Download GATE (Graduate Aptitude Test in Engineering) Last 10 Years 2020, 2019, 2018, 2017, 2016, 2015, 2014, 2013, 2012, 2011 and 2010 CE01 Civil Engineering Question Papers With Solutions And Answer Keys
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and
usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn?t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, ?Give me a lever long enough and a fulcrum on which to place it, and I will move
the world.?
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ?relftaga? means carefree, ?otaga? means careful and ?fertaga? means careless, which of the
following could mean ?aftercare??
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed
from every corner of the cube. The resulting surface area of the body (in square units) after the
removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
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GATE 2016 General Aptitude - GA Set-5
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and
usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn?t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, ?Give me a lever long enough and a fulcrum on which to place it, and I will move
the world.?
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ?relftaga? means carefree, ?otaga? means careful and ?fertaga? means careless, which of the
following could mean ?aftercare??
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed
from every corner of the cube. The resulting surface area of the body (in square units) after the
removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
GATE 2016 General Aptitude - GA Set-5
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive.
Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The
table below shows the numbers of each razor sold in each quarter of a year.
Quarter \ Product Elegance Smooth Soft Executive
Q1 27300 20009 17602 9999
Q2 25222 19392 18445 8942
Q3 28976 22429 19544 10234
Q4 21012 18229 16595 10109
Which product contributes the greatest fraction to the revenue of the company in that year?
(A) Elegance (B) Executive (C) Smooth (D) Soft
Q.7 Indian currency notes show the denomination indicated in at least seventeen languages. If this is not
an indication of the nation?s diversity, nothing else is.
Which of the following can be logically inferred from the above sentences?
(A) India is a country of exactly seventeen languages.
(B) Linguistic pluralism is the only indicator of a nation?s diversity.
(C) Indian currency notes have sufficient space for all the Indian languages.
(D) Linguistic pluralism is strong evidence of India?s diversity.
Q.8 Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
(A) (i) only (B) (ii) only (C) (i) and (ii) (D) neither (i) nor (ii)
Q.9
If f( ???? ) = 2 ???? 7
+ 3 ???? ? 5, which of the following is a factor of f(x)?
(A) (x
3
+8) (B) (x-1) (C) (2x-5) (D) (x+1)
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GATE 2016 General Aptitude - GA Set-5
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and
usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn?t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, ?Give me a lever long enough and a fulcrum on which to place it, and I will move
the world.?
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ?relftaga? means carefree, ?otaga? means careful and ?fertaga? means careless, which of the
following could mean ?aftercare??
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed
from every corner of the cube. The resulting surface area of the body (in square units) after the
removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
GATE 2016 General Aptitude - GA Set-5
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive.
Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The
table below shows the numbers of each razor sold in each quarter of a year.
Quarter \ Product Elegance Smooth Soft Executive
Q1 27300 20009 17602 9999
Q2 25222 19392 18445 8942
Q3 28976 22429 19544 10234
Q4 21012 18229 16595 10109
Which product contributes the greatest fraction to the revenue of the company in that year?
(A) Elegance (B) Executive (C) Smooth (D) Soft
Q.7 Indian currency notes show the denomination indicated in at least seventeen languages. If this is not
an indication of the nation?s diversity, nothing else is.
Which of the following can be logically inferred from the above sentences?
(A) India is a country of exactly seventeen languages.
(B) Linguistic pluralism is the only indicator of a nation?s diversity.
(C) Indian currency notes have sufficient space for all the Indian languages.
(D) Linguistic pluralism is strong evidence of India?s diversity.
Q.8 Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
(A) (i) only (B) (ii) only (C) (i) and (ii) (D) neither (i) nor (ii)
Q.9
If f( ???? ) = 2 ???? 7
+ 3 ???? ? 5, which of the following is a factor of f(x)?
(A) (x
3
+8) (B) (x-1) (C) (2x-5) (D) (x+1)
GATE 2016 General Aptitude - GA Set-5
3/3
Q.10 In a process, the number of cycles to failure decreases exponentially with an increase in load. At a
load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for
failure. The load for which the failure will happen in 5000 cycles is ________.
(A) 40.00 (B) 46.02 (C) 60.01 (D) 92.02
END OF THE QUESTION PAPER
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GATE 2016 General Aptitude - GA Set-5
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and
usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn?t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, ?Give me a lever long enough and a fulcrum on which to place it, and I will move
the world.?
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ?relftaga? means carefree, ?otaga? means careful and ?fertaga? means careless, which of the
following could mean ?aftercare??
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed
from every corner of the cube. The resulting surface area of the body (in square units) after the
removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
GATE 2016 General Aptitude - GA Set-5
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive.
Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The
table below shows the numbers of each razor sold in each quarter of a year.
Quarter \ Product Elegance Smooth Soft Executive
Q1 27300 20009 17602 9999
Q2 25222 19392 18445 8942
Q3 28976 22429 19544 10234
Q4 21012 18229 16595 10109
Which product contributes the greatest fraction to the revenue of the company in that year?
(A) Elegance (B) Executive (C) Smooth (D) Soft
Q.7 Indian currency notes show the denomination indicated in at least seventeen languages. If this is not
an indication of the nation?s diversity, nothing else is.
Which of the following can be logically inferred from the above sentences?
(A) India is a country of exactly seventeen languages.
(B) Linguistic pluralism is the only indicator of a nation?s diversity.
(C) Indian currency notes have sufficient space for all the Indian languages.
(D) Linguistic pluralism is strong evidence of India?s diversity.
Q.8 Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
(A) (i) only (B) (ii) only (C) (i) and (ii) (D) neither (i) nor (ii)
Q.9
If f( ???? ) = 2 ???? 7
+ 3 ???? ? 5, which of the following is a factor of f(x)?
(A) (x
3
+8) (B) (x-1) (C) (2x-5) (D) (x+1)
GATE 2016 General Aptitude - GA Set-5
3/3
Q.10 In a process, the number of cycles to failure decreases exponentially with an increase in load. At a
load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for
failure. The load for which the failure will happen in 5000 cycles is ________.
(A) 40.00 (B) 46.02 (C) 60.01 (D) 92.02
END OF THE QUESTION PAPER
GATE 2016 Civil Engineering Set-1
CE(1) 1/14
Q. 1 ? Q. 25 carry one mark each
Q.1 Newton-Raphson method is to be used to find root of equation 3 ???? ? ???? ???? + sin ???? = 0. If the initial
trial value for the root is taken as 0.333, the next approximation for the root would be _________
(note: answer up to three decimal)
Q.2
The type of partial differential equation
???? 2
???? ???? ???? 2
+
???? 2
???? ???? ???? 2
+ 3
???? 2
???? ???????????????? + 2
???????? ???????? ?
???????? ???????? = 0 is
(A) elliptic (B) parabolic (C) hyperbolic (D) none of these
Q.3 If the entries in each column of a square matrix ???? add up to 1, then an eigenvalue of ???? is
(A) 4 (B) 3 (C) 2 (D) 1
Q.4 Type II error in hypothesis testing is
(A) acceptance of the null hypothesis when it is false and should be rejected
(B) rejection of the null hypothesis when it is true and should be accepted
(C) rejection of the null hypothesis when it is false and should be rejected
(D) acceptance of the null hypothesis when it is true and should be accepted
Q.5
The solution of the partial differential equation
2
2
x
u
t
u
?
?
=
?
?
?
is of the form
(A) ( )
( )
[ ]
x k x k
e C e C kt C
? ? ?
+
2
) (
1
cos
(B)
( )
[ ]
x k x k kt
e C e C Ce
? ? ?
+
2
) (
1
(C) ( ) [ ] x k C x k C Ce
kt
) sin( cos
2 1
? ? ? +
(D) ( ) ( ) [ ] x k C x k C kt C ) sin( cos sin
2 1
? ? ? +
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GATE 2016 General Aptitude - GA Set-5
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and
usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn?t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, ?Give me a lever long enough and a fulcrum on which to place it, and I will move
the world.?
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ?relftaga? means carefree, ?otaga? means careful and ?fertaga? means careless, which of the
following could mean ?aftercare??
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed
from every corner of the cube. The resulting surface area of the body (in square units) after the
removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
GATE 2016 General Aptitude - GA Set-5
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive.
Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The
table below shows the numbers of each razor sold in each quarter of a year.
Quarter \ Product Elegance Smooth Soft Executive
Q1 27300 20009 17602 9999
Q2 25222 19392 18445 8942
Q3 28976 22429 19544 10234
Q4 21012 18229 16595 10109
Which product contributes the greatest fraction to the revenue of the company in that year?
(A) Elegance (B) Executive (C) Smooth (D) Soft
Q.7 Indian currency notes show the denomination indicated in at least seventeen languages. If this is not
an indication of the nation?s diversity, nothing else is.
Which of the following can be logically inferred from the above sentences?
(A) India is a country of exactly seventeen languages.
(B) Linguistic pluralism is the only indicator of a nation?s diversity.
(C) Indian currency notes have sufficient space for all the Indian languages.
(D) Linguistic pluralism is strong evidence of India?s diversity.
Q.8 Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
(A) (i) only (B) (ii) only (C) (i) and (ii) (D) neither (i) nor (ii)
Q.9
If f( ???? ) = 2 ???? 7
+ 3 ???? ? 5, which of the following is a factor of f(x)?
(A) (x
3
+8) (B) (x-1) (C) (2x-5) (D) (x+1)
GATE 2016 General Aptitude - GA Set-5
3/3
Q.10 In a process, the number of cycles to failure decreases exponentially with an increase in load. At a
load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for
failure. The load for which the failure will happen in 5000 cycles is ________.
(A) 40.00 (B) 46.02 (C) 60.01 (D) 92.02
END OF THE QUESTION PAPER
GATE 2016 Civil Engineering Set-1
CE(1) 1/14
Q. 1 ? Q. 25 carry one mark each
Q.1 Newton-Raphson method is to be used to find root of equation 3 ???? ? ???? ???? + sin ???? = 0. If the initial
trial value for the root is taken as 0.333, the next approximation for the root would be _________
(note: answer up to three decimal)
Q.2
The type of partial differential equation
???? 2
???? ???? ???? 2
+
???? 2
???? ???? ???? 2
+ 3
???? 2
???? ???????????????? + 2
???????? ???????? ?
???????? ???????? = 0 is
(A) elliptic (B) parabolic (C) hyperbolic (D) none of these
Q.3 If the entries in each column of a square matrix ???? add up to 1, then an eigenvalue of ???? is
(A) 4 (B) 3 (C) 2 (D) 1
Q.4 Type II error in hypothesis testing is
(A) acceptance of the null hypothesis when it is false and should be rejected
(B) rejection of the null hypothesis when it is true and should be accepted
(C) rejection of the null hypothesis when it is false and should be rejected
(D) acceptance of the null hypothesis when it is true and should be accepted
Q.5
The solution of the partial differential equation
2
2
x
u
t
u
?
?
=
?
?
?
is of the form
(A) ( )
( )
[ ]
x k x k
e C e C kt C
? ? ?
+
2
) (
1
cos
(B)
( )
[ ]
x k x k kt
e C e C Ce
? ? ?
+
2
) (
1
(C) ( ) [ ] x k C x k C Ce
kt
) sin( cos
2 1
? ? ? +
(D) ( ) ( ) [ ] x k C x k C kt C ) sin( cos sin
2 1
? ? ? +
GATE 2016 Civil Engineering Set-1
CE(1) 2/14
Q.6 Consider the plane truss with load P as shown in the figure. Let the horizontal and vertical reactions
at the joint B be H
B
and V
B
, respectively and V
C
be the vertical reaction at the joint C.
Which one of the following sets gives the correct values of V
B
, H
B
and V
C
?
(A) V
B
= 0; H
B
= 0; V
C
= P
(B) V
B
= P/2; H
B
= 0; V
C
= P/2
(C) V
B
= P/2; H
B
= P (sin 60?); V
C
= P/2
(D) V
B
= P; H
B
= P (cos 60?); V
C
= 0
Q.7
In shear design of an RC beam, other than the allowable shear strength of concrete ( )
c
? , there is
also an additional check suggested in IS 456-2000 with respect to the maximum permissible shear
stress ( )
max c
? . The check for
max c
? is required to take care of
(A) additional shear resistance from reinforcing steel
(B) additional shear stress that comes from accidental loading
(C) possibility of failure of concrete by diagonal tension
(D) possibility of crushing of concrete by diagonal compression
Q.8 The semi-compact section of a laterally unsupported steel beam has an elastic section modulus,
plastic section modulus and design bending compressive stress of 500 cm
3
, 650 cm
3
and 200 MPa,
respectively. The design flexural capacity (expressed in kNm) of the section is _________
Q.9 Bull's trench kiln is used in the manufacturing of
(A) lime (B) cement (C) bricks (D) none of these
Q.10 The compound which is largely responsible for initial setting and early strength gain of Ordinary
Portland Cement is
(A) C
3
A (B) C
3
S (C) C
2
S (D) C
4
AF
P
60? 60?
60?
L L
L
L
L
60?
C B
A G
F E
D
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GATE 2016 General Aptitude - GA Set-5
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and
usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn?t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, ?Give me a lever long enough and a fulcrum on which to place it, and I will move
the world.?
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ?relftaga? means carefree, ?otaga? means careful and ?fertaga? means careless, which of the
following could mean ?aftercare??
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed
from every corner of the cube. The resulting surface area of the body (in square units) after the
removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
GATE 2016 General Aptitude - GA Set-5
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive.
Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The
table below shows the numbers of each razor sold in each quarter of a year.
Quarter \ Product Elegance Smooth Soft Executive
Q1 27300 20009 17602 9999
Q2 25222 19392 18445 8942
Q3 28976 22429 19544 10234
Q4 21012 18229 16595 10109
Which product contributes the greatest fraction to the revenue of the company in that year?
(A) Elegance (B) Executive (C) Smooth (D) Soft
Q.7 Indian currency notes show the denomination indicated in at least seventeen languages. If this is not
an indication of the nation?s diversity, nothing else is.
Which of the following can be logically inferred from the above sentences?
(A) India is a country of exactly seventeen languages.
(B) Linguistic pluralism is the only indicator of a nation?s diversity.
(C) Indian currency notes have sufficient space for all the Indian languages.
(D) Linguistic pluralism is strong evidence of India?s diversity.
Q.8 Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
(A) (i) only (B) (ii) only (C) (i) and (ii) (D) neither (i) nor (ii)
Q.9
If f( ???? ) = 2 ???? 7
+ 3 ???? ? 5, which of the following is a factor of f(x)?
(A) (x
3
+8) (B) (x-1) (C) (2x-5) (D) (x+1)
GATE 2016 General Aptitude - GA Set-5
3/3
Q.10 In a process, the number of cycles to failure decreases exponentially with an increase in load. At a
load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for
failure. The load for which the failure will happen in 5000 cycles is ________.
(A) 40.00 (B) 46.02 (C) 60.01 (D) 92.02
END OF THE QUESTION PAPER
GATE 2016 Civil Engineering Set-1
CE(1) 1/14
Q. 1 ? Q. 25 carry one mark each
Q.1 Newton-Raphson method is to be used to find root of equation 3 ???? ? ???? ???? + sin ???? = 0. If the initial
trial value for the root is taken as 0.333, the next approximation for the root would be _________
(note: answer up to three decimal)
Q.2
The type of partial differential equation
???? 2
???? ???? ???? 2
+
???? 2
???? ???? ???? 2
+ 3
???? 2
???? ???????????????? + 2
???????? ???????? ?
???????? ???????? = 0 is
(A) elliptic (B) parabolic (C) hyperbolic (D) none of these
Q.3 If the entries in each column of a square matrix ???? add up to 1, then an eigenvalue of ???? is
(A) 4 (B) 3 (C) 2 (D) 1
Q.4 Type II error in hypothesis testing is
(A) acceptance of the null hypothesis when it is false and should be rejected
(B) rejection of the null hypothesis when it is true and should be accepted
(C) rejection of the null hypothesis when it is false and should be rejected
(D) acceptance of the null hypothesis when it is true and should be accepted
Q.5
The solution of the partial differential equation
2
2
x
u
t
u
?
?
=
?
?
?
is of the form
(A) ( )
( )
[ ]
x k x k
e C e C kt C
? ? ?
+
2
) (
1
cos
(B)
( )
[ ]
x k x k kt
e C e C Ce
? ? ?
+
2
) (
1
(C) ( ) [ ] x k C x k C Ce
kt
) sin( cos
2 1
? ? ? +
(D) ( ) ( ) [ ] x k C x k C kt C ) sin( cos sin
2 1
? ? ? +
GATE 2016 Civil Engineering Set-1
CE(1) 2/14
Q.6 Consider the plane truss with load P as shown in the figure. Let the horizontal and vertical reactions
at the joint B be H
B
and V
B
, respectively and V
C
be the vertical reaction at the joint C.
Which one of the following sets gives the correct values of V
B
, H
B
and V
C
?
(A) V
B
= 0; H
B
= 0; V
C
= P
(B) V
B
= P/2; H
B
= 0; V
C
= P/2
(C) V
B
= P/2; H
B
= P (sin 60?); V
C
= P/2
(D) V
B
= P; H
B
= P (cos 60?); V
C
= 0
Q.7
In shear design of an RC beam, other than the allowable shear strength of concrete ( )
c
? , there is
also an additional check suggested in IS 456-2000 with respect to the maximum permissible shear
stress ( )
max c
? . The check for
max c
? is required to take care of
(A) additional shear resistance from reinforcing steel
(B) additional shear stress that comes from accidental loading
(C) possibility of failure of concrete by diagonal tension
(D) possibility of crushing of concrete by diagonal compression
Q.8 The semi-compact section of a laterally unsupported steel beam has an elastic section modulus,
plastic section modulus and design bending compressive stress of 500 cm
3
, 650 cm
3
and 200 MPa,
respectively. The design flexural capacity (expressed in kNm) of the section is _________
Q.9 Bull's trench kiln is used in the manufacturing of
(A) lime (B) cement (C) bricks (D) none of these
Q.10 The compound which is largely responsible for initial setting and early strength gain of Ordinary
Portland Cement is
(A) C
3
A (B) C
3
S (C) C
2
S (D) C
4
AF
P
60? 60?
60?
L L
L
L
L
60?
C B
A G
F E
D
GATE 2016 Civil Engineering Set-1
CE(1) 3/14
Q.11 In the consolidated undrained triaxial test on a saturated soil sample, the pore water pressure is zero
(A) during shearing stage only
(B) at the end of consolidation stage only
(C) both at the end of consolidation and during shearing stages
(D) under none of the above conditions
Q.12 A fine grained soil is found to be plastic in the water content range of 26-48%. As per Indian
Standard Classification System, the soil is classified as
(A) CL
(B) CH
(C) CL-ML (D) CI
Q.13 A vertical cut is to be made in a soil mass having cohesion c, angle of internal friction ?, and unit
weight ?. Considering K
a
and K
p
as the coefficients of active and passive earth pressures,
respectively, the maximum depth of unsupported excavation is
(A)
4
p
c
K ?
(B)
2
p
cK
?
(C)
4
a
cK
?
(D)
4
a
c
K ?
Q.14 The direct runoff hydrograph in response to 5 cm rainfall excess in a catchment is shown in the
figure. The area of the catchment (expressed in hectares) is________
Q.15 The type of flood routing (Group I) and the equation(s) used for the purpose (Group II) are given
below.
Group I Group II
P Hydrologic flood routing 1. Continuity equation
Q Hydraulic flood routing 2. Momentum equation
3. Energy equation
The correct match is
(A) P - 1; Q - 1, 2 & 3 (B) P - 1; Q - 1 & 2
(C) P - 1 & 2; Q - 1 (D) P - 1 & 2; Q - 1 & 2
Q.16 The pre-jump Froude Number for a particular flow in a horizontal rectangular channel is 10. The
ratio of sequent depths (i.e., post-jump depth to pre-jump depth) is ________
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7
Discharge (m
3
/s)
Time (hours)
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-5
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and
usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn?t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, ?Give me a lever long enough and a fulcrum on which to place it, and I will move
the world.?
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ?relftaga? means carefree, ?otaga? means careful and ?fertaga? means careless, which of the
following could mean ?aftercare??
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed
from every corner of the cube. The resulting surface area of the body (in square units) after the
removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
GATE 2016 General Aptitude - GA Set-5
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive.
Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The
table below shows the numbers of each razor sold in each quarter of a year.
Quarter \ Product Elegance Smooth Soft Executive
Q1 27300 20009 17602 9999
Q2 25222 19392 18445 8942
Q3 28976 22429 19544 10234
Q4 21012 18229 16595 10109
Which product contributes the greatest fraction to the revenue of the company in that year?
(A) Elegance (B) Executive (C) Smooth (D) Soft
Q.7 Indian currency notes show the denomination indicated in at least seventeen languages. If this is not
an indication of the nation?s diversity, nothing else is.
Which of the following can be logically inferred from the above sentences?
(A) India is a country of exactly seventeen languages.
(B) Linguistic pluralism is the only indicator of a nation?s diversity.
(C) Indian currency notes have sufficient space for all the Indian languages.
(D) Linguistic pluralism is strong evidence of India?s diversity.
Q.8 Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
(A) (i) only (B) (ii) only (C) (i) and (ii) (D) neither (i) nor (ii)
Q.9
If f( ???? ) = 2 ???? 7
+ 3 ???? ? 5, which of the following is a factor of f(x)?
(A) (x
3
+8) (B) (x-1) (C) (2x-5) (D) (x+1)
GATE 2016 General Aptitude - GA Set-5
3/3
Q.10 In a process, the number of cycles to failure decreases exponentially with an increase in load. At a
load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for
failure. The load for which the failure will happen in 5000 cycles is ________.
(A) 40.00 (B) 46.02 (C) 60.01 (D) 92.02
END OF THE QUESTION PAPER
GATE 2016 Civil Engineering Set-1
CE(1) 1/14
Q. 1 ? Q. 25 carry one mark each
Q.1 Newton-Raphson method is to be used to find root of equation 3 ???? ? ???? ???? + sin ???? = 0. If the initial
trial value for the root is taken as 0.333, the next approximation for the root would be _________
(note: answer up to three decimal)
Q.2
The type of partial differential equation
???? 2
???? ???? ???? 2
+
???? 2
???? ???? ???? 2
+ 3
???? 2
???? ???????????????? + 2
???????? ???????? ?
???????? ???????? = 0 is
(A) elliptic (B) parabolic (C) hyperbolic (D) none of these
Q.3 If the entries in each column of a square matrix ???? add up to 1, then an eigenvalue of ???? is
(A) 4 (B) 3 (C) 2 (D) 1
Q.4 Type II error in hypothesis testing is
(A) acceptance of the null hypothesis when it is false and should be rejected
(B) rejection of the null hypothesis when it is true and should be accepted
(C) rejection of the null hypothesis when it is false and should be rejected
(D) acceptance of the null hypothesis when it is true and should be accepted
Q.5
The solution of the partial differential equation
2
2
x
u
t
u
?
?
=
?
?
?
is of the form
(A) ( )
( )
[ ]
x k x k
e C e C kt C
? ? ?
+
2
) (
1
cos
(B)
( )
[ ]
x k x k kt
e C e C Ce
? ? ?
+
2
) (
1
(C) ( ) [ ] x k C x k C Ce
kt
) sin( cos
2 1
? ? ? +
(D) ( ) ( ) [ ] x k C x k C kt C ) sin( cos sin
2 1
? ? ? +
GATE 2016 Civil Engineering Set-1
CE(1) 2/14
Q.6 Consider the plane truss with load P as shown in the figure. Let the horizontal and vertical reactions
at the joint B be H
B
and V
B
, respectively and V
C
be the vertical reaction at the joint C.
Which one of the following sets gives the correct values of V
B
, H
B
and V
C
?
(A) V
B
= 0; H
B
= 0; V
C
= P
(B) V
B
= P/2; H
B
= 0; V
C
= P/2
(C) V
B
= P/2; H
B
= P (sin 60?); V
C
= P/2
(D) V
B
= P; H
B
= P (cos 60?); V
C
= 0
Q.7
In shear design of an RC beam, other than the allowable shear strength of concrete ( )
c
? , there is
also an additional check suggested in IS 456-2000 with respect to the maximum permissible shear
stress ( )
max c
? . The check for
max c
? is required to take care of
(A) additional shear resistance from reinforcing steel
(B) additional shear stress that comes from accidental loading
(C) possibility of failure of concrete by diagonal tension
(D) possibility of crushing of concrete by diagonal compression
Q.8 The semi-compact section of a laterally unsupported steel beam has an elastic section modulus,
plastic section modulus and design bending compressive stress of 500 cm
3
, 650 cm
3
and 200 MPa,
respectively. The design flexural capacity (expressed in kNm) of the section is _________
Q.9 Bull's trench kiln is used in the manufacturing of
(A) lime (B) cement (C) bricks (D) none of these
Q.10 The compound which is largely responsible for initial setting and early strength gain of Ordinary
Portland Cement is
(A) C
3
A (B) C
3
S (C) C
2
S (D) C
4
AF
P
60? 60?
60?
L L
L
L
L
60?
C B
A G
F E
D
GATE 2016 Civil Engineering Set-1
CE(1) 3/14
Q.11 In the consolidated undrained triaxial test on a saturated soil sample, the pore water pressure is zero
(A) during shearing stage only
(B) at the end of consolidation stage only
(C) both at the end of consolidation and during shearing stages
(D) under none of the above conditions
Q.12 A fine grained soil is found to be plastic in the water content range of 26-48%. As per Indian
Standard Classification System, the soil is classified as
(A) CL
(B) CH
(C) CL-ML (D) CI
Q.13 A vertical cut is to be made in a soil mass having cohesion c, angle of internal friction ?, and unit
weight ?. Considering K
a
and K
p
as the coefficients of active and passive earth pressures,
respectively, the maximum depth of unsupported excavation is
(A)
4
p
c
K ?
(B)
2
p
cK
?
(C)
4
a
cK
?
(D)
4
a
c
K ?
Q.14 The direct runoff hydrograph in response to 5 cm rainfall excess in a catchment is shown in the
figure. The area of the catchment (expressed in hectares) is________
Q.15 The type of flood routing (Group I) and the equation(s) used for the purpose (Group II) are given
below.
Group I Group II
P Hydrologic flood routing 1. Continuity equation
Q Hydraulic flood routing 2. Momentum equation
3. Energy equation
The correct match is
(A) P - 1; Q - 1, 2 & 3 (B) P - 1; Q - 1 & 2
(C) P - 1 & 2; Q - 1 (D) P - 1 & 2; Q - 1 & 2
Q.16 The pre-jump Froude Number for a particular flow in a horizontal rectangular channel is 10. The
ratio of sequent depths (i.e., post-jump depth to pre-jump depth) is ________
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7
Discharge (m
3
/s)
Time (hours)
GATE 2016 Civil Engineering Set-1
CE(1) 4/14
Q.17 Pre-cursors to photochemical oxidants are
(A) NO
X
, VOCs and sunlight
(B) SO
2
, CO
2
and sunlight
(C) H
2
S, CO and sunlight
(D) SO
2
, NH
3
and sunlight
Q.18 Crown corrosion in a reinforced concrete sewer is caused by:
(A) H
2
S (B) CO
2
(C) CH
4
(D) NH
3
Q.19 It was decided to construct a fabric filter, using bags of 0.45 m diameter and 7.5 m long, for
removing industrial stack gas containing particulates. The expected rate of airflow into the filter is
10 m
3
/s. If the filtering velocity is 2.0 m/min, the minimum number of bags (rounded to nearest
higher integer) required for continuous cleaning operation is
(A) 27 (B) 29 (C) 31 (D) 32
Q.20 Match the items in Group ? I with those in Group ? II and choose the right combination.
Group - I
P. Activated sludge process
Q. Rising of sludge
R. Conventional nitrification
S. Biological nitrogen removal
Group - II
1. Nitrifiers and denitrifiers
2. Autotrophic bacteria
3. Heterotrophic bacteria
4. Denitrifiers
(A) P-3, Q-4, R-2, S-1 (B) P-2, Q-3, R-4, S-1
(C) P-3, Q-2, R-4, S-1 (D) P-1, Q-4, R-2, S-3
Q.21 During a forensic investigation of pavement failure, an engineer reconstructed the graphs P, Q, R
and S, using partial and damaged old reports.
Theoretically plausible correct graphs according to the 'Marshall mixture design output' are
(A) P, Q, R (B) P, Q, S (C) Q, R, S (D) R, S, P
Q.22 In a one-lane one-way homogeneous traffic stream, the observed average headway is 3.0 s. The
flow (expressed in vehicles/hr) in this traffic stream is________
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude - GA Set-5
1/3
Q. 1 ? Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and
usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn?t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, ?Give me a lever long enough and a fulcrum on which to place it, and I will move
the world.?
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ?relftaga? means carefree, ?otaga? means careful and ?fertaga? means careless, which of the
following could mean ?aftercare??
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed
from every corner of the cube. The resulting surface area of the body (in square units) after the
removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
GATE 2016 General Aptitude - GA Set-5
2/3
Q. 6 ? Q. 10 carry two marks each.
Q.6 A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive.
Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The
table below shows the numbers of each razor sold in each quarter of a year.
Quarter \ Product Elegance Smooth Soft Executive
Q1 27300 20009 17602 9999
Q2 25222 19392 18445 8942
Q3 28976 22429 19544 10234
Q4 21012 18229 16595 10109
Which product contributes the greatest fraction to the revenue of the company in that year?
(A) Elegance (B) Executive (C) Smooth (D) Soft
Q.7 Indian currency notes show the denomination indicated in at least seventeen languages. If this is not
an indication of the nation?s diversity, nothing else is.
Which of the following can be logically inferred from the above sentences?
(A) India is a country of exactly seventeen languages.
(B) Linguistic pluralism is the only indicator of a nation?s diversity.
(C) Indian currency notes have sufficient space for all the Indian languages.
(D) Linguistic pluralism is strong evidence of India?s diversity.
Q.8 Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
(A) (i) only (B) (ii) only (C) (i) and (ii) (D) neither (i) nor (ii)
Q.9
If f( ???? ) = 2 ???? 7
+ 3 ???? ? 5, which of the following is a factor of f(x)?
(A) (x
3
+8) (B) (x-1) (C) (2x-5) (D) (x+1)
GATE 2016 General Aptitude - GA Set-5
3/3
Q.10 In a process, the number of cycles to failure decreases exponentially with an increase in load. At a
load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for
failure. The load for which the failure will happen in 5000 cycles is ________.
(A) 40.00 (B) 46.02 (C) 60.01 (D) 92.02
END OF THE QUESTION PAPER
GATE 2016 Civil Engineering Set-1
CE(1) 1/14
Q. 1 ? Q. 25 carry one mark each
Q.1 Newton-Raphson method is to be used to find root of equation 3 ???? ? ???? ???? + sin ???? = 0. If the initial
trial value for the root is taken as 0.333, the next approximation for the root would be _________
(note: answer up to three decimal)
Q.2
The type of partial differential equation
???? 2
???? ???? ???? 2
+
???? 2
???? ???? ???? 2
+ 3
???? 2
???? ???????????????? + 2
???????? ???????? ?
???????? ???????? = 0 is
(A) elliptic (B) parabolic (C) hyperbolic (D) none of these
Q.3 If the entries in each column of a square matrix ???? add up to 1, then an eigenvalue of ???? is
(A) 4 (B) 3 (C) 2 (D) 1
Q.4 Type II error in hypothesis testing is
(A) acceptance of the null hypothesis when it is false and should be rejected
(B) rejection of the null hypothesis when it is true and should be accepted
(C) rejection of the null hypothesis when it is false and should be rejected
(D) acceptance of the null hypothesis when it is true and should be accepted
Q.5
The solution of the partial differential equation
2
2
x
u
t
u
?
?
=
?
?
?
is of the form
(A) ( )
( )
[ ]
x k x k
e C e C kt C
? ? ?
+
2
) (
1
cos
(B)
( )
[ ]
x k x k kt
e C e C Ce
? ? ?
+
2
) (
1
(C) ( ) [ ] x k C x k C Ce
kt
) sin( cos
2 1
? ? ? +
(D) ( ) ( ) [ ] x k C x k C kt C ) sin( cos sin
2 1
? ? ? +
GATE 2016 Civil Engineering Set-1
CE(1) 2/14
Q.6 Consider the plane truss with load P as shown in the figure. Let the horizontal and vertical reactions
at the joint B be H
B
and V
B
, respectively and V
C
be the vertical reaction at the joint C.
Which one of the following sets gives the correct values of V
B
, H
B
and V
C
?
(A) V
B
= 0; H
B
= 0; V
C
= P
(B) V
B
= P/2; H
B
= 0; V
C
= P/2
(C) V
B
= P/2; H
B
= P (sin 60?); V
C
= P/2
(D) V
B
= P; H
B
= P (cos 60?); V
C
= 0
Q.7
In shear design of an RC beam, other than the allowable shear strength of concrete ( )
c
? , there is
also an additional check suggested in IS 456-2000 with respect to the maximum permissible shear
stress ( )
max c
? . The check for
max c
? is required to take care of
(A) additional shear resistance from reinforcing steel
(B) additional shear stress that comes from accidental loading
(C) possibility of failure of concrete by diagonal tension
(D) possibility of crushing of concrete by diagonal compression
Q.8 The semi-compact section of a laterally unsupported steel beam has an elastic section modulus,
plastic section modulus and design bending compressive stress of 500 cm
3
, 650 cm
3
and 200 MPa,
respectively. The design flexural capacity (expressed in kNm) of the section is _________
Q.9 Bull's trench kiln is used in the manufacturing of
(A) lime (B) cement (C) bricks (D) none of these
Q.10 The compound which is largely responsible for initial setting and early strength gain of Ordinary
Portland Cement is
(A) C
3
A (B) C
3
S (C) C
2
S (D) C
4
AF
P
60? 60?
60?
L L
L
L
L
60?
C B
A G
F E
D
GATE 2016 Civil Engineering Set-1
CE(1) 3/14
Q.11 In the consolidated undrained triaxial test on a saturated soil sample, the pore water pressure is zero
(A) during shearing stage only
(B) at the end of consolidation stage only
(C) both at the end of consolidation and during shearing stages
(D) under none of the above conditions
Q.12 A fine grained soil is found to be plastic in the water content range of 26-48%. As per Indian
Standard Classification System, the soil is classified as
(A) CL
(B) CH
(C) CL-ML (D) CI
Q.13 A vertical cut is to be made in a soil mass having cohesion c, angle of internal friction ?, and unit
weight ?. Considering K
a
and K
p
as the coefficients of active and passive earth pressures,
respectively, the maximum depth of unsupported excavation is
(A)
4
p
c
K ?
(B)
2
p
cK
?
(C)
4
a
cK
?
(D)
4
a
c
K ?
Q.14 The direct runoff hydrograph in response to 5 cm rainfall excess in a catchment is shown in the
figure. The area of the catchment (expressed in hectares) is________
Q.15 The type of flood routing (Group I) and the equation(s) used for the purpose (Group II) are given
below.
Group I Group II
P Hydrologic flood routing 1. Continuity equation
Q Hydraulic flood routing 2. Momentum equation
3. Energy equation
The correct match is
(A) P - 1; Q - 1, 2 & 3 (B) P - 1; Q - 1 & 2
(C) P - 1 & 2; Q - 1 (D) P - 1 & 2; Q - 1 & 2
Q.16 The pre-jump Froude Number for a particular flow in a horizontal rectangular channel is 10. The
ratio of sequent depths (i.e., post-jump depth to pre-jump depth) is ________
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7
Discharge (m
3
/s)
Time (hours)
GATE 2016 Civil Engineering Set-1
CE(1) 4/14
Q.17 Pre-cursors to photochemical oxidants are
(A) NO
X
, VOCs and sunlight
(B) SO
2
, CO
2
and sunlight
(C) H
2
S, CO and sunlight
(D) SO
2
, NH
3
and sunlight
Q.18 Crown corrosion in a reinforced concrete sewer is caused by:
(A) H
2
S (B) CO
2
(C) CH
4
(D) NH
3
Q.19 It was decided to construct a fabric filter, using bags of 0.45 m diameter and 7.5 m long, for
removing industrial stack gas containing particulates. The expected rate of airflow into the filter is
10 m
3
/s. If the filtering velocity is 2.0 m/min, the minimum number of bags (rounded to nearest
higher integer) required for continuous cleaning operation is
(A) 27 (B) 29 (C) 31 (D) 32
Q.20 Match the items in Group ? I with those in Group ? II and choose the right combination.
Group - I
P. Activated sludge process
Q. Rising of sludge
R. Conventional nitrification
S. Biological nitrogen removal
Group - II
1. Nitrifiers and denitrifiers
2. Autotrophic bacteria
3. Heterotrophic bacteria
4. Denitrifiers
(A) P-3, Q-4, R-2, S-1 (B) P-2, Q-3, R-4, S-1
(C) P-3, Q-2, R-4, S-1 (D) P-1, Q-4, R-2, S-3
Q.21 During a forensic investigation of pavement failure, an engineer reconstructed the graphs P, Q, R
and S, using partial and damaged old reports.
Theoretically plausible correct graphs according to the 'Marshall mixture design output' are
(A) P, Q, R (B) P, Q, S (C) Q, R, S (D) R, S, P
Q.22 In a one-lane one-way homogeneous traffic stream, the observed average headway is 3.0 s. The
flow (expressed in vehicles/hr) in this traffic stream is________
GATE 2016 Civil Engineering Set-1
CE(1) 5/14
Q.23 The minimum number of satellites needed for a GPS to determine its position precisely is
(A) 2 (B) 3 (C) 4 (D) 24
Q.24 The system that uses the Sun as a source of electromagnetic energy and records the naturally
radiated and reflected energy from the object is called
(A) Geographical Information System
(B) Global Positioning System
(C) Passive Remote Sensing
(D) Active Remote Sensing
Q.25 The staff reading taken on a workshop floor using a level is 0.645 m. The inverted staff reading
taken to the bottom of a beam is 2.960 m. The reduced level of the floor is 40.500 m. The reduced
level (expressed in m) of the bottom of the beam is
(A) 44.105 (B) 43.460 (C) 42.815 (D) 41.145
Q. 26 ? Q. 55 carry two marks each
Q.26 Probability density function of a random variable X is given below
???? ( ???? ) = ?
0.25 if 1 ? ???? ? 5
0 otherwise