ? 1) (m ? 2) = 0
i.e. m = 1 & m = 2
? solution of equation
y = c1e
t
+ c2e
2t

? Putting et as x
? y = c1x + c2X
2




29

? y(1)= 0
? c1 + c2 = 0 ...(i)
& y(2) = 2
? 2c1 + 4c2 = 2
? c1 + 2c2 = 1 ?(ii)
(ii) ? (i)
? c2 = 1
c1 = ?1
? y = ?x + x
2

Then y(3) = ?3 + 3
2
= 6

43.A 3 m ? 3 m square precast reinforced concrete segments to be installed by pushing them
through an existing railway embankment for making an underpass as shown in the figure. A
reaction arrangement using precast PCC blocks placed on the ground is to be made for the
jacks.

At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The
jacks will react against the rigid steel plate placed against the reaction arrangement. The
footprint area of reaction arrangement on natural ground are: c = 17 kPa; ? = 25
o
and ? = 18
kN/m
3
. Assuming that the reaction arrangement has rough interface and has the same
properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure
is __________.
Answer :
Solution :
FOS against shear failure



30





44.A parabolic vertical curve is being designed to join a road of grade + 5% with a road of
grade ?3%. The length of the vertical curve is 400 m measured along the horizontal. The
vertical point of curvature (VPC) is located on the road of grade
+5%. The difference in height between VPC and vertical point of intersection (VPI) (in m,
round off to the nearest integer) is ______________
Answer :
Solution :

Height difference between
VPI & VPC = 5% of 200 m = 10 m




31

45.If the section shown in the figure turns from fully-elastic to fully-plastic, the depth of
neutral axis (N.A.), decreases by

All dimensions are in mm
A.
13.75 mm

B. 10.75 mm
C. 15.25 mm
D. 12.25 mm

Answer :A
Solution :

For fully elastic case,

For fully plastic case,



32

y = Equal area axis = 5
N.A reduces by = 18.75 ? 5 = 13.75 mm

46.A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a
roller support at joint R. A point load of 50 kN is acting at joint R in the horizontal direction.
The flexural rigidity. EI, of each member is 10
6
kNm
2
. Under the applied load, the horizontal
displacement (in mm, round off to 1 decimal place) of joint R would be __________

Answer :
Solution :

For reaction
?Mp = 0
?W ? 5 + 50 ? 10 = 0

When unit load at R is acting in the direction of 50kN load, then reaction at
R = 2 (downward)



33




Alternatively:





34





47.A box measuring 50 cm ? 50 cm ? 50 cm is filled to the top with dry coarse aggregate of
mass 187.5 kg. The water absorption and specific gravity of the aggregate are 0.5% and 2.5,
respectively. The maximum quantity of water (in kg, round off to 2 decimal places) required
to fill the box completely is _________
Answer :
Solution :
Volume of the box = 0.5 ? 0.5 ? 0.5
= 0.125 m
3

Mass of aggregate = 187.5 kg
Gagg = 2.5
Volume of aggregate
Volume of empty space = 0.125 ? 0.075
= 0.05 m
3

Water absorption = 0.5%
Volume of water absorbed



35


Total volume of water that can be filled
= 9.375 ? 10
?4
+ 0.05
= 0.0509 m
3

Mass of water = 50.94 kg

48.A wastewater is to be disinfected with 35mg/L of chlorine to obtain 99% kill of
microorganisms. The number of micro-organisms remaining alive (Nt) at time t, is modelled
by Nt = N0e
?kt
, where N0 is number of microorganisms at t = 0, and k is the rate of kill. The
wastewater flow rate is 36m
3
/h, and k = 0.23 min-If the depth and width of the chlorination
tank are 1.5 m and 1.0m, respectively, the length of the tank (in m, round off to 2 decimal
places) is _________
Answer :
Solution :
For 99% kill of mircoorganision

?0.23t = ?4.605
t = 20.022 min
Volume of tank req. = Q.t





36



49.The cross-section of a built-up wooden beam as shown in the figure (not drawn to scale) is
subjected to a vertical shear force of 8kN. The beam is symmetrical about the neutral axis
(N.A.) shown, and the moment of inertia about N.A. is 1.5 ? 10
9
mm
4
. Considering that the
nails at the location P are spaced longitudinally (along the length of the beam) at 60 mm, each
of the nails at P will be subjected to the shear force of

All dimensions are in mm
A.
60 N

B. 120 N
C. 240 N
D. 480 N

Answer :C
Solution :




37

Shear force in nail at

So shear force in nail = 22 ? 60 = 1320 N

50.A staff is placed on a benchmark (BM) of reduced level (RL) 100.000 m and a theodolite
is placed at a horizontal distance of 50m from the BM to measure the vertical angles. The
measured vertical angles from the horizontal at the staff readings of 0.400m and 2.400 m are
found to be the same. Taking the height of the instrument as 1.400 m, the RL (in m) of the
theodolite station is _________
Answer :
Solution :


2x = 2.8
x = 1.4m
H.O.I = 100 + 1.4
= 101.4m
RL of theodelite station = 101.4 ? theodolite hight
= 101.4 ? 1.4
= 100m




38

51.A 0.80 m deep bed of sand filter (length 4m and width 3m) is made of uniform particles
(diameter = 0.40 mm, specific gravity = 2.65, shape factor = 0.85) with bed porosity of 0.the
bed has to be backwashed at a flow rate of 3.60 m
3
/min. During backwashing, if the terminal
settling velocity of sand particles is 0.05 m/s, the expanded bed depth (in m, round off to 2
decimal places) is ______
Answer :
Solution :


then L ex (1 ? nex) = L(1 ? n)
? Lex (1 ? 0.6025) = 0.8 ? (1 ? 0.4)


52.A reinforced concrete circular pile of 12m length and 0.6 m diameter is embedded in stiff
clay which has an undrained unit cohesion of 110 kN/m
2
. The adhesion factor is 0.The Net
Ultimate Pullout (Uplift) Load for the pile (in kN, round off to 1 decimal place is) is
_________
Answer :
Solution :
Pull out load
p = perimeter
? = length
= 0.5 ? 110 ? 12 ? ?(0.6)
= 1244.07 kN



39


53.A survey line was measured to be 285.5m with a tape having a nominal length of 30m. On
checking, the true length of the tape was found to be 0.05 m too short. If the line lay on a
slope of 1 in 10, the reduced length (horizontal length) of the line for plotting of survey work
would be
A. 285.0 m
B. 284.5 m
C. 285.6 m
D. 283.6 m

Answer :D
Solution :
Measured length = 285.5 m
Nominal length of tape = 30 m
Slope = 1 in 10
The tape is 0.05 m too short
Actual length of tape = 30 ? 0.05 = 29.95 m
Actual length measured
Measured length

Now slope correction
? Slope = 1 in 10




40


? Length to be plotted
= Actual length measured + correction
= 285.024 + (-1.42512)
= 283.599 m
Hence, option (d) is correct.

54.The rigid-joined plane frame QRS shown in the figure is subjected to a load P at the joint
R. Let the axial deformation in the frame be neglected. If the support S undergoes a
settlement of the vertical reaction at the support S will become zero when ? is equal
to

A. 3.0
B. 7.5
C. 0.1
D. 48.0

Answer :B
Solution :



41


Using slope deflection method,

If reaction at S is equal to zero


From equilibrium of joint




42

? From (i) & (ii)



55.Which one of the following is NOT a correct statement?
A. The function x?x, (x > 0), has the global minima at x = e
B. The function x?x, (x > 0), has the global maxima at x = e
C. The function x
3
has neither global minima nor global maxima
D. The function |x| has the global minima at x = 0

Answer :A
Solution :
y = x
1/x


For
? x = e
Thus point x = e is the critical point for
y = x
1/x

Now at x = e, dy/dx changes its sign from (+ve) to (-ve). Thus point (x = e) is point of global
maxima.
y = x
3
has neither global minima nor global maxima, it only have saddle point at x = 0
y | x |; attains its minimum value at x = 0; so x = 0 is the global minima for y = f(x)



43


56.A rectangular open channel has a width of 5m and a bed slope of 0.001. For a uniform
flow of depth 2m, the velocity is 2m/s. The Manning?s roughness coefficient for the channel
is
A. 0.033
B. 0.050
C. 0.002
D. 0.017

Answer :D
Solution :
For a rectangular channel
Width of channel = 5 m
Depth of flow = 2 m
Bed slope = 0.001
Velocity V = 2 m/sec.
From manning?s

Where


57.The hyetograph of a storm event of duration 140 minutes is shown in the figure.



44


The infiltration capacity at the start of this event (t = 0) is 17mm/hour, which linearly
decreases to 10 mm/hour after 40 minutes duration. As the event progresses, the infiltration
rate further drops down linearly to attain a value of 4mm/ hour at t = 100 minutes and
remains constant thereafter till the end of the storm event. The value of the infiltration
index, ? (in mm/hour, round off to 2 decimal places), is _______
Answer :
Solution :

Depth of infiltration = Area of hyetograph above Horton?s curve

Now, assuming



45




58.Consider a laminar flow in the x-direction between two infinite parallel plates (Couette
flow). The lower plate is stationary and the upper plate is moving with a velocity of 1 cm/ s in
the x-direction. The distance between the plates is 5mm and the dynamic viscosity of the
fluid is 0.01 N-s/mIf the shear stress on the lower plate is zero, the pressure gradient, (in
N/m
2
per m, round off to 1 decimal place) is______
Answer :
Solution :
Given data ;
Velocity of plate, V = 1 cm/sec
Distance between the late = 5 mm
Dynamic viscosity of fluid = 0.01 N-S/m
2

Shear stress at lower plate = 0
Pressure gradient
We know that, in case of couette flow, shear stress ( ? ) is given by




46

At lower plate, y = 0; ? = 0 [Given]


59.A granular soil has a saturated unit weight of 20 kN/m
3
and an effective angle of shearing
resistance of 30?. The unit weight of water is 9.81 kN/m
3
. A slope is to be made on this soil
deposit in which the seepage occurs parallel to the slope up to the free surface. Under this
seepage condition for a factor of safety of 1.5, the safe slope angle (in degree, round off to 1
decimal place) would be ____
Answer :
Solution :
?sat = 20KN/m
2

? = 30?
?w = 9.81 KN/m
2

FOS = 1.5
We know that

[i = safe slope angle]

? i = 11.0953

60.Two water reservoirs are connected by a siphon (running full) of total length 5000 m and
diameter of 0.10 m, as shown below (figure not drawn to scale).



47


The inlet leg length of the siphon to its summit is 2000 m. The difference in the water surface
levels of the two reservoirs is 5m. Assume the permissible minimum absolute pressure at the
summit of siphon to be 2.5m of water when running full. Given: friction factor f = 0.02
throughout, atmospheric pressure = 10.3 m of water, and acceleration due to gravity g = 9.81
m/s
2
. Considering only major loss using Darcy- Weisbach equation the maximum height of
the summit of siphon from the water level of upper reservoir, h (in m round off to 1 decimal
place) is _____
Answer :
Solution :
Given data :

d = 0.1 m
Length of siphon = 5000 m
Length of siphon upto summit = 2000 m
Friction Factor, f = 0.02
Acceleration due to gravity, g = 9.81 m/sec
2

Applying Energy equation between point 1 and 3 to get

[From Darcy Weisback equation



48


[ ? Z1 - Z3 = 5m]
? Q = 2.4597 ? 10
-3
m
3
/sec
Now applying energy equation between 1 and 2 to get




61.Sedimentation basin in a water treatment plant is designed for a flow rate of 0.2 m
3
/s. The
basin is rectangular with a length of 32m, width of 8m and depth of 4m. Assume that the
settling velocity of these particles is governed by the Stokes? law. Given: density of the
particles = 2.5 g/cm
3
; density of water = 1 g/cm3; dynamic viscosity of water = 0.01 g/(cm.s);
gravitational acceleration = 980 cm/s
2
. If the incoming water contains particles of diameter 25
?m (spherical and uniform) the removal efficiency of these particles is
A. 100%
B. 65%
C. 78%
D. 51%

Answer :B
Solution :
Given :
Flow rate = 0.2 m
3
/sec



49

Dimension of tank = 32m ? 8 m ? 4 m
Density of particles = 2.5 g/cc
Density of water = 1 g/cc
Dynamic viscosity of water = 0.01 g/cm-S
Diameter of particle = 25 ?m
We know that
Over flow rate of tank
= 7.8125 ? 10
-4
m/sec
And settling velocity of particle (vs),

Now, % removal efficiency

Hence option (b) is correct.

62.A square footing of 4m side is placed at 1 m depth in a sand deposit. The dry unit weight
(?) of sand is 15 kN/m
3
. This footing has an ultimate bearing capacity of 600 kPa. Consider
the depth factors; dq = d? = 1.0 and the bearing capacity factor: N? = 18.This footing is placed
at a depth of 2m in the same soil deposit. For a factor of safety of 3.0 per Terzaghi?s theory,
the safe bearing capacity (in kPa) of this footing would be ________
Answer :
Solution :
Side of square footing = 4 m
FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C



27

and 1 atm pressure as 22.4 litres per mole. The equivalent NO2 concentration (in microgram
per cubic meter, round off to 2 decimal places) would be _______
Answer :
Solution :
0.02 ppm of NO2 means


41.Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number
of vehicles arriving on this highway follows Poisson distribution, the probability (round off to
2 decimal places) that the headway between successive vehicles lies between 6 and 10
seconds is _________
Answer :
Solution :
? = 360 veh/hr





28

42.Consider the ordinary differential equation Given the values of y(1)
= 0 and y(2) = 2, the value of y(3) (round off to 1 decimal place), is ______
Answer :
Solution :

y(1) = 0 & y(2) = 2
Assume x = e
t


Then

Putting this into ordinary differential equation
D(D ? 1)y ? 2Dy + 2y = 0
[D
2
? 3D + 2] = 0
Auxillary equation is
m
2
? 3m + 2 = 0
(m ? 1) (m ? 2) = 0
i.e. m = 1 & m = 2
? solution of equation
y = c1e
t
+ c2e
2t

? Putting et as x
? y = c1x + c2X
2




29

? y(1)= 0
? c1 + c2 = 0 ...(i)
& y(2) = 2
? 2c1 + 4c2 = 2
? c1 + 2c2 = 1 ?(ii)
(ii) ? (i)
? c2 = 1
c1 = ?1
? y = ?x + x
2

Then y(3) = ?3 + 3
2
= 6

43.A 3 m ? 3 m square precast reinforced concrete segments to be installed by pushing them
through an existing railway embankment for making an underpass as shown in the figure. A
reaction arrangement using precast PCC blocks placed on the ground is to be made for the
jacks.

At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The
jacks will react against the rigid steel plate placed against the reaction arrangement. The
footprint area of reaction arrangement on natural ground are: c = 17 kPa; ? = 25
o
and ? = 18
kN/m
3
. Assuming that the reaction arrangement has rough interface and has the same
properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure
is __________.
Answer :
Solution :
FOS against shear failure



30





44.A parabolic vertical curve is being designed to join a road of grade + 5% with a road of
grade ?3%. The length of the vertical curve is 400 m measured along the horizontal. The
vertical point of curvature (VPC) is located on the road of grade
+5%. The difference in height between VPC and vertical point of intersection (VPI) (in m,
round off to the nearest integer) is ______________
Answer :
Solution :

Height difference between
VPI & VPC = 5% of 200 m = 10 m




31

45.If the section shown in the figure turns from fully-elastic to fully-plastic, the depth of
neutral axis (N.A.), decreases by

All dimensions are in mm
A.
13.75 mm

B. 10.75 mm
C. 15.25 mm
D. 12.25 mm

Answer :A
Solution :

For fully elastic case,

For fully plastic case,



32

y = Equal area axis = 5
N.A reduces by = 18.75 ? 5 = 13.75 mm

46.A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a
roller support at joint R. A point load of 50 kN is acting at joint R in the horizontal direction.
The flexural rigidity. EI, of each member is 10
6
kNm
2
. Under the applied load, the horizontal
displacement (in mm, round off to 1 decimal place) of joint R would be __________

Answer :
Solution :

For reaction
?Mp = 0
?W ? 5 + 50 ? 10 = 0

When unit load at R is acting in the direction of 50kN load, then reaction at
R = 2 (downward)



33




Alternatively:





34





47.A box measuring 50 cm ? 50 cm ? 50 cm is filled to the top with dry coarse aggregate of
mass 187.5 kg. The water absorption and specific gravity of the aggregate are 0.5% and 2.5,
respectively. The maximum quantity of water (in kg, round off to 2 decimal places) required
to fill the box completely is _________
Answer :
Solution :
Volume of the box = 0.5 ? 0.5 ? 0.5
= 0.125 m
3

Mass of aggregate = 187.5 kg
Gagg = 2.5
Volume of aggregate
Volume of empty space = 0.125 ? 0.075
= 0.05 m
3

Water absorption = 0.5%
Volume of water absorbed



35


Total volume of water that can be filled
= 9.375 ? 10
?4
+ 0.05
= 0.0509 m
3

Mass of water = 50.94 kg

48.A wastewater is to be disinfected with 35mg/L of chlorine to obtain 99% kill of
microorganisms. The number of micro-organisms remaining alive (Nt) at time t, is modelled
by Nt = N0e
?kt
, where N0 is number of microorganisms at t = 0, and k is the rate of kill. The
wastewater flow rate is 36m
3
/h, and k = 0.23 min-If the depth and width of the chlorination
tank are 1.5 m and 1.0m, respectively, the length of the tank (in m, round off to 2 decimal
places) is _________
Answer :
Solution :
For 99% kill of mircoorganision

?0.23t = ?4.605
t = 20.022 min
Volume of tank req. = Q.t





36



49.The cross-section of a built-up wooden beam as shown in the figure (not drawn to scale) is
subjected to a vertical shear force of 8kN. The beam is symmetrical about the neutral axis
(N.A.) shown, and the moment of inertia about N.A. is 1.5 ? 10
9
mm
4
. Considering that the
nails at the location P are spaced longitudinally (along the length of the beam) at 60 mm, each
of the nails at P will be subjected to the shear force of

All dimensions are in mm
A.
60 N

B. 120 N
C. 240 N
D. 480 N

Answer :C
Solution :




37

Shear force in nail at

So shear force in nail = 22 ? 60 = 1320 N

50.A staff is placed on a benchmark (BM) of reduced level (RL) 100.000 m and a theodolite
is placed at a horizontal distance of 50m from the BM to measure the vertical angles. The
measured vertical angles from the horizontal at the staff readings of 0.400m and 2.400 m are
found to be the same. Taking the height of the instrument as 1.400 m, the RL (in m) of the
theodolite station is _________
Answer :
Solution :


2x = 2.8
x = 1.4m
H.O.I = 100 + 1.4
= 101.4m
RL of theodelite station = 101.4 ? theodolite hight
= 101.4 ? 1.4
= 100m




38

51.A 0.80 m deep bed of sand filter (length 4m and width 3m) is made of uniform particles
(diameter = 0.40 mm, specific gravity = 2.65, shape factor = 0.85) with bed porosity of 0.the
bed has to be backwashed at a flow rate of 3.60 m
3
/min. During backwashing, if the terminal
settling velocity of sand particles is 0.05 m/s, the expanded bed depth (in m, round off to 2
decimal places) is ______
Answer :
Solution :


then L ex (1 ? nex) = L(1 ? n)
? Lex (1 ? 0.6025) = 0.8 ? (1 ? 0.4)


52.A reinforced concrete circular pile of 12m length and 0.6 m diameter is embedded in stiff
clay which has an undrained unit cohesion of 110 kN/m
2
. The adhesion factor is 0.The Net
Ultimate Pullout (Uplift) Load for the pile (in kN, round off to 1 decimal place is) is
_________
Answer :
Solution :
Pull out load
p = perimeter
? = length
= 0.5 ? 110 ? 12 ? ?(0.6)
= 1244.07 kN



39


53.A survey line was measured to be 285.5m with a tape having a nominal length of 30m. On
checking, the true length of the tape was found to be 0.05 m too short. If the line lay on a
slope of 1 in 10, the reduced length (horizontal length) of the line for plotting of survey work
would be
A. 285.0 m
B. 284.5 m
C. 285.6 m
D. 283.6 m

Answer :D
Solution :
Measured length = 285.5 m
Nominal length of tape = 30 m
Slope = 1 in 10
The tape is 0.05 m too short
Actual length of tape = 30 ? 0.05 = 29.95 m
Actual length measured
Measured length

Now slope correction
? Slope = 1 in 10




40


? Length to be plotted
= Actual length measured + correction
= 285.024 + (-1.42512)
= 283.599 m
Hence, option (d) is correct.

54.The rigid-joined plane frame QRS shown in the figure is subjected to a load P at the joint
R. Let the axial deformation in the frame be neglected. If the support S undergoes a
settlement of the vertical reaction at the support S will become zero when ? is equal
to

A. 3.0
B. 7.5
C. 0.1
D. 48.0

Answer :B
Solution :



41


Using slope deflection method,

If reaction at S is equal to zero


From equilibrium of joint




42

? From (i) & (ii)



55.Which one of the following is NOT a correct statement?
A. The function x?x, (x > 0), has the global minima at x = e
B. The function x?x, (x > 0), has the global maxima at x = e
C. The function x
3
has neither global minima nor global maxima
D. The function |x| has the global minima at x = 0

Answer :A
Solution :
y = x
1/x


For
? x = e
Thus point x = e is the critical point for
y = x
1/x

Now at x = e, dy/dx changes its sign from (+ve) to (-ve). Thus point (x = e) is point of global
maxima.
y = x
3
has neither global minima nor global maxima, it only have saddle point at x = 0
y | x |; attains its minimum value at x = 0; so x = 0 is the global minima for y = f(x)



43


56.A rectangular open channel has a width of 5m and a bed slope of 0.001. For a uniform
flow of depth 2m, the velocity is 2m/s. The Manning?s roughness coefficient for the channel
is
A. 0.033
B. 0.050
C. 0.002
D. 0.017

Answer :D
Solution :
For a rectangular channel
Width of channel = 5 m
Depth of flow = 2 m
Bed slope = 0.001
Velocity V = 2 m/sec.
From manning?s

Where


57.The hyetograph of a storm event of duration 140 minutes is shown in the figure.



44


The infiltration capacity at the start of this event (t = 0) is 17mm/hour, which linearly
decreases to 10 mm/hour after 40 minutes duration. As the event progresses, the infiltration
rate further drops down linearly to attain a value of 4mm/ hour at t = 100 minutes and
remains constant thereafter till the end of the storm event. The value of the infiltration
index, ? (in mm/hour, round off to 2 decimal places), is _______
Answer :
Solution :

Depth of infiltration = Area of hyetograph above Horton?s curve

Now, assuming



45




58.Consider a laminar flow in the x-direction between two infinite parallel plates (Couette
flow). The lower plate is stationary and the upper plate is moving with a velocity of 1 cm/ s in
the x-direction. The distance between the plates is 5mm and the dynamic viscosity of the
fluid is 0.01 N-s/mIf the shear stress on the lower plate is zero, the pressure gradient, (in
N/m
2
per m, round off to 1 decimal place) is______
Answer :
Solution :
Given data ;
Velocity of plate, V = 1 cm/sec
Distance between the late = 5 mm
Dynamic viscosity of fluid = 0.01 N-S/m
2

Shear stress at lower plate = 0
Pressure gradient
We know that, in case of couette flow, shear stress ( ? ) is given by




46

At lower plate, y = 0; ? = 0 [Given]


59.A granular soil has a saturated unit weight of 20 kN/m
3
and an effective angle of shearing
resistance of 30?. The unit weight of water is 9.81 kN/m
3
. A slope is to be made on this soil
deposit in which the seepage occurs parallel to the slope up to the free surface. Under this
seepage condition for a factor of safety of 1.5, the safe slope angle (in degree, round off to 1
decimal place) would be ____
Answer :
Solution :
?sat = 20KN/m
2

? = 30?
?w = 9.81 KN/m
2

FOS = 1.5
We know that

[i = safe slope angle]

? i = 11.0953

60.Two water reservoirs are connected by a siphon (running full) of total length 5000 m and
diameter of 0.10 m, as shown below (figure not drawn to scale).



47


The inlet leg length of the siphon to its summit is 2000 m. The difference in the water surface
levels of the two reservoirs is 5m. Assume the permissible minimum absolute pressure at the
summit of siphon to be 2.5m of water when running full. Given: friction factor f = 0.02
throughout, atmospheric pressure = 10.3 m of water, and acceleration due to gravity g = 9.81
m/s
2
. Considering only major loss using Darcy- Weisbach equation the maximum height of
the summit of siphon from the water level of upper reservoir, h (in m round off to 1 decimal
place) is _____
Answer :
Solution :
Given data :

d = 0.1 m
Length of siphon = 5000 m
Length of siphon upto summit = 2000 m
Friction Factor, f = 0.02
Acceleration due to gravity, g = 9.81 m/sec
2

Applying Energy equation between point 1 and 3 to get

[From Darcy Weisback equation



48


[ ? Z1 - Z3 = 5m]
? Q = 2.4597 ? 10
-3
m
3
/sec
Now applying energy equation between 1 and 2 to get




61.Sedimentation basin in a water treatment plant is designed for a flow rate of 0.2 m
3
/s. The
basin is rectangular with a length of 32m, width of 8m and depth of 4m. Assume that the
settling velocity of these particles is governed by the Stokes? law. Given: density of the
particles = 2.5 g/cm
3
; density of water = 1 g/cm3; dynamic viscosity of water = 0.01 g/(cm.s);
gravitational acceleration = 980 cm/s
2
. If the incoming water contains particles of diameter 25
?m (spherical and uniform) the removal efficiency of these particles is
A. 100%
B. 65%
C. 78%
D. 51%

Answer :B
Solution :
Given :
Flow rate = 0.2 m
3
/sec



49

Dimension of tank = 32m ? 8 m ? 4 m
Density of particles = 2.5 g/cc
Density of water = 1 g/cc
Dynamic viscosity of water = 0.01 g/cm-S
Diameter of particle = 25 ?m
We know that
Over flow rate of tank
= 7.8125 ? 10
-4
m/sec
And settling velocity of particle (vs),

Now, % removal efficiency

Hence option (b) is correct.

62.A square footing of 4m side is placed at 1 m depth in a sand deposit. The dry unit weight
(?) of sand is 15 kN/m
3
. This footing has an ultimate bearing capacity of 600 kPa. Consider
the depth factors; dq = d? = 1.0 and the bearing capacity factor: N? = 18.This footing is placed
at a depth of 2m in the same soil deposit. For a factor of safety of 3.0 per Terzaghi?s theory,
the safe bearing capacity (in kPa) of this footing would be ________
Answer :
Solution :
Side of square footing = 4 m



50

Depth of footing = 1 m
Unit weight of soil = 15 KN/m
3

Ultimate bearing capacity = 600 KPa
Depth factors, dq = d? = 1
N? = 18.75
According to terzaghi, the ultimate bearing capacity of square footing is given as
At depth of footing = 1 m
qu = 1.3CNC + qNqdq + 04B?N?d?
For sand, C = 0, q = ?Df = 15 ? 1 = 15KN m
2

600 = 0 + 15 ? Nq ? 1 + 0.4 ? 4 ? 15 ? 18.75 ? 1
? Nq = 10
Now at depth of footing at 2m
qu = 1.3 CNC + qNq + 0.4B?N?d?
qu = 0 + (2 ? 15)10 ? 1 + 0.4 ? 4 ? 15 ? 18.75 ? 1
qu = 750 KPa
? We know that
qnu = qu - ?Df
qnu = 750 ? 15 ? 2
qnu = 720 KPa
and safe bearing capacity qsafe


FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C



27

and 1 atm pressure as 22.4 litres per mole. The equivalent NO2 concentration (in microgram
per cubic meter, round off to 2 decimal places) would be _______
Answer :
Solution :
0.02 ppm of NO2 means


41.Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number
of vehicles arriving on this highway follows Poisson distribution, the probability (round off to
2 decimal places) that the headway between successive vehicles lies between 6 and 10
seconds is _________
Answer :
Solution :
? = 360 veh/hr





28

42.Consider the ordinary differential equation Given the values of y(1)
= 0 and y(2) = 2, the value of y(3) (round off to 1 decimal place), is ______
Answer :
Solution :

y(1) = 0 & y(2) = 2
Assume x = e
t


Then

Putting this into ordinary differential equation
D(D ? 1)y ? 2Dy + 2y = 0
[D
2
? 3D + 2] = 0
Auxillary equation is
m
2
? 3m + 2 = 0
(m ? 1) (m ? 2) = 0
i.e. m = 1 & m = 2
? solution of equation
y = c1e
t
+ c2e
2t

? Putting et as x
? y = c1x + c2X
2




29

? y(1)= 0
? c1 + c2 = 0 ...(i)
& y(2) = 2
? 2c1 + 4c2 = 2
? c1 + 2c2 = 1 ?(ii)
(ii) ? (i)
? c2 = 1
c1 = ?1
? y = ?x + x
2

Then y(3) = ?3 + 3
2
= 6

43.A 3 m ? 3 m square precast reinforced concrete segments to be installed by pushing them
through an existing railway embankment for making an underpass as shown in the figure. A
reaction arrangement using precast PCC blocks placed on the ground is to be made for the
jacks.

At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The
jacks will react against the rigid steel plate placed against the reaction arrangement. The
footprint area of reaction arrangement on natural ground are: c = 17 kPa; ? = 25
o
and ? = 18
kN/m
3
. Assuming that the reaction arrangement has rough interface and has the same
properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure
is __________.
Answer :
Solution :
FOS against shear failure



30





44.A parabolic vertical curve is being designed to join a road of grade + 5% with a road of
grade ?3%. The length of the vertical curve is 400 m measured along the horizontal. The
vertical point of curvature (VPC) is located on the road of grade
+5%. The difference in height between VPC and vertical point of intersection (VPI) (in m,
round off to the nearest integer) is ______________
Answer :
Solution :

Height difference between
VPI & VPC = 5% of 200 m = 10 m




31

45.If the section shown in the figure turns from fully-elastic to fully-plastic, the depth of
neutral axis (N.A.), decreases by

All dimensions are in mm
A.
13.75 mm

B. 10.75 mm
C. 15.25 mm
D. 12.25 mm

Answer :A
Solution :

For fully elastic case,

For fully plastic case,



32

y = Equal area axis = 5
N.A reduces by = 18.75 ? 5 = 13.75 mm

46.A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a
roller support at joint R. A point load of 50 kN is acting at joint R in the horizontal direction.
The flexural rigidity. EI, of each member is 10
6
kNm
2
. Under the applied load, the horizontal
displacement (in mm, round off to 1 decimal place) of joint R would be __________

Answer :
Solution :

For reaction
?Mp = 0
?W ? 5 + 50 ? 10 = 0

When unit load at R is acting in the direction of 50kN load, then reaction at
R = 2 (downward)



33




Alternatively:





34





47.A box measuring 50 cm ? 50 cm ? 50 cm is filled to the top with dry coarse aggregate of
mass 187.5 kg. The water absorption and specific gravity of the aggregate are 0.5% and 2.5,
respectively. The maximum quantity of water (in kg, round off to 2 decimal places) required
to fill the box completely is _________
Answer :
Solution :
Volume of the box = 0.5 ? 0.5 ? 0.5
= 0.125 m
3

Mass of aggregate = 187.5 kg
Gagg = 2.5
Volume of aggregate
Volume of empty space = 0.125 ? 0.075
= 0.05 m
3

Water absorption = 0.5%
Volume of water absorbed



35


Total volume of water that can be filled
= 9.375 ? 10
?4
+ 0.05
= 0.0509 m
3

Mass of water = 50.94 kg

48.A wastewater is to be disinfected with 35mg/L of chlorine to obtain 99% kill of
microorganisms. The number of micro-organisms remaining alive (Nt) at time t, is modelled
by Nt = N0e
?kt
, where N0 is number of microorganisms at t = 0, and k is the rate of kill. The
wastewater flow rate is 36m
3
/h, and k = 0.23 min-If the depth and width of the chlorination
tank are 1.5 m and 1.0m, respectively, the length of the tank (in m, round off to 2 decimal
places) is _________
Answer :
Solution :
For 99% kill of mircoorganision

?0.23t = ?4.605
t = 20.022 min
Volume of tank req. = Q.t





36



49.The cross-section of a built-up wooden beam as shown in the figure (not drawn to scale) is
subjected to a vertical shear force of 8kN. The beam is symmetrical about the neutral axis
(N.A.) shown, and the moment of inertia about N.A. is 1.5 ? 10
9
mm
4
. Considering that the
nails at the location P are spaced longitudinally (along the length of the beam) at 60 mm, each
of the nails at P will be subjected to the shear force of

All dimensions are in mm
A.
60 N

B. 120 N
C. 240 N
D. 480 N

Answer :C
Solution :




37

Shear force in nail at

So shear force in nail = 22 ? 60 = 1320 N

50.A staff is placed on a benchmark (BM) of reduced level (RL) 100.000 m and a theodolite
is placed at a horizontal distance of 50m from the BM to measure the vertical angles. The
measured vertical angles from the horizontal at the staff readings of 0.400m and 2.400 m are
found to be the same. Taking the height of the instrument as 1.400 m, the RL (in m) of the
theodolite station is _________
Answer :
Solution :


2x = 2.8
x = 1.4m
H.O.I = 100 + 1.4
= 101.4m
RL of theodelite station = 101.4 ? theodolite hight
= 101.4 ? 1.4
= 100m




38

51.A 0.80 m deep bed of sand filter (length 4m and width 3m) is made of uniform particles
(diameter = 0.40 mm, specific gravity = 2.65, shape factor = 0.85) with bed porosity of 0.the
bed has to be backwashed at a flow rate of 3.60 m
3
/min. During backwashing, if the terminal
settling velocity of sand particles is 0.05 m/s, the expanded bed depth (in m, round off to 2
decimal places) is ______
Answer :
Solution :


then L ex (1 ? nex) = L(1 ? n)
? Lex (1 ? 0.6025) = 0.8 ? (1 ? 0.4)


52.A reinforced concrete circular pile of 12m length and 0.6 m diameter is embedded in stiff
clay which has an undrained unit cohesion of 110 kN/m
2
. The adhesion factor is 0.The Net
Ultimate Pullout (Uplift) Load for the pile (in kN, round off to 1 decimal place is) is
_________
Answer :
Solution :
Pull out load
p = perimeter
? = length
= 0.5 ? 110 ? 12 ? ?(0.6)
= 1244.07 kN



39


53.A survey line was measured to be 285.5m with a tape having a nominal length of 30m. On
checking, the true length of the tape was found to be 0.05 m too short. If the line lay on a
slope of 1 in 10, the reduced length (horizontal length) of the line for plotting of survey work
would be
A. 285.0 m
B. 284.5 m
C. 285.6 m
D. 283.6 m

Answer :D
Solution :
Measured length = 285.5 m
Nominal length of tape = 30 m
Slope = 1 in 10
The tape is 0.05 m too short
Actual length of tape = 30 ? 0.05 = 29.95 m
Actual length measured
Measured length

Now slope correction
? Slope = 1 in 10




40


? Length to be plotted
= Actual length measured + correction
= 285.024 + (-1.42512)
= 283.599 m
Hence, option (d) is correct.

54.The rigid-joined plane frame QRS shown in the figure is subjected to a load P at the joint
R. Let the axial deformation in the frame be neglected. If the support S undergoes a
settlement of the vertical reaction at the support S will become zero when ? is equal
to

A. 3.0
B. 7.5
C. 0.1
D. 48.0

Answer :B
Solution :



41


Using slope deflection method,

If reaction at S is equal to zero


From equilibrium of joint




42

? From (i) & (ii)



55.Which one of the following is NOT a correct statement?
A. The function x?x, (x > 0), has the global minima at x = e
B. The function x?x, (x > 0), has the global maxima at x = e
C. The function x
3
has neither global minima nor global maxima
D. The function |x| has the global minima at x = 0

Answer :A
Solution :
y = x
1/x


For
? x = e
Thus point x = e is the critical point for
y = x
1/x

Now at x = e, dy/dx changes its sign from (+ve) to (-ve). Thus point (x = e) is point of global
maxima.
y = x
3
has neither global minima nor global maxima, it only have saddle point at x = 0
y | x |; attains its minimum value at x = 0; so x = 0 is the global minima for y = f(x)



43


56.A rectangular open channel has a width of 5m and a bed slope of 0.001. For a uniform
flow of depth 2m, the velocity is 2m/s. The Manning?s roughness coefficient for the channel
is
A. 0.033
B. 0.050
C. 0.002
D. 0.017

Answer :D
Solution :
For a rectangular channel
Width of channel = 5 m
Depth of flow = 2 m
Bed slope = 0.001
Velocity V = 2 m/sec.
From manning?s

Where


57.The hyetograph of a storm event of duration 140 minutes is shown in the figure.



44


The infiltration capacity at the start of this event (t = 0) is 17mm/hour, which linearly
decreases to 10 mm/hour after 40 minutes duration. As the event progresses, the infiltration
rate further drops down linearly to attain a value of 4mm/ hour at t = 100 minutes and
remains constant thereafter till the end of the storm event. The value of the infiltration
index, ? (in mm/hour, round off to 2 decimal places), is _______
Answer :
Solution :

Depth of infiltration = Area of hyetograph above Horton?s curve

Now, assuming



45




58.Consider a laminar flow in the x-direction between two infinite parallel plates (Couette
flow). The lower plate is stationary and the upper plate is moving with a velocity of 1 cm/ s in
the x-direction. The distance between the plates is 5mm and the dynamic viscosity of the
fluid is 0.01 N-s/mIf the shear stress on the lower plate is zero, the pressure gradient, (in
N/m
2
per m, round off to 1 decimal place) is______
Answer :
Solution :
Given data ;
Velocity of plate, V = 1 cm/sec
Distance between the late = 5 mm
Dynamic viscosity of fluid = 0.01 N-S/m
2

Shear stress at lower plate = 0
Pressure gradient
We know that, in case of couette flow, shear stress ( ? ) is given by




46

At lower plate, y = 0; ? = 0 [Given]


59.A granular soil has a saturated unit weight of 20 kN/m
3
and an effective angle of shearing
resistance of 30?. The unit weight of water is 9.81 kN/m
3
. A slope is to be made on this soil
deposit in which the seepage occurs parallel to the slope up to the free surface. Under this
seepage condition for a factor of safety of 1.5, the safe slope angle (in degree, round off to 1
decimal place) would be ____
Answer :
Solution :
?sat = 20KN/m
2

? = 30?
?w = 9.81 KN/m
2

FOS = 1.5
We know that

[i = safe slope angle]

? i = 11.0953

60.Two water reservoirs are connected by a siphon (running full) of total length 5000 m and
diameter of 0.10 m, as shown below (figure not drawn to scale).



47


The inlet leg length of the siphon to its summit is 2000 m. The difference in the water surface
levels of the two reservoirs is 5m. Assume the permissible minimum absolute pressure at the
summit of siphon to be 2.5m of water when running full. Given: friction factor f = 0.02
throughout, atmospheric pressure = 10.3 m of water, and acceleration due to gravity g = 9.81
m/s
2
. Considering only major loss using Darcy- Weisbach equation the maximum height of
the summit of siphon from the water level of upper reservoir, h (in m round off to 1 decimal
place) is _____
Answer :
Solution :
Given data :

d = 0.1 m
Length of siphon = 5000 m
Length of siphon upto summit = 2000 m
Friction Factor, f = 0.02
Acceleration due to gravity, g = 9.81 m/sec
2

Applying Energy equation between point 1 and 3 to get

[From Darcy Weisback equation



48


[ ? Z1 - Z3 = 5m]
? Q = 2.4597 ? 10
-3
m
3
/sec
Now applying energy equation between 1 and 2 to get




61.Sedimentation basin in a water treatment plant is designed for a flow rate of 0.2 m
3
/s. The
basin is rectangular with a length of 32m, width of 8m and depth of 4m. Assume that the
settling velocity of these particles is governed by the Stokes? law. Given: density of the
particles = 2.5 g/cm
3
; density of water = 1 g/cm3; dynamic viscosity of water = 0.01 g/(cm.s);
gravitational acceleration = 980 cm/s
2
. If the incoming water contains particles of diameter 25
?m (spherical and uniform) the removal efficiency of these particles is
A. 100%
B. 65%
C. 78%
D. 51%

Answer :B
Solution :
Given :
Flow rate = 0.2 m
3
/sec



49

Dimension of tank = 32m ? 8 m ? 4 m
Density of particles = 2.5 g/cc
Density of water = 1 g/cc
Dynamic viscosity of water = 0.01 g/cm-S
Diameter of particle = 25 ?m
We know that
Over flow rate of tank
= 7.8125 ? 10
-4
m/sec
And settling velocity of particle (vs),

Now, % removal efficiency

Hence option (b) is correct.

62.A square footing of 4m side is placed at 1 m depth in a sand deposit. The dry unit weight
(?) of sand is 15 kN/m
3
. This footing has an ultimate bearing capacity of 600 kPa. Consider
the depth factors; dq = d? = 1.0 and the bearing capacity factor: N? = 18.This footing is placed
at a depth of 2m in the same soil deposit. For a factor of safety of 3.0 per Terzaghi?s theory,
the safe bearing capacity (in kPa) of this footing would be ________
Answer :
Solution :
Side of square footing = 4 m



50

Depth of footing = 1 m
Unit weight of soil = 15 KN/m
3

Ultimate bearing capacity = 600 KPa
Depth factors, dq = d? = 1
N? = 18.75
According to terzaghi, the ultimate bearing capacity of square footing is given as
At depth of footing = 1 m
qu = 1.3CNC + qNqdq + 04B?N?d?
For sand, C = 0, q = ?Df = 15 ? 1 = 15KN m
2

600 = 0 + 15 ? Nq ? 1 + 0.4 ? 4 ? 15 ? 18.75 ? 1
? Nq = 10
Now at depth of footing at 2m
qu = 1.3 CNC + qNq + 0.4B?N?d?
qu = 0 + (2 ? 15)10 ? 1 + 0.4 ? 4 ? 15 ? 18.75 ? 1
qu = 750 KPa
? We know that
qnu = qu - ?Df
qnu = 750 ? 15 ? 2
qnu = 720 KPa
and safe bearing capacity qsafe





51

63.Consider two functions: x = ? ln ? and y = ? ln ?. Which one of the following is the
correct expression for ?
A.
B.
C.
D.

Answer :C
Solution :
...(i)

Putting value of ? in (i)
...(ii)
Assuming y constant and differentating w.r.t. x.
?(iii)
Puttting value of from (ii) in equation (iii)

FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C



27

and 1 atm pressure as 22.4 litres per mole. The equivalent NO2 concentration (in microgram
per cubic meter, round off to 2 decimal places) would be _______
Answer :
Solution :
0.02 ppm of NO2 means


41.Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number
of vehicles arriving on this highway follows Poisson distribution, the probability (round off to
2 decimal places) that the headway between successive vehicles lies between 6 and 10
seconds is _________
Answer :
Solution :
? = 360 veh/hr





28

42.Consider the ordinary differential equation Given the values of y(1)
= 0 and y(2) = 2, the value of y(3) (round off to 1 decimal place), is ______
Answer :
Solution :

y(1) = 0 & y(2) = 2
Assume x = e
t


Then

Putting this into ordinary differential equation
D(D ? 1)y ? 2Dy + 2y = 0
[D
2
? 3D + 2] = 0
Auxillary equation is
m
2
? 3m + 2 = 0
(m ? 1) (m ? 2) = 0
i.e. m = 1 & m = 2
? solution of equation
y = c1e
t
+ c2e
2t

? Putting et as x
? y = c1x + c2X
2




29

? y(1)= 0
? c1 + c2 = 0 ...(i)
& y(2) = 2
? 2c1 + 4c2 = 2
? c1 + 2c2 = 1 ?(ii)
(ii) ? (i)
? c2 = 1
c1 = ?1
? y = ?x + x
2

Then y(3) = ?3 + 3
2
= 6

43.A 3 m ? 3 m square precast reinforced concrete segments to be installed by pushing them
through an existing railway embankment for making an underpass as shown in the figure. A
reaction arrangement using precast PCC blocks placed on the ground is to be made for the
jacks.

At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The
jacks will react against the rigid steel plate placed against the reaction arrangement. The
footprint area of reaction arrangement on natural ground are: c = 17 kPa; ? = 25
o
and ? = 18
kN/m
3
. Assuming that the reaction arrangement has rough interface and has the same
properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure
is __________.
Answer :
Solution :
FOS against shear failure



30





44.A parabolic vertical curve is being designed to join a road of grade + 5% with a road of
grade ?3%. The length of the vertical curve is 400 m measured along the horizontal. The
vertical point of curvature (VPC) is located on the road of grade
+5%. The difference in height between VPC and vertical point of intersection (VPI) (in m,
round off to the nearest integer) is ______________
Answer :
Solution :

Height difference between
VPI & VPC = 5% of 200 m = 10 m




31

45.If the section shown in the figure turns from fully-elastic to fully-plastic, the depth of
neutral axis (N.A.), decreases by

All dimensions are in mm
A.
13.75 mm

B. 10.75 mm
C. 15.25 mm
D. 12.25 mm

Answer :A
Solution :

For fully elastic case,

For fully plastic case,



32

y = Equal area axis = 5
N.A reduces by = 18.75 ? 5 = 13.75 mm

46.A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a
roller support at joint R. A point load of 50 kN is acting at joint R in the horizontal direction.
The flexural rigidity. EI, of each member is 10
6
kNm
2
. Under the applied load, the horizontal
displacement (in mm, round off to 1 decimal place) of joint R would be __________

Answer :
Solution :

For reaction
?Mp = 0
?W ? 5 + 50 ? 10 = 0

When unit load at R is acting in the direction of 50kN load, then reaction at
R = 2 (downward)



33




Alternatively:





34





47.A box measuring 50 cm ? 50 cm ? 50 cm is filled to the top with dry coarse aggregate of
mass 187.5 kg. The water absorption and specific gravity of the aggregate are 0.5% and 2.5,
respectively. The maximum quantity of water (in kg, round off to 2 decimal places) required
to fill the box completely is _________
Answer :
Solution :
Volume of the box = 0.5 ? 0.5 ? 0.5
= 0.125 m
3

Mass of aggregate = 187.5 kg
Gagg = 2.5
Volume of aggregate
Volume of empty space = 0.125 ? 0.075
= 0.05 m
3

Water absorption = 0.5%
Volume of water absorbed



35


Total volume of water that can be filled
= 9.375 ? 10
?4
+ 0.05
= 0.0509 m
3

Mass of water = 50.94 kg

48.A wastewater is to be disinfected with 35mg/L of chlorine to obtain 99% kill of
microorganisms. The number of micro-organisms remaining alive (Nt) at time t, is modelled
by Nt = N0e
?kt
, where N0 is number of microorganisms at t = 0, and k is the rate of kill. The
wastewater flow rate is 36m
3
/h, and k = 0.23 min-If the depth and width of the chlorination
tank are 1.5 m and 1.0m, respectively, the length of the tank (in m, round off to 2 decimal
places) is _________
Answer :
Solution :
For 99% kill of mircoorganision

?0.23t = ?4.605
t = 20.022 min
Volume of tank req. = Q.t





36



49.The cross-section of a built-up wooden beam as shown in the figure (not drawn to scale) is
subjected to a vertical shear force of 8kN. The beam is symmetrical about the neutral axis
(N.A.) shown, and the moment of inertia about N.A. is 1.5 ? 10
9
mm
4
. Considering that the
nails at the location P are spaced longitudinally (along the length of the beam) at 60 mm, each
of the nails at P will be subjected to the shear force of

All dimensions are in mm
A.
60 N

B. 120 N
C. 240 N
D. 480 N

Answer :C
Solution :




37

Shear force in nail at

So shear force in nail = 22 ? 60 = 1320 N

50.A staff is placed on a benchmark (BM) of reduced level (RL) 100.000 m and a theodolite
is placed at a horizontal distance of 50m from the BM to measure the vertical angles. The
measured vertical angles from the horizontal at the staff readings of 0.400m and 2.400 m are
found to be the same. Taking the height of the instrument as 1.400 m, the RL (in m) of the
theodolite station is _________
Answer :
Solution :


2x = 2.8
x = 1.4m
H.O.I = 100 + 1.4
= 101.4m
RL of theodelite station = 101.4 ? theodolite hight
= 101.4 ? 1.4
= 100m




38

51.A 0.80 m deep bed of sand filter (length 4m and width 3m) is made of uniform particles
(diameter = 0.40 mm, specific gravity = 2.65, shape factor = 0.85) with bed porosity of 0.the
bed has to be backwashed at a flow rate of 3.60 m
3
/min. During backwashing, if the terminal
settling velocity of sand particles is 0.05 m/s, the expanded bed depth (in m, round off to 2
decimal places) is ______
Answer :
Solution :


then L ex (1 ? nex) = L(1 ? n)
? Lex (1 ? 0.6025) = 0.8 ? (1 ? 0.4)


52.A reinforced concrete circular pile of 12m length and 0.6 m diameter is embedded in stiff
clay which has an undrained unit cohesion of 110 kN/m
2
. The adhesion factor is 0.The Net
Ultimate Pullout (Uplift) Load for the pile (in kN, round off to 1 decimal place is) is
_________
Answer :
Solution :
Pull out load
p = perimeter
? = length
= 0.5 ? 110 ? 12 ? ?(0.6)
= 1244.07 kN



39


53.A survey line was measured to be 285.5m with a tape having a nominal length of 30m. On
checking, the true length of the tape was found to be 0.05 m too short. If the line lay on a
slope of 1 in 10, the reduced length (horizontal length) of the line for plotting of survey work
would be
A. 285.0 m
B. 284.5 m
C. 285.6 m
D. 283.6 m

Answer :D
Solution :
Measured length = 285.5 m
Nominal length of tape = 30 m
Slope = 1 in 10
The tape is 0.05 m too short
Actual length of tape = 30 ? 0.05 = 29.95 m
Actual length measured
Measured length

Now slope correction
? Slope = 1 in 10




40


? Length to be plotted
= Actual length measured + correction
= 285.024 + (-1.42512)
= 283.599 m
Hence, option (d) is correct.

54.The rigid-joined plane frame QRS shown in the figure is subjected to a load P at the joint
R. Let the axial deformation in the frame be neglected. If the support S undergoes a
settlement of the vertical reaction at the support S will become zero when ? is equal
to

A. 3.0
B. 7.5
C. 0.1
D. 48.0

Answer :B
Solution :



41


Using slope deflection method,

If reaction at S is equal to zero


From equilibrium of joint




42

? From (i) & (ii)



55.Which one of the following is NOT a correct statement?
A. The function x?x, (x > 0), has the global minima at x = e
B. The function x?x, (x > 0), has the global maxima at x = e
C. The function x
3
has neither global minima nor global maxima
D. The function |x| has the global minima at x = 0

Answer :A
Solution :
y = x
1/x


For
? x = e
Thus point x = e is the critical point for
y = x
1/x

Now at x = e, dy/dx changes its sign from (+ve) to (-ve). Thus point (x = e) is point of global
maxima.
y = x
3
has neither global minima nor global maxima, it only have saddle point at x = 0
y | x |; attains its minimum value at x = 0; so x = 0 is the global minima for y = f(x)



43


56.A rectangular open channel has a width of 5m and a bed slope of 0.001. For a uniform
flow of depth 2m, the velocity is 2m/s. The Manning?s roughness coefficient for the channel
is
A. 0.033
B. 0.050
C. 0.002
D. 0.017

Answer :D
Solution :
For a rectangular channel
Width of channel = 5 m
Depth of flow = 2 m
Bed slope = 0.001
Velocity V = 2 m/sec.
From manning?s

Where


57.The hyetograph of a storm event of duration 140 minutes is shown in the figure.



44


The infiltration capacity at the start of this event (t = 0) is 17mm/hour, which linearly
decreases to 10 mm/hour after 40 minutes duration. As the event progresses, the infiltration
rate further drops down linearly to attain a value of 4mm/ hour at t = 100 minutes and
remains constant thereafter till the end of the storm event. The value of the infiltration
index, ? (in mm/hour, round off to 2 decimal places), is _______
Answer :
Solution :

Depth of infiltration = Area of hyetograph above Horton?s curve

Now, assuming



45




58.Consider a laminar flow in the x-direction between two infinite parallel plates (Couette
flow). The lower plate is stationary and the upper plate is moving with a velocity of 1 cm/ s in
the x-direction. The distance between the plates is 5mm and the dynamic viscosity of the
fluid is 0.01 N-s/mIf the shear stress on the lower plate is zero, the pressure gradient, (in
N/m
2
per m, round off to 1 decimal place) is______
Answer :
Solution :
Given data ;
Velocity of plate, V = 1 cm/sec
Distance between the late = 5 mm
Dynamic viscosity of fluid = 0.01 N-S/m
2

Shear stress at lower plate = 0
Pressure gradient
We know that, in case of couette flow, shear stress ( ? ) is given by




46

At lower plate, y = 0; ? = 0 [Given]


59.A granular soil has a saturated unit weight of 20 kN/m
3
and an effective angle of shearing
resistance of 30?. The unit weight of water is 9.81 kN/m
3
. A slope is to be made on this soil
deposit in which the seepage occurs parallel to the slope up to the free surface. Under this
seepage condition for a factor of safety of 1.5, the safe slope angle (in degree, round off to 1
decimal place) would be ____
Answer :
Solution :
?sat = 20KN/m
2

? = 30?
?w = 9.81 KN/m
2

FOS = 1.5
We know that

[i = safe slope angle]

? i = 11.0953

60.Two water reservoirs are connected by a siphon (running full) of total length 5000 m and
diameter of 0.10 m, as shown below (figure not drawn to scale).



47


The inlet leg length of the siphon to its summit is 2000 m. The difference in the water surface
levels of the two reservoirs is 5m. Assume the permissible minimum absolute pressure at the
summit of siphon to be 2.5m of water when running full. Given: friction factor f = 0.02
throughout, atmospheric pressure = 10.3 m of water, and acceleration due to gravity g = 9.81
m/s
2
. Considering only major loss using Darcy- Weisbach equation the maximum height of
the summit of siphon from the water level of upper reservoir, h (in m round off to 1 decimal
place) is _____
Answer :
Solution :
Given data :

d = 0.1 m
Length of siphon = 5000 m
Length of siphon upto summit = 2000 m
Friction Factor, f = 0.02
Acceleration due to gravity, g = 9.81 m/sec
2

Applying Energy equation between point 1 and 3 to get

[From Darcy Weisback equation



48


[ ? Z1 - Z3 = 5m]
? Q = 2.4597 ? 10
-3
m
3
/sec
Now applying energy equation between 1 and 2 to get




61.Sedimentation basin in a water treatment plant is designed for a flow rate of 0.2 m
3
/s. The
basin is rectangular with a length of 32m, width of 8m and depth of 4m. Assume that the
settling velocity of these particles is governed by the Stokes? law. Given: density of the
particles = 2.5 g/cm
3
; density of water = 1 g/cm3; dynamic viscosity of water = 0.01 g/(cm.s);
gravitational acceleration = 980 cm/s
2
. If the incoming water contains particles of diameter 25
?m (spherical and uniform) the removal efficiency of these particles is
A. 100%
B. 65%
C. 78%
D. 51%

Answer :B
Solution :
Given :
Flow rate = 0.2 m
3
/sec



49

Dimension of tank = 32m ? 8 m ? 4 m
Density of particles = 2.5 g/cc
Density of water = 1 g/cc
Dynamic viscosity of water = 0.01 g/cm-S
Diameter of particle = 25 ?m
We know that
Over flow rate of tank
= 7.8125 ? 10
-4
m/sec
And settling velocity of particle (vs),

Now, % removal efficiency

Hence option (b) is correct.

62.A square footing of 4m side is placed at 1 m depth in a sand deposit. The dry unit weight
(?) of sand is 15 kN/m
3
. This footing has an ultimate bearing capacity of 600 kPa. Consider
the depth factors; dq = d? = 1.0 and the bearing capacity factor: N? = 18.This footing is placed
at a depth of 2m in the same soil deposit. For a factor of safety of 3.0 per Terzaghi?s theory,
the safe bearing capacity (in kPa) of this footing would be ________
Answer :
Solution :
Side of square footing = 4 m



50

Depth of footing = 1 m
Unit weight of soil = 15 KN/m
3

Ultimate bearing capacity = 600 KPa
Depth factors, dq = d? = 1
N? = 18.75
According to terzaghi, the ultimate bearing capacity of square footing is given as
At depth of footing = 1 m
qu = 1.3CNC + qNqdq + 04B?N?d?
For sand, C = 0, q = ?Df = 15 ? 1 = 15KN m
2

600 = 0 + 15 ? Nq ? 1 + 0.4 ? 4 ? 15 ? 18.75 ? 1
? Nq = 10
Now at depth of footing at 2m
qu = 1.3 CNC + qNq + 0.4B?N?d?
qu = 0 + (2 ? 15)10 ? 1 + 0.4 ? 4 ? 15 ? 18.75 ? 1
qu = 750 KPa
? We know that
qnu = qu - ?Df
qnu = 750 ? 15 ? 2
qnu = 720 KPa
and safe bearing capacity qsafe





51

63.Consider two functions: x = ? ln ? and y = ? ln ?. Which one of the following is the
correct expression for ?
A.
B.
C.
D.

Answer :C
Solution :
...(i)

Putting value of ? in (i)
...(ii)
Assuming y constant and differentating w.r.t. x.
?(iii)
Puttting value of from (ii) in equation (iii)




52



(replacing x by in ?)


64. A 16 mm thick gusset plate is connected to the 12 mm thick flange plate of an I-section
using fillet welds on both sides as shown in the figure (not drawn to scale). The gusset plate
is subjected to a point load of 350 kN acting at a distance of 100 mm from the flange plate.
Size of fillet weld is 10 mm.

The maximum resultant stress (in MPa, round off to 1 decimal place) on the fillet weld along
the vertical plane would be ___________
Answer :
Solution :
Given Data :
Thickness of gusset plate (t) = 16 mm
Point load (P) = 350 KN
FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C



27

and 1 atm pressure as 22.4 litres per mole. The equivalent NO2 concentration (in microgram
per cubic meter, round off to 2 decimal places) would be _______
Answer :
Solution :
0.02 ppm of NO2 means


41.Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number
of vehicles arriving on this highway follows Poisson distribution, the probability (round off to
2 decimal places) that the headway between successive vehicles lies between 6 and 10
seconds is _________
Answer :
Solution :
? = 360 veh/hr





28

42.Consider the ordinary differential equation Given the values of y(1)
= 0 and y(2) = 2, the value of y(3) (round off to 1 decimal place), is ______
Answer :
Solution :

y(1) = 0 & y(2) = 2
Assume x = e
t


Then

Putting this into ordinary differential equation
D(D ? 1)y ? 2Dy + 2y = 0
[D
2
? 3D + 2] = 0
Auxillary equation is
m
2
? 3m + 2 = 0
(m ? 1) (m ? 2) = 0
i.e. m = 1 & m = 2
? solution of equation
y = c1e
t
+ c2e
2t

? Putting et as x
? y = c1x + c2X
2




29

? y(1)= 0
? c1 + c2 = 0 ...(i)
& y(2) = 2
? 2c1 + 4c2 = 2
? c1 + 2c2 = 1 ?(ii)
(ii) ? (i)
? c2 = 1
c1 = ?1
? y = ?x + x
2

Then y(3) = ?3 + 3
2
= 6

43.A 3 m ? 3 m square precast reinforced concrete segments to be installed by pushing them
through an existing railway embankment for making an underpass as shown in the figure. A
reaction arrangement using precast PCC blocks placed on the ground is to be made for the
jacks.

At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The
jacks will react against the rigid steel plate placed against the reaction arrangement. The
footprint area of reaction arrangement on natural ground are: c = 17 kPa; ? = 25
o
and ? = 18
kN/m
3
. Assuming that the reaction arrangement has rough interface and has the same
properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure
is __________.
Answer :
Solution :
FOS against shear failure



30





44.A parabolic vertical curve is being designed to join a road of grade + 5% with a road of
grade ?3%. The length of the vertical curve is 400 m measured along the horizontal. The
vertical point of curvature (VPC) is located on the road of grade
+5%. The difference in height between VPC and vertical point of intersection (VPI) (in m,
round off to the nearest integer) is ______________
Answer :
Solution :

Height difference between
VPI & VPC = 5% of 200 m = 10 m




31

45.If the section shown in the figure turns from fully-elastic to fully-plastic, the depth of
neutral axis (N.A.), decreases by

All dimensions are in mm
A.
13.75 mm

B. 10.75 mm
C. 15.25 mm
D. 12.25 mm

Answer :A
Solution :

For fully elastic case,

For fully plastic case,



32

y = Equal area axis = 5
N.A reduces by = 18.75 ? 5 = 13.75 mm

46.A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a
roller support at joint R. A point load of 50 kN is acting at joint R in the horizontal direction.
The flexural rigidity. EI, of each member is 10
6
kNm
2
. Under the applied load, the horizontal
displacement (in mm, round off to 1 decimal place) of joint R would be __________

Answer :
Solution :

For reaction
?Mp = 0
?W ? 5 + 50 ? 10 = 0

When unit load at R is acting in the direction of 50kN load, then reaction at
R = 2 (downward)



33




Alternatively:





34





47.A box measuring 50 cm ? 50 cm ? 50 cm is filled to the top with dry coarse aggregate of
mass 187.5 kg. The water absorption and specific gravity of the aggregate are 0.5% and 2.5,
respectively. The maximum quantity of water (in kg, round off to 2 decimal places) required
to fill the box completely is _________
Answer :
Solution :
Volume of the box = 0.5 ? 0.5 ? 0.5
= 0.125 m
3

Mass of aggregate = 187.5 kg
Gagg = 2.5
Volume of aggregate
Volume of empty space = 0.125 ? 0.075
= 0.05 m
3

Water absorption = 0.5%
Volume of water absorbed



35


Total volume of water that can be filled
= 9.375 ? 10
?4
+ 0.05
= 0.0509 m
3

Mass of water = 50.94 kg

48.A wastewater is to be disinfected with 35mg/L of chlorine to obtain 99% kill of
microorganisms. The number of micro-organisms remaining alive (Nt) at time t, is modelled
by Nt = N0e
?kt
, where N0 is number of microorganisms at t = 0, and k is the rate of kill. The
wastewater flow rate is 36m
3
/h, and k = 0.23 min-If the depth and width of the chlorination
tank are 1.5 m and 1.0m, respectively, the length of the tank (in m, round off to 2 decimal
places) is _________
Answer :
Solution :
For 99% kill of mircoorganision

?0.23t = ?4.605
t = 20.022 min
Volume of tank req. = Q.t





36



49.The cross-section of a built-up wooden beam as shown in the figure (not drawn to scale) is
subjected to a vertical shear force of 8kN. The beam is symmetrical about the neutral axis
(N.A.) shown, and the moment of inertia about N.A. is 1.5 ? 10
9
mm
4
. Considering that the
nails at the location P are spaced longitudinally (along the length of the beam) at 60 mm, each
of the nails at P will be subjected to the shear force of

All dimensions are in mm
A.
60 N

B. 120 N
C. 240 N
D. 480 N

Answer :C
Solution :




37

Shear force in nail at

So shear force in nail = 22 ? 60 = 1320 N

50.A staff is placed on a benchmark (BM) of reduced level (RL) 100.000 m and a theodolite
is placed at a horizontal distance of 50m from the BM to measure the vertical angles. The
measured vertical angles from the horizontal at the staff readings of 0.400m and 2.400 m are
found to be the same. Taking the height of the instrument as 1.400 m, the RL (in m) of the
theodolite station is _________
Answer :
Solution :


2x = 2.8
x = 1.4m
H.O.I = 100 + 1.4
= 101.4m
RL of theodelite station = 101.4 ? theodolite hight
= 101.4 ? 1.4
= 100m




38

51.A 0.80 m deep bed of sand filter (length 4m and width 3m) is made of uniform particles
(diameter = 0.40 mm, specific gravity = 2.65, shape factor = 0.85) with bed porosity of 0.the
bed has to be backwashed at a flow rate of 3.60 m
3
/min. During backwashing, if the terminal
settling velocity of sand particles is 0.05 m/s, the expanded bed depth (in m, round off to 2
decimal places) is ______
Answer :
Solution :


then L ex (1 ? nex) = L(1 ? n)
? Lex (1 ? 0.6025) = 0.8 ? (1 ? 0.4)


52.A reinforced concrete circular pile of 12m length and 0.6 m diameter is embedded in stiff
clay which has an undrained unit cohesion of 110 kN/m
2
. The adhesion factor is 0.The Net
Ultimate Pullout (Uplift) Load for the pile (in kN, round off to 1 decimal place is) is
_________
Answer :
Solution :
Pull out load
p = perimeter
? = length
= 0.5 ? 110 ? 12 ? ?(0.6)
= 1244.07 kN



39


53.A survey line was measured to be 285.5m with a tape having a nominal length of 30m. On
checking, the true length of the tape was found to be 0.05 m too short. If the line lay on a
slope of 1 in 10, the reduced length (horizontal length) of the line for plotting of survey work
would be
A. 285.0 m
B. 284.5 m
C. 285.6 m
D. 283.6 m

Answer :D
Solution :
Measured length = 285.5 m
Nominal length of tape = 30 m
Slope = 1 in 10
The tape is 0.05 m too short
Actual length of tape = 30 ? 0.05 = 29.95 m
Actual length measured
Measured length

Now slope correction
? Slope = 1 in 10




40


? Length to be plotted
= Actual length measured + correction
= 285.024 + (-1.42512)
= 283.599 m
Hence, option (d) is correct.

54.The rigid-joined plane frame QRS shown in the figure is subjected to a load P at the joint
R. Let the axial deformation in the frame be neglected. If the support S undergoes a
settlement of the vertical reaction at the support S will become zero when ? is equal
to

A. 3.0
B. 7.5
C. 0.1
D. 48.0

Answer :B
Solution :



41


Using slope deflection method,

If reaction at S is equal to zero


From equilibrium of joint




42

? From (i) & (ii)



55.Which one of the following is NOT a correct statement?
A. The function x?x, (x > 0), has the global minima at x = e
B. The function x?x, (x > 0), has the global maxima at x = e
C. The function x
3
has neither global minima nor global maxima
D. The function |x| has the global minima at x = 0

Answer :A
Solution :
y = x
1/x


For
? x = e
Thus point x = e is the critical point for
y = x
1/x

Now at x = e, dy/dx changes its sign from (+ve) to (-ve). Thus point (x = e) is point of global
maxima.
y = x
3
has neither global minima nor global maxima, it only have saddle point at x = 0
y | x |; attains its minimum value at x = 0; so x = 0 is the global minima for y = f(x)



43


56.A rectangular open channel has a width of 5m and a bed slope of 0.001. For a uniform
flow of depth 2m, the velocity is 2m/s. The Manning?s roughness coefficient for the channel
is
A. 0.033
B. 0.050
C. 0.002
D. 0.017

Answer :D
Solution :
For a rectangular channel
Width of channel = 5 m
Depth of flow = 2 m
Bed slope = 0.001
Velocity V = 2 m/sec.
From manning?s

Where


57.The hyetograph of a storm event of duration 140 minutes is shown in the figure.



44


The infiltration capacity at the start of this event (t = 0) is 17mm/hour, which linearly
decreases to 10 mm/hour after 40 minutes duration. As the event progresses, the infiltration
rate further drops down linearly to attain a value of 4mm/ hour at t = 100 minutes and
remains constant thereafter till the end of the storm event. The value of the infiltration
index, ? (in mm/hour, round off to 2 decimal places), is _______
Answer :
Solution :

Depth of infiltration = Area of hyetograph above Horton?s curve

Now, assuming



45




58.Consider a laminar flow in the x-direction between two infinite parallel plates (Couette
flow). The lower plate is stationary and the upper plate is moving with a velocity of 1 cm/ s in
the x-direction. The distance between the plates is 5mm and the dynamic viscosity of the
fluid is 0.01 N-s/mIf the shear stress on the lower plate is zero, the pressure gradient, (in
N/m
2
per m, round off to 1 decimal place) is______
Answer :
Solution :
Given data ;
Velocity of plate, V = 1 cm/sec
Distance between the late = 5 mm
Dynamic viscosity of fluid = 0.01 N-S/m
2

Shear stress at lower plate = 0
Pressure gradient
We know that, in case of couette flow, shear stress ( ? ) is given by




46

At lower plate, y = 0; ? = 0 [Given]


59.A granular soil has a saturated unit weight of 20 kN/m
3
and an effective angle of shearing
resistance of 30?. The unit weight of water is 9.81 kN/m
3
. A slope is to be made on this soil
deposit in which the seepage occurs parallel to the slope up to the free surface. Under this
seepage condition for a factor of safety of 1.5, the safe slope angle (in degree, round off to 1
decimal place) would be ____
Answer :
Solution :
?sat = 20KN/m
2

? = 30?
?w = 9.81 KN/m
2

FOS = 1.5
We know that

[i = safe slope angle]

? i = 11.0953

60.Two water reservoirs are connected by a siphon (running full) of total length 5000 m and
diameter of 0.10 m, as shown below (figure not drawn to scale).



47


The inlet leg length of the siphon to its summit is 2000 m. The difference in the water surface
levels of the two reservoirs is 5m. Assume the permissible minimum absolute pressure at the
summit of siphon to be 2.5m of water when running full. Given: friction factor f = 0.02
throughout, atmospheric pressure = 10.3 m of water, and acceleration due to gravity g = 9.81
m/s
2
. Considering only major loss using Darcy- Weisbach equation the maximum height of
the summit of siphon from the water level of upper reservoir, h (in m round off to 1 decimal
place) is _____
Answer :
Solution :
Given data :

d = 0.1 m
Length of siphon = 5000 m
Length of siphon upto summit = 2000 m
Friction Factor, f = 0.02
Acceleration due to gravity, g = 9.81 m/sec
2

Applying Energy equation between point 1 and 3 to get

[From Darcy Weisback equation



48


[ ? Z1 - Z3 = 5m]
? Q = 2.4597 ? 10
-3
m
3
/sec
Now applying energy equation between 1 and 2 to get




61.Sedimentation basin in a water treatment plant is designed for a flow rate of 0.2 m
3
/s. The
basin is rectangular with a length of 32m, width of 8m and depth of 4m. Assume that the
settling velocity of these particles is governed by the Stokes? law. Given: density of the
particles = 2.5 g/cm
3
; density of water = 1 g/cm3; dynamic viscosity of water = 0.01 g/(cm.s);
gravitational acceleration = 980 cm/s
2
. If the incoming water contains particles of diameter 25
?m (spherical and uniform) the removal efficiency of these particles is
A. 100%
B. 65%
C. 78%
D. 51%

Answer :B
Solution :
Given :
Flow rate = 0.2 m
3
/sec



49

Dimension of tank = 32m ? 8 m ? 4 m
Density of particles = 2.5 g/cc
Density of water = 1 g/cc
Dynamic viscosity of water = 0.01 g/cm-S
Diameter of particle = 25 ?m
We know that
Over flow rate of tank
= 7.8125 ? 10
-4
m/sec
And settling velocity of particle (vs),

Now, % removal efficiency

Hence option (b) is correct.

62.A square footing of 4m side is placed at 1 m depth in a sand deposit. The dry unit weight
(?) of sand is 15 kN/m
3
. This footing has an ultimate bearing capacity of 600 kPa. Consider
the depth factors; dq = d? = 1.0 and the bearing capacity factor: N? = 18.This footing is placed
at a depth of 2m in the same soil deposit. For a factor of safety of 3.0 per Terzaghi?s theory,
the safe bearing capacity (in kPa) of this footing would be ________
Answer :
Solution :
Side of square footing = 4 m



50

Depth of footing = 1 m
Unit weight of soil = 15 KN/m
3

Ultimate bearing capacity = 600 KPa
Depth factors, dq = d? = 1
N? = 18.75
According to terzaghi, the ultimate bearing capacity of square footing is given as
At depth of footing = 1 m
qu = 1.3CNC + qNqdq + 04B?N?d?
For sand, C = 0, q = ?Df = 15 ? 1 = 15KN m
2

600 = 0 + 15 ? Nq ? 1 + 0.4 ? 4 ? 15 ? 18.75 ? 1
? Nq = 10
Now at depth of footing at 2m
qu = 1.3 CNC + qNq + 0.4B?N?d?
qu = 0 + (2 ? 15)10 ? 1 + 0.4 ? 4 ? 15 ? 18.75 ? 1
qu = 750 KPa
? We know that
qnu = qu - ?Df
qnu = 750 ? 15 ? 2
qnu = 720 KPa
and safe bearing capacity qsafe





51

63.Consider two functions: x = ? ln ? and y = ? ln ?. Which one of the following is the
correct expression for ?
A.
B.
C.
D.

Answer :C
Solution :
...(i)

Putting value of ? in (i)
...(ii)
Assuming y constant and differentating w.r.t. x.
?(iii)
Puttting value of from (ii) in equation (iii)




52



(replacing x by in ?)


64. A 16 mm thick gusset plate is connected to the 12 mm thick flange plate of an I-section
using fillet welds on both sides as shown in the figure (not drawn to scale). The gusset plate
is subjected to a point load of 350 kN acting at a distance of 100 mm from the flange plate.
Size of fillet weld is 10 mm.

The maximum resultant stress (in MPa, round off to 1 decimal place) on the fillet weld along
the vertical plane would be ___________
Answer :
Solution :
Given Data :
Thickness of gusset plate (t) = 16 mm
Point load (P) = 350 KN



53

Eccentricity (e) = 100 mm
Direct shear stress,

And bending stress on the extreme edge of weld (f)

For checking the safety
Resultant Stress,
= 105.36 N/mm
2


65.A one-dimensional domain is discretized into N sub-domains of width
?x with node numbers i = 0, 1, 2, 3, ...., N. If the time scale is
discretized in steps of ?t, the forward-time and centered-space finite
difference approximation at n
th
node and nth time step, for the partial
differential equation is
A.
B.
C.
D.

Answer : D
FirstRanker.com - FirstRanker's Choice



2

GATE CE 2019 Set 1: Questions & Solutions
General Aptitude
1.They have come a long way in _______ trust among the users.
A. created
B. creating
C. creation
D. create

Answer :B
Solution :
They have come a long way in "creating" trust among the users.

2.The CEO?s decision to quit was as shocking to the Board as it was to __________.
A. myself
B. me
C. I
D. my

Answer :B
Solution :
?me?

3.The lecture was attended by quite _________ students, so the hall was not
very___________.
A. few, quite
B. a few, quite
C. few, quiet
D. a few, quiet

Answer :D



3

Solution :
a few, quiet

4.If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?
A. 82
B. 164
C. 120
D. 51

Answer :C
Solution :
P = 16 ? 2 = 32
E = 5 ? 2 = 10
S = 19 ? 2 = 38
T = 20 ? 2 = 40
P + E + S + T = 120

5.On a horizontal ground, the base of straight ladder is 6m away from the base of a vertical
pole. The ladder makes an angle of 45? to the horizontal. If the ladder is resting at a point
located at one-fifth of the height of the pole from the bottom, the height of the pole is
_____meter.
Answer :
Solution :



4




6.P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the
wife of P. R and T are the children of the siblings P and S respectively. Which one of the
following statements is necessarily FALSE?
A. S is the sister-in-law of Q
B. S is the aunt of T
C. S is the aunt of R
D. S is the brother of P

Answer :B
Solution :

?T? is child of ?S?. So option (b) is right.

7.A square has sides 5cm smaller than the sides of a second square. The area of the larger
square is four times the area of the smaller square. The side of the larger square is
________cm.



5

A. 15.10
B. 18.50
C. 10.00
D. 8.50

Answer :C
Solution :

Given,
(Area)B = 4 ? (Area)A
? x
2
= 4(x ? 5)
2

? x
2
= 4[x
2
+ 25 ? 10x]
? x
2
= 4x
2
+ 100 ? 40x
? 3x
2
? 40x + 100 = 0
? 3x
2
? 30x ? 10x + 100 = 0
? 3x(x ? 10) ? 10(x ? 10) = 0
? x = 10 or

8.In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only
football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both
cricket and football. The rest of them play all three sports. What is percentage of people who
play at least two sports?
A. 23.30
B. 50.00
C. 28.00
D. 25.00




6

Answer :D
Solution :

Total = 300
C = 105
H = 70
F = 50
C + H = 25
H + F = 15
C + F = 30
C + H + F = 300 ? (295) = 5
% of people playing at least 25 sports


9.The increasing interest in tribal characters might be a mere coincidence, but the timing is of
interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that
the new crop of characters represents the acceptance of the tribal character in the industry.
The films and characters are too few to be described as a pattern.
Who does the word ?arrived? mean in the paragraph above?
A. reached a terminus
B. came to a conclusion
C. attained a status



7

D. went to a place

Answer :C
Solution :
The word ?arrived? mean in the above para is to ?Attained a status?

10.The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a
thriving business in India. However, the commercial use of this technology is not legal in
India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been
purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton,
and planted in 15% of the cotton growing area in the 2017 Kharif season.
Which one of the following statements can be inferred from the given passage?
A. Farmers want to access the new technology for experimental purposes
B. Farmers want to access the new technology if India benefits from it
C. Farmers want to access the new technology by paying high price
D. Farmers want to access the new technology even if it is not legal

Answer :D
Solution :
Farmers want to access the new technology even if it is not legal

Civil Engineering
11.In a soil specimen, the total stress, effective stress, hydraulic gradient and critical
hydraulic gradient are ?, ??, i and ic, respectively. For initiation of quicksand condition,
which one of the following statement is TRUE?
A. ?? = 0 and i ? ic
B. ? = 0 and i = ic
C. ? ? ? 0 and i ? ic
D. ?? = 0 and i = ic

Answer :D
Solution :



8

During quick sand condition, the effective stress is reduced to zero [i.e, ? ? = 0]

12.Assuming that there is no possibility of shear buckling in the web, the maximum reduction
permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel
section due to high shear is
A. 25%
B. 50%
C. governed by the area of the flange
D. zero

Answer :D
Solution :
Maximum reduction permitted by IS 800-2007 is zero.

13.The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade
of this road is doubled, what will be the percentage change in the braking distance (for the
design vehicle to come to stop) measured along the horizontal (assume all other parameters
are kept unchanged)?
A.
B.
C.
D.

Answer :C
Solution :
Case I: Braking distance
Case II: Braking distance



9

Percentage change


14.A circular duct carrying water gradually contracts from a diameter of 30cm to 15cm. The
figure (not drawn to scale) shows the arrangement of differential manometer attached to the
duct.

When the water flows, the differential manometer shows a deflection of 8cm of mercury
(Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively.
Consider the acceleration due to gravity, g = 9.81 m/s
2
. Assuming frictionless flow, the flow
rate (in m
3
/s, round off to 3 decimal places) through the duct is __________.
Answer :
Solution :


h = 100.8 cm = 1.008 m
Flow rate

A1 = 4A2, g 9.81m/sec
2




10


= 0.01767 m
2




15.A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase
in vertical normal stress at depths of 2m and 4m along the point of the loading, as per
Boussinesq?s theory, would be _______.
Answer :
Solution :
Boussinesq?s theory
r = 0


16.A retaining wall of height H with smooth vertical backface supports a backfill inclined at
an angle ? with the horizontal. The backfill consists of cohesionless soil having angle of
internal friction ?. If the active lateral thrust acting on the wall is Pa which one of the
following statements is TRUE?
A. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal
B. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal



11

C. Pa acts at a height H/2 from the base of the wall and at an angle ? with the horizontal
D. Pa acts at a height H/3 from the base of the wall and at an angle ? with the horizontal

Answer :A
Solution :

active thurst act at a height H/3 from the base of the wall and at an angle equal to backfill
inclination.

17.In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow
condition, is
A.
B.
C.
D. 2

Answer :A
Solution :
Velocity head for a critical flow

So, ratio of velocity head to critical flow depth



12


18.The probability that the annual maximum flood discharge will exceed 25000 m
3
/s, at least
once in next 5 years is found to be 0.The return period of this flood event (in years, round off
to 1 decimal place) is _____________.
Answer :
Solution :
Probability exceed maximum discharge at least once in next 5 years is given by
= 1 (1? p)
n

? 0.25 = 1 - (1 - P)
n
[n = 5 year]
? P = 0.559

? T = 17.9 year

19.The interior angles of four triangles are given below:

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?
A. Both P and R
B. Both Q and S
C. Both P and S
D. Both Q and R

Answer :B
Solution :



13

A triangle is said to be ill condition when angle is less than 30? and more than 120?.
So, triangle S is ill conditioned.
For well conditioned of triangulation two angle should not be almost equal.
So, only triangle Q or triangle R is ill-conditioned
So, ill-condition S and Q or S and R. option S and Q is given. So option (b) correct.

20.A catchment may be idealised as a rectangle. There are three rain gauges located inside
the catchment at arbitrary locations. The average precipitation over the catchment is
estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT). Which of
the following statements is correct?
A. PA is always smaller than PT
B. There is no definite relationship between PA and PT
C. PA is always equal to PT
D. PA is always greater than PT

Answer :B
Solution :
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly
distributed as compared to arithmetic mean.

21.An isolated concrete pavement slab of length L is resting on a frictionless base. The
temperature of the top and bottom fibre of the slab are Tt and Tb, respecitvely. Given: the
coefficient of thermal expansion = ? and the elastic modulus = E. Assuming Tt > Tb and the
unit weight of concrete as zero, the maximum thermal stress is calculated as
A. zero
B.
C.
D.




14

Answer :A
Solution :
Here thermal stress is zero.

22.For a given loading on a rectangular plain concrete beam with an overall depth of 500
mm, the compressive strain and tensile strain developed at the extreme fibers are of the same
magnitude of 2.5 ? 10
-4
. The curvature in the beam cross-section (in
m
-1
, round off to 3 decimal places), is __________.
Answer :
Solution :

Given,
y = 250 mm = 0.25 m
As per flexure formula:

Curvature of beam cross-section

= 0.001 m
?1


23.For a small value of h, the Taylor series expansion of f(x + h) is



15

A.
B.
C.
D.

Answer :B
Solution :
For the small value of h, the Taylor?s series expansion of


So option (b) is correct

24.If the path of an irrigation canal is below the level of a natural stream, the type of cross
drainage structure provided is
A. Aqueduct
B. Super passage
C. Sluice gate
D. Level crossing

Answer :B
Solution :
If the path of an irrigation canal is below the bed level of a natural stream, the type of cross-
drainage work provided is super passage.



16



25.In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover
provided at the bottom of the beam as per IS 456?2000, is

All dimensions are in mm
A. 36 mm
B. 50 mm
C. 30 mm
D. 42 mm

Answer :C
Solution :



17




26.Consider a two-dimensional flow through isotropic soil along x-direction and z-direction.
If h is the hydraulic head, the Laplace?s equation of continuity is expressed as
A.
B.
C.
D.

Answer :B
Solution :

For homogeneous isotropic soils, the laplace?s equation of continuity is expressed as:


27.A soil has specific gravity of its solids equal to 2.The mass density of water is 1000 kg/m
3
.
Considering zero air voids and 10% moisture content of the soil sample, the dry density (in
kg/m
3
, round off to 1 decimal place) would be _______.



18

Answer :
Solution :
Gs = 2.65
?w = 1000 kg/m
3

?a = 0
w = 10% = 0.10

= 2094.862 kg/m
3


28.Which one of the following is correct?
A. and
B. and
C. and
D. and

Answer :A
Solution :


So, option (a) is correct.



19


29.A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?
A. FI, HI, PR, RS
B. FI, FG, RS, PR
C. FG, FI, HI, RS
D. FG, FH, HI, RS

Answer :B
Solution :
Only 4 member having zero force member GF, FI and SR, PR

30.A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of
stiffness k. Considering z as the displacement of the system at any time t, the equation of
motion for the free vibration of the system is The natural frequency of the system
is
A.
B.
C.
D.

Answer :A
Solution :
For simple harmonic motion



20


Standard equation is


31.A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40,
0.45 and 0.50mm are filled in a transparent glass column of diameter 10 cm and height 2.50
m. The suspension is allowed to settle without any disturbance. It is observed that all particles
of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30s,
the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50
mm from the suspension is _____________.
Answer :
Solution :
As we know that settling velocity for discrete particles is given by stokes law as-


For 30 second duration if 0.35 mm particle size settles completely then % removal of particle
size 0.45 mm and 0.50 mm will be 100% respectively for each. As settling velocity of
particle size 0.45 mm and 0.50 mm will be greater than settling velocity of size 0.35
mm

32.The maximum number of vehicles observed in any five minute period during the peak
hour, If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor
(round off to 2 decimal places) is ___________.
Answer :
Solution :



21

Five minute peak hour factor


33.Which one of the following is secondary pollutant?
A. Carbon Monoxide
B. Hydrocarbon
C. Volatile Organic Carbon (VOC)
D. Ozone

Answer :D
Solution :
Ozone is a secondary pollutant

34.An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal
strain in the plane of maximum shear strain is
A. 0.0050
B. Zero
C. 0.0025
D. 0.0010

Answer :C
Solution :






22

35.Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ,
and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R,
respectively, on the truss. The correct combination of (RP, RQ, RR) is represented by

A. (20, 0, 10) kN
B. (10, 30, ? 10) kN
C. (30, ?30, 30) kN
D. (0, 60, ? 30) kN

Answer :C
Solution :


?(i)


?(ii)

F2 = F3 ?(iii)



23

F2 ? 3 + 30 ? 3 ? F3 ? 1 = 0
F2 ? 3 ? F2 ? 1 + 90 = 0
2F2 = ? 90
F2 = ? 45
? F3 = ?45

Q + R = 0 ?(iv)
F3 ? 2 + R ? 3 = 0
? 45 ? 2 + R ? 3 = 0


36.For the following statements:
P ? The lateral stress in the soil while being tested in an oedometer is always at-rest.
Q ? For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal
contact stress at the footing edge is greater than that at its centre.
R ? The corrections for overburden pressure and dilatancy are not applied to measured SPTN
values in case of clay deposits.
The correct combination of the statements is
A. P ? TRUE; Q ? TRUE; R ? FALSE
B. P ? TRUE; Q ? TRUE; R ? TRUE
C. P ? FALSE; Q ? FALSE; R ? TRUE
D. P ? FALSE; Q ? FALSE; R ? FALSE

Answer :B
Solution :



24

P ? TRUE; Q ? TRUE; R ? TRUE

37.Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working
tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and
concrete is 2 MPa, and the joint gap between the slab is 10mm. Ignoring the loss of bond and
the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer)
is ___________.
Answer :
Solution :
Given:
d = 12 mm
?st = 230 MPa = 230 N/mm
2

Sb = 2 MPa = 2 N/mm
2

t = 10 mm
Length of tie bar
= 10 + 690
= 700 mm

38.Average free flow speed and the jam density observed on a road stretch are 60 km/h and
120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on
the road stretch (in vehicles/h) is _________.
Answer :
Solution :
Vf = 60km/h
kJ = 120 Veh/km



25



39.The network of a small construction project awarded to a contractor is shown in the
following figure. The normal duration, crash duration, normal cost, and crash cost of all the
activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per
day.


If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by
the contractor would be _____
Answer :
Solution :

Path PRTV is critical path and corres-ponding normal duration is 18 days.



26


For 18 days:
Direct cost = 66000
Indirect cost = 18 ? 5000 = 90000
Total project cost = 156000
1st stage crashing :
Crash activity R by 1 day.
New project duration = 17 days.
T.P.C = 156000 + 1 ? 750 ? 1 ? 5000 = 151750

2nd stage crashing :
Crash activity Q & R simultaneously by 1 day. New project duration = 16 days.
T.P.C = 151750 + 1 ? (750 + 2000) ? 5000 = 149500

40.A sample of air analyzed at 0?C and 1 atm pressure is reported to contain 0.02 ppm (parts
per million) of NO2. Assume the gram molecular mass of NO2 as 46 and its volume at 0?C



27

and 1 atm pressure as 22.4 litres per mole. The equivalent NO2 concentration (in microgram
per cubic meter, round off to 2 decimal places) would be _______
Answer :
Solution :
0.02 ppm of NO2 means


41.Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number
of vehicles arriving on this highway follows Poisson distribution, the probability (round off to
2 decimal places) that the headway between successive vehicles lies between 6 and 10
seconds is _________
Answer :
Solution :
? = 360 veh/hr





28

42.Consider the ordinary differential equation Given the values of y(1)
= 0 and y(2) = 2, the value of y(3) (round off to 1 decimal place), is ______
Answer :
Solution :

y(1) = 0 & y(2) = 2
Assume x = e
t


Then

Putting this into ordinary differential equation
D(D ? 1)y ? 2Dy + 2y = 0
[D
2
? 3D + 2] = 0
Auxillary equation is
m
2
? 3m + 2 = 0
(m ? 1) (m ? 2) = 0
i.e. m = 1 & m = 2
? solution of equation
y = c1e
t
+ c2e
2t

? Putting et as x
? y = c1x + c2X
2




29

? y(1)= 0
? c1 + c2 = 0 ...(i)
& y(2) = 2
? 2c1 + 4c2 = 2
? c1 + 2c2 = 1 ?(ii)
(ii) ? (i)
? c2 = 1
c1 = ?1
? y = ?x + x
2

Then y(3) = ?3 + 3
2
= 6

43.A 3 m ? 3 m square precast reinforced concrete segments to be installed by pushing them
through an existing railway embankment for making an underpass as shown in the figure. A
reaction arrangement using precast PCC blocks placed on the ground is to be made for the
jacks.

At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The
jacks will react against the rigid steel plate placed against the reaction arrangement. The
footprint area of reaction arrangement on natural ground are: c = 17 kPa; ? = 25
o
and ? = 18
kN/m
3
. Assuming that the reaction arrangement has rough interface and has the same
properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure
is __________.
Answer :
Solution :
FOS against shear failure



30





44.A parabolic vertical curve is being designed to join a road of grade + 5% with a road of
grade ?3%. The length of the vertical curve is 400 m measured along the horizontal. The
vertical point of curvature (VPC) is located on the road of grade
+5%. The difference in height between VPC and vertical point of intersection (VPI) (in m,
round off to the nearest integer) is ______________
Answer :
Solution :

Height difference between
VPI & VPC = 5% of 200 m = 10 m




31

45.If the section shown in the figure turns from fully-elastic to fully-plastic, the depth of
neutral axis (N.A.), decreases by

All dimensions are in mm
A.
13.75 mm

B. 10.75 mm
C. 15.25 mm
D. 12.25 mm

Answer :A
Solution :

For fully elastic case,

For fully plastic case,



32

y = Equal area axis = 5
N.A reduces by = 18.75 ? 5 = 13.75 mm

46.A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a
roller support at joint R. A point load of 50 kN is acting at joint R in the horizontal direction.
The flexural rigidity. EI, of each member is 10
6
kNm
2
. Under the applied load, the horizontal
displacement (in mm, round off to 1 decimal place) of joint R would be __________

Answer :
Solution :

For reaction
?Mp = 0
?W ? 5 + 50 ? 10 = 0

When unit load at R is acting in the direction of 50kN load, then reaction at
R = 2 (downward)



33




Alternatively:





34





47.A box measuring 50 cm ? 50 cm ? 50 cm is filled to the top with dry coarse aggregate of
mass 187.5 kg. The water absorption and specific gravity of the aggregate are 0.5% and 2.5,
respectively. The maximum quantity of water (in kg, round off to 2 decimal places) required
to fill the box completely is _________
Answer :
Solution :
Volume of the box = 0.5 ? 0.5 ? 0.5
= 0.125 m
3

Mass of aggregate = 187.5 kg
Gagg = 2.5
Volume of aggregate
Volume of empty space = 0.125 ? 0.075
= 0.05 m
3

Water absorption = 0.5%
Volume of water absorbed



35


Total volume of water that can be filled
= 9.375 ? 10
?4
+ 0.05
= 0.0509 m
3

Mass of water = 50.94 kg

48.A wastewater is to be disinfected with 35mg/L of chlorine to obtain 99% kill of
microorganisms. The number of micro-organisms remaining alive (Nt) at time t, is modelled
by Nt = N0e
?kt
, where N0 is number of microorganisms at t = 0, and k is the rate of kill. The
wastewater flow rate is 36m
3
/h, and k = 0.23 min-If the depth and width of the chlorination
tank are 1.5 m and 1.0m, respectively, the length of the tank (in m, round off to 2 decimal
places) is _________
Answer :
Solution :
For 99% kill of mircoorganision

?0.23t = ?4.605
t = 20.022 min
Volume of tank req. = Q.t





36



49.The cross-section of a built-up wooden beam as shown in the figure (not drawn to scale) is
subjected to a vertical shear force of 8kN. The beam is symmetrical about the neutral axis
(N.A.) shown, and the moment of inertia about N.A. is 1.5 ? 10
9
mm
4
. Considering that the
nails at the location P are spaced longitudinally (along the length of the beam) at 60 mm, each
of the nails at P will be subjected to the shear force of

All dimensions are in mm
A.
60 N

B. 120 N
C. 240 N
D. 480 N

Answer :C
Solution :




37

Shear force in nail at

So shear force in nail = 22 ? 60 = 1320 N

50.A staff is placed on a benchmark (BM) of reduced level (RL) 100.000 m and a theodolite
is placed at a horizontal distance of 50m from the BM to measure the vertical angles. The
measured vertical angles from the horizontal at the staff readings of 0.400m and 2.400 m are
found to be the same. Taking the height of the instrument as 1.400 m, the RL (in m) of the
theodolite station is _________
Answer :
Solution :


2x = 2.8
x = 1.4m
H.O.I = 100 + 1.4
= 101.4m
RL of theodelite station = 101.4 ? theodolite hight
= 101.4 ? 1.4
= 100m




38

51.A 0.80 m deep bed of sand filter (length 4m and width 3m) is made of uniform particles
(diameter = 0.40 mm, specific gravity = 2.65, shape factor = 0.85) with bed porosity of 0.the
bed has to be backwashed at a flow rate of 3.60 m
3
/min. During backwashing, if the terminal
settling velocity of sand particles is 0.05 m/s, the expanded bed depth (in m, round off to 2
decimal places) is ______
Answer :
Solution :


then L ex (1 ? nex) = L(1 ? n)
? Lex (1 ? 0.6025) = 0.8 ? (1 ? 0.4)


52.A reinforced concrete circular pile of 12m length and 0.6 m diameter is embedded in stiff
clay which has an undrained unit cohesion of 110 kN/m
2
. The adhesion factor is 0.The Net
Ultimate Pullout (Uplift) Load for the pile (in kN, round off to 1 decimal place is) is
_________
Answer :
Solution :
Pull out load
p = perimeter
? = length
= 0.5 ? 110 ? 12 ? ?(0.6)
= 1244.07 kN



39


53.A survey line was measured to be 285.5m with a tape having a nominal length of 30m. On
checking, the true length of the tape was found to be 0.05 m too short. If the line lay on a
slope of 1 in 10, the reduced length (horizontal length) of the line for plotting of survey work
would be
A. 285.0 m
B. 284.5 m
C. 285.6 m
D. 283.6 m

Answer :D
Solution :
Measured length = 285.5 m
Nominal length of tape = 30 m
Slope = 1 in 10
The tape is 0.05 m too short
Actual length of tape = 30 ? 0.05 = 29.95 m
Actual length measured
Measured length

Now slope correction
? Slope = 1 in 10




40


? Length to be plotted
= Actual length measured + correction
= 285.024 + (-1.42512)
= 283.599 m
Hence, option (d) is correct.

54.The rigid-joined plane frame QRS shown in the figure is subjected to a load P at the joint
R. Let the axial deformation in the frame be neglected. If the support S undergoes a
settlement of the vertical reaction at the support S will become zero when ? is equal
to

A. 3.0
B. 7.5
C. 0.1
D. 48.0

Answer :B
Solution :



41


Using slope deflection method,

If reaction at S is equal to zero


From equilibrium of joint




42

? From (i) & (ii)



55.Which one of the following is NOT a correct statement?
A. The function x?x, (x > 0), has the global minima at x = e
B. The function x?x, (x > 0), has the global maxima at x = e
C. The function x
3
has neither global minima nor global maxima
D. The function |x| has the global minima at x = 0

Answer :A
Solution :
y = x
1/x


For
? x = e
Thus point x = e is the critical point for
y = x
1/x

Now at x = e, dy/dx changes its sign from (+ve) to (-ve). Thus point (x = e) is point of global
maxima.
y = x
3
has neither global minima nor global maxima, it only have saddle point at x = 0
y | x |; attains its minimum value at x = 0; so x = 0 is the global minima for y = f(x)



43


56.A rectangular open channel has a width of 5m and a bed slope of 0.001. For a uniform
flow of depth 2m, the velocity is 2m/s. The Manning?s roughness coefficient for the channel
is
A. 0.033
B. 0.050
C. 0.002
D. 0.017

Answer :D
Solution :
For a rectangular channel
Width of channel = 5 m
Depth of flow = 2 m
Bed slope = 0.001
Velocity V = 2 m/sec.
From manning?s

Where


57.The hyetograph of a storm event of duration 140 minutes is shown in the figure.



44


The infiltration capacity at the start of this event (t = 0) is 17mm/hour, which linearly
decreases to 10 mm/hour after 40 minutes duration. As the event progresses, the infiltration
rate further drops down linearly to attain a value of 4mm/ hour at t = 100 minutes and
remains constant thereafter till the end of the storm event. The value of the infiltration
index, ? (in mm/hour, round off to 2 decimal places), is _______
Answer :
Solution :

Depth of infiltration = Area of hyetograph above Horton?s curve

Now, assuming



45




58.Consider a laminar flow in the x-direction between two infinite parallel plates (Couette
flow). The lower plate is stationary and the upper plate is moving with a velocity of 1 cm/ s in
the x-direction. The distance between the plates is 5mm and the dynamic viscosity of the
fluid is 0.01 N-s/mIf the shear stress on the lower plate is zero, the pressure gradient, (in
N/m
2
per m, round off to 1 decimal place) is______
Answer :
Solution :
Given data ;
Velocity of plate, V = 1 cm/sec
Distance between the late = 5 mm
Dynamic viscosity of fluid = 0.01 N-S/m
2

Shear stress at lower plate = 0
Pressure gradient
We know that, in case of couette flow, shear stress ( ? ) is given by




46

At lower plate, y = 0; ? = 0 [Given]


59.A granular soil has a saturated unit weight of 20 kN/m
3
and an effective angle of shearing
resistance of 30?. The unit weight of water is 9.81 kN/m
3
. A slope is to be made on this soil
deposit in which the seepage occurs parallel to the slope up to the free surface. Under this
seepage condition for a factor of safety of 1.5, the safe slope angle (in degree, round off to 1
decimal place) would be ____
Answer :
Solution :
?sat = 20KN/m
2

? = 30?
?w = 9.81 KN/m
2

FOS = 1.5
We know that

[i = safe slope angle]

? i = 11.0953

60.Two water reservoirs are connected by a siphon (running full) of total length 5000 m and
diameter of 0.10 m, as shown below (figure not drawn to scale).



47


The inlet leg length of the siphon to its summit is 2000 m. The difference in the water surface
levels of the two reservoirs is 5m. Assume the permissible minimum absolute pressure at the
summit of siphon to be 2.5m of water when running full. Given: friction factor f = 0.02
throughout, atmospheric pressure = 10.3 m of water, and acceleration due to gravity g = 9.81
m/s
2
. Considering only major loss using Darcy- Weisbach equation the maximum height of
the summit of siphon from the water level of upper reservoir, h (in m round off to 1 decimal
place) is _____
Answer :
Solution :
Given data :

d = 0.1 m
Length of siphon = 5000 m
Length of siphon upto summit = 2000 m
Friction Factor, f = 0.02
Acceleration due to gravity, g = 9.81 m/sec
2

Applying Energy equation between point 1 and 3 to get

[From Darcy Weisback equation



48


[ ? Z1 - Z3 = 5m]
? Q = 2.4597 ? 10
-3
m
3
/sec
Now applying energy equation between 1 and 2 to get




61.Sedimentation basin in a water treatment plant is designed for a flow rate of 0.2 m
3
/s. The
basin is rectangular with a length of 32m, width of 8m and depth of 4m. Assume that the
settling velocity of these particles is governed by the Stokes? law. Given: density of the
particles = 2.5 g/cm
3
; density of water = 1 g/cm3; dynamic viscosity of water = 0.01 g/(cm.s);
gravitational acceleration = 980 cm/s
2
. If the incoming water contains particles of diameter 25
?m (spherical and uniform) the removal efficiency of these particles is
A. 100%
B. 65%
C. 78%
D. 51%

Answer :B
Solution :
Given :
Flow rate = 0.2 m
3
/sec



49

Dimension of tank = 32m ? 8 m ? 4 m
Density of particles = 2.5 g/cc
Density of water = 1 g/cc
Dynamic viscosity of water = 0.01 g/cm-S
Diameter of particle = 25 ?m
We know that
Over flow rate of tank
= 7.8125 ? 10
-4
m/sec
And settling velocity of particle (vs),

Now, % removal efficiency

Hence option (b) is correct.

62.A square footing of 4m side is placed at 1 m depth in a sand deposit. The dry unit weight
(?) of sand is 15 kN/m
3
. This footing has an ultimate bearing capacity of 600 kPa. Consider
the depth factors; dq = d? = 1.0 and the bearing capacity factor: N? = 18.This footing is placed
at a depth of 2m in the same soil deposit. For a factor of safety of 3.0 per Terzaghi?s theory,
the safe bearing capacity (in kPa) of this footing would be ________
Answer :
Solution :
Side of square footing = 4 m



50

Depth of footing = 1 m
Unit weight of soil = 15 KN/m
3

Ultimate bearing capacity = 600 KPa
Depth factors, dq = d? = 1
N? = 18.75
According to terzaghi, the ultimate bearing capacity of square footing is given as
At depth of footing = 1 m
qu = 1.3CNC + qNqdq + 04B?N?d?
For sand, C = 0, q = ?Df = 15 ? 1 = 15KN m
2

600 = 0 + 15 ? Nq ? 1 + 0.4 ? 4 ? 15 ? 18.75 ? 1
? Nq = 10
Now at depth of footing at 2m
qu = 1.3 CNC + qNq + 0.4B?N?d?
qu = 0 + (2 ? 15)10 ? 1 + 0.4 ? 4 ? 15 ? 18.75 ? 1
qu = 750 KPa
? We know that
qnu = qu - ?Df
qnu = 750 ? 15 ? 2
qnu = 720 KPa
and safe bearing capacity qsafe





51

63.Consider two functions: x = ? ln ? and y = ? ln ?. Which one of the following is the
correct expression for ?
A.
B.
C.
D.

Answer :C
Solution :
...(i)

Putting value of ? in (i)
...(ii)
Assuming y constant and differentating w.r.t. x.
?(iii)
Puttting value of from (ii) in equation (iii)




52



(replacing x by in ?)


64. A 16 mm thick gusset plate is connected to the 12 mm thick flange plate of an I-section
using fillet welds on both sides as shown in the figure (not drawn to scale). The gusset plate
is subjected to a point load of 350 kN acting at a distance of 100 mm from the flange plate.
Size of fillet weld is 10 mm.

The maximum resultant stress (in MPa, round off to 1 decimal place) on the fillet weld along
the vertical plane would be ___________
Answer :
Solution :
Given Data :
Thickness of gusset plate (t) = 16 mm
Point load (P) = 350 KN



53

Eccentricity (e) = 100 mm
Direct shear stress,

And bending stress on the extreme edge of weld (f)

For checking the safety
Resultant Stress,
= 105.36 N/mm
2


65.A one-dimensional domain is discretized into N sub-domains of width
?x with node numbers i = 0, 1, 2, 3, ...., N. If the time scale is
discretized in steps of ?t, the forward-time and centered-space finite
difference approximation at n
th
node and nth time step, for the partial
differential equation is
A.
B.
C.
D.

Answer : D



54

Solution :
Given differential equation

?(i)
Using forward time finite difference
?(ii)
Using centred space finite difference

Putting (i) and (ii) in PDE

So, option (d) is correct.


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