Download GATE GATE ME Question Paper With Solutions

Download GATE (Graduate Aptitude Test in Engineering) GATE ME Question Paper With Solutions

2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6

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2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6




3

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of ?? =
8+6
2
=7

6. X is an online media provider. By offering unlimited and exclusive online content at attractive
prices for a loyalty membership, X is almost forcing its customers towards its loyalty
membership. If its loyalty membership continues to grow at its current rate, within the next
eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
A. Most households that subscribe to X?s loyalty membership discontinue watching cable
television
B. Non-members prefer to watch cable television
C. The X is cancelling accounts of non-members
D. Cable television operators don?t subscribe to X?s loyalty membership
Ans: option (A)
Sol: option A is the most appropriate solution

7. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased
by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.
A. 35.70 B. 10.00
C. 37.50 D. 25.00
Ans: option (C)
Sol: Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04??? =0.04??
And the fiscal deficit in 2016 = 0.05?1.1?? =0.055??
Increase in fiscal deficit = 0.055x ? 0.04x = 0.015x
So, the percentage increase in fiscal deficit =
0.015?? 0.04?? ?100=37.5%

8. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can
empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is
opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is
_________.
A. 16.50 B. 14.50
C. 15.50 D. 13.50
Ans: option (B)
Sol: 1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(
1
6
? ?
1
12
? )=
1
3
?
Tank filled by when Q and R works for another 6 hours = 6(
1
9
? ?
1
12
? )=
1
6
?
Total tank filled in these 10 hours =
1
3
? +
1
6
? =0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in
9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours

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2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6




3

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of ?? =
8+6
2
=7

6. X is an online media provider. By offering unlimited and exclusive online content at attractive
prices for a loyalty membership, X is almost forcing its customers towards its loyalty
membership. If its loyalty membership continues to grow at its current rate, within the next
eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
A. Most households that subscribe to X?s loyalty membership discontinue watching cable
television
B. Non-members prefer to watch cable television
C. The X is cancelling accounts of non-members
D. Cable television operators don?t subscribe to X?s loyalty membership
Ans: option (A)
Sol: option A is the most appropriate solution

7. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased
by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.
A. 35.70 B. 10.00
C. 37.50 D. 25.00
Ans: option (C)
Sol: Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04??? =0.04??
And the fiscal deficit in 2016 = 0.05?1.1?? =0.055??
Increase in fiscal deficit = 0.055x ? 0.04x = 0.015x
So, the percentage increase in fiscal deficit =
0.015?? 0.04?? ?100=37.5%

8. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can
empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is
opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is
_________.
A. 16.50 B. 14.50
C. 15.50 D. 13.50
Ans: option (B)
Sol: 1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(
1
6
? ?
1
12
? )=
1
3
?
Tank filled by when Q and R works for another 6 hours = 6(
1
9
? ?
1
12
? )=
1
6
?
Total tank filled in these 10 hours =
1
3
? +
1
6
? =0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in
9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours




4

9. While teaching a creative writing class in India, I was surprised at receiving stories from the
students that were all set in distant places: in the American West with cowboys and in
Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave
the writers in the once-colonised countries the confidence to see the shabby lives around them
as worthy of being ?told?.
The writer of this passage is surprised by the creative writing assignments of his students,
because __________.
A. Some of the students had written about ice cubes and cowboys
B. None of the students had written about ice cubes and cowboys
C. Some of the students had written stories set in foreign places
D. None of the students had written stories set in India
Ans: option (C)
Sol: option C is the most appropriate solution

10. Mola is a digital platform for taxis in a city. It offers three types of rides ? Pool, Mini and Prime.
The Table below presents the number of rides for the past four months. The platform earns one
US dollar per ride. What is the percentage share of revenue contributed by Prime to the total
revenues of Mola, for the entire duration?
Type
Month
January February March April
Pool 170 320 215 190
Mini 110 220 180 70
Prime 75 180 120 90

A. 38.74 B. 23.97
C. 25.86 D. 16.24

Ans: option (B)
Sol: Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580
Revenue contributed by Prime = 75 + 180 + 120 +90 = 465
Total revenue of Mola = 895 + 580 + 465 = 1940
So, the percentage share =
465
1940
?100=23.97%

MECHANICAL ENGINEERING
1. A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by
application of pure bending moments at its ends. The Young?s modulus of the material of the
wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.
Ans: 50
Sol: Tensile stress
?? =
?? ?? ?? =
100?10
3
1
(
1
1000?2
)=50 ??????


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2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6




3

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of ?? =
8+6
2
=7

6. X is an online media provider. By offering unlimited and exclusive online content at attractive
prices for a loyalty membership, X is almost forcing its customers towards its loyalty
membership. If its loyalty membership continues to grow at its current rate, within the next
eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
A. Most households that subscribe to X?s loyalty membership discontinue watching cable
television
B. Non-members prefer to watch cable television
C. The X is cancelling accounts of non-members
D. Cable television operators don?t subscribe to X?s loyalty membership
Ans: option (A)
Sol: option A is the most appropriate solution

7. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased
by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.
A. 35.70 B. 10.00
C. 37.50 D. 25.00
Ans: option (C)
Sol: Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04??? =0.04??
And the fiscal deficit in 2016 = 0.05?1.1?? =0.055??
Increase in fiscal deficit = 0.055x ? 0.04x = 0.015x
So, the percentage increase in fiscal deficit =
0.015?? 0.04?? ?100=37.5%

8. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can
empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is
opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is
_________.
A. 16.50 B. 14.50
C. 15.50 D. 13.50
Ans: option (B)
Sol: 1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(
1
6
? ?
1
12
? )=
1
3
?
Tank filled by when Q and R works for another 6 hours = 6(
1
9
? ?
1
12
? )=
1
6
?
Total tank filled in these 10 hours =
1
3
? +
1
6
? =0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in
9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours




4

9. While teaching a creative writing class in India, I was surprised at receiving stories from the
students that were all set in distant places: in the American West with cowboys and in
Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave
the writers in the once-colonised countries the confidence to see the shabby lives around them
as worthy of being ?told?.
The writer of this passage is surprised by the creative writing assignments of his students,
because __________.
A. Some of the students had written about ice cubes and cowboys
B. None of the students had written about ice cubes and cowboys
C. Some of the students had written stories set in foreign places
D. None of the students had written stories set in India
Ans: option (C)
Sol: option C is the most appropriate solution

10. Mola is a digital platform for taxis in a city. It offers three types of rides ? Pool, Mini and Prime.
The Table below presents the number of rides for the past four months. The platform earns one
US dollar per ride. What is the percentage share of revenue contributed by Prime to the total
revenues of Mola, for the entire duration?
Type
Month
January February March April
Pool 170 320 215 190
Mini 110 220 180 70
Prime 75 180 120 90

A. 38.74 B. 23.97
C. 25.86 D. 16.24

Ans: option (B)
Sol: Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580
Revenue contributed by Prime = 75 + 180 + 120 +90 = 465
Total revenue of Mola = 895 + 580 + 465 = 1940
So, the percentage share =
465
1940
?100=23.97%

MECHANICAL ENGINEERING
1. A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by
application of pure bending moments at its ends. The Young?s modulus of the material of the
wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.
Ans: 50
Sol: Tensile stress
?? =
?? ?? ?? =
100?10
3
1
(
1
1000?2
)=50 ??????





5

2. In an electrical discharge machining process, the breakdown voltage across inter electrode gap
(IEG) is 200 V and the capacitance of the RC circuit is 50 ?F. The energy (in J) released per
spark across the IEG is __________
Ans: 1
Sol:
?? =
1
2
??????????????????????? ????????????? ?? 2

?? =0.5?50?10
?6
?200
2
=1 ??


3. If x is the mean of data 3, x, 2 and 4, then the mode is _________
Ans: 3
Sol: ?? =
3+?? +2+4
4

4??? =3+?? +2+4
4??? ??? =3+2+4=9
?? =3
Mode is 3. (Maximum repeated value)

4. The cold forming process in which a hardened tool is pressed against a workpiece (when there is
relative motion between the tool and the workpiece) to produce a roughened surface with a
regular pattern is
A. Strip rolling B. Knurling
C. Roll forming D. Chamfering
Ans: option (B)
Sol: We provide special pattern to prevent the relative motion between contact surface. This special
pattern is known as Knurling.


5. Endurance limit of a beam subjected to pure bending decreases with
A. increase in the surface roughness and increase in the size of the beam
B. decrease in the surface roughness and decrease in the size of the beam
C. decrease in the surface roughness and increase in the size of the beam
D. increase in the surface roughness and decrease in the size of the beam
Ans: option (A)
Sol: Formula for endurance limit
?? ?? =?? ?? ??? ?? ??? ?? ??? ?? ??? ?? ?

?? ???????
?? ?? ????????? ????????????
?? ?? ??????????????? ????????????
?? ?? ????????? ????????????
?? ?? ??????????????????????? ????????????
?? ?? ?
??????????????????? ?????????????? ?
Form above formula it is clear that the Endurance limit increases with increase in size,
surface, load, temp and endurance strength.




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2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6




3

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of ?? =
8+6
2
=7

6. X is an online media provider. By offering unlimited and exclusive online content at attractive
prices for a loyalty membership, X is almost forcing its customers towards its loyalty
membership. If its loyalty membership continues to grow at its current rate, within the next
eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
A. Most households that subscribe to X?s loyalty membership discontinue watching cable
television
B. Non-members prefer to watch cable television
C. The X is cancelling accounts of non-members
D. Cable television operators don?t subscribe to X?s loyalty membership
Ans: option (A)
Sol: option A is the most appropriate solution

7. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased
by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.
A. 35.70 B. 10.00
C. 37.50 D. 25.00
Ans: option (C)
Sol: Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04??? =0.04??
And the fiscal deficit in 2016 = 0.05?1.1?? =0.055??
Increase in fiscal deficit = 0.055x ? 0.04x = 0.015x
So, the percentage increase in fiscal deficit =
0.015?? 0.04?? ?100=37.5%

8. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can
empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is
opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is
_________.
A. 16.50 B. 14.50
C. 15.50 D. 13.50
Ans: option (B)
Sol: 1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(
1
6
? ?
1
12
? )=
1
3
?
Tank filled by when Q and R works for another 6 hours = 6(
1
9
? ?
1
12
? )=
1
6
?
Total tank filled in these 10 hours =
1
3
? +
1
6
? =0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in
9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours




4

9. While teaching a creative writing class in India, I was surprised at receiving stories from the
students that were all set in distant places: in the American West with cowboys and in
Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave
the writers in the once-colonised countries the confidence to see the shabby lives around them
as worthy of being ?told?.
The writer of this passage is surprised by the creative writing assignments of his students,
because __________.
A. Some of the students had written about ice cubes and cowboys
B. None of the students had written about ice cubes and cowboys
C. Some of the students had written stories set in foreign places
D. None of the students had written stories set in India
Ans: option (C)
Sol: option C is the most appropriate solution

10. Mola is a digital platform for taxis in a city. It offers three types of rides ? Pool, Mini and Prime.
The Table below presents the number of rides for the past four months. The platform earns one
US dollar per ride. What is the percentage share of revenue contributed by Prime to the total
revenues of Mola, for the entire duration?
Type
Month
January February March April
Pool 170 320 215 190
Mini 110 220 180 70
Prime 75 180 120 90

A. 38.74 B. 23.97
C. 25.86 D. 16.24

Ans: option (B)
Sol: Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580
Revenue contributed by Prime = 75 + 180 + 120 +90 = 465
Total revenue of Mola = 895 + 580 + 465 = 1940
So, the percentage share =
465
1940
?100=23.97%

MECHANICAL ENGINEERING
1. A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by
application of pure bending moments at its ends. The Young?s modulus of the material of the
wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.
Ans: 50
Sol: Tensile stress
?? =
?? ?? ?? =
100?10
3
1
(
1
1000?2
)=50 ??????





5

2. In an electrical discharge machining process, the breakdown voltage across inter electrode gap
(IEG) is 200 V and the capacitance of the RC circuit is 50 ?F. The energy (in J) released per
spark across the IEG is __________
Ans: 1
Sol:
?? =
1
2
??????????????????????? ????????????? ?? 2

?? =0.5?50?10
?6
?200
2
=1 ??


3. If x is the mean of data 3, x, 2 and 4, then the mode is _________
Ans: 3
Sol: ?? =
3+?? +2+4
4

4??? =3+?? +2+4
4??? ??? =3+2+4=9
?? =3
Mode is 3. (Maximum repeated value)

4. The cold forming process in which a hardened tool is pressed against a workpiece (when there is
relative motion between the tool and the workpiece) to produce a roughened surface with a
regular pattern is
A. Strip rolling B. Knurling
C. Roll forming D. Chamfering
Ans: option (B)
Sol: We provide special pattern to prevent the relative motion between contact surface. This special
pattern is known as Knurling.


5. Endurance limit of a beam subjected to pure bending decreases with
A. increase in the surface roughness and increase in the size of the beam
B. decrease in the surface roughness and decrease in the size of the beam
C. decrease in the surface roughness and increase in the size of the beam
D. increase in the surface roughness and decrease in the size of the beam
Ans: option (A)
Sol: Formula for endurance limit
?? ?? =?? ?? ??? ?? ??? ?? ??? ?? ??? ?? ?

?? ???????
?? ?? ????????? ????????????
?? ?? ??????????????? ????????????
?? ?? ????????? ????????????
?? ?? ??????????????????????? ????????????
?? ?? ?
??????????????????? ?????????????? ?
Form above formula it is clear that the Endurance limit increases with increase in size,
surface, load, temp and endurance strength.







6

6. In matrix equation [A] {X} = {R}.
? ?
4 8 4 2
8 16 4 , 1
4 4 15 4
AX
? ? ? ?
?? ??
= ? = ??
??
????
??
??
?
? ? ? ?
and ? ?
32
16 .
64
R
??
??
=
??
??
??

One of the eigenvalues of matrix [A] is
A. 4 B. 15
C. 8 D. 16
Ans: option (D)
Sol: [A] {X} = {R}.

We know ???? = ???? ;?? ??????? ?? ??????????? ??????????

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}={
32
16
64
}

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}=16{
2
1
4
}

Hence, ?? =????

7. Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number
ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit.
The Reynolds number at the exit of the pipe is___________.
Ans: 500
Sol: Reynold?s Number
???? =
?? ?? ????
?? ??
Where: -
?? ??????????? ??????????????
?? ????
??????????????? ????????????????
?? ??????????????? ???? ????????
?? ? Dynamic viscosity of Fluid
?? ?? =(
?? ?? ????
?? ?? )=
(

?? (
?? ???????? ?? ???????? ) ?? ?? )


From above expiration, Reynold?s Number is independent of flow profile. Hence, Reynold?s
Number for parabolic flow profile is 500.

8. For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure
and temperature, respectively. As per Maxwell?s relations,
p
v
s
? ??
??
?
??
is equal to
A.
T
p
v
? ??
??
?
??
B.
p
s
T
? ??
??
?
??
C.
s
T
p
?? ?
??
?
??
D.
p
T
v
? ??
?
??
?
??

Ans: option (C)
Sol: From mathematical relation expiration
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2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6




3

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of ?? =
8+6
2
=7

6. X is an online media provider. By offering unlimited and exclusive online content at attractive
prices for a loyalty membership, X is almost forcing its customers towards its loyalty
membership. If its loyalty membership continues to grow at its current rate, within the next
eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
A. Most households that subscribe to X?s loyalty membership discontinue watching cable
television
B. Non-members prefer to watch cable television
C. The X is cancelling accounts of non-members
D. Cable television operators don?t subscribe to X?s loyalty membership
Ans: option (A)
Sol: option A is the most appropriate solution

7. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased
by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.
A. 35.70 B. 10.00
C. 37.50 D. 25.00
Ans: option (C)
Sol: Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04??? =0.04??
And the fiscal deficit in 2016 = 0.05?1.1?? =0.055??
Increase in fiscal deficit = 0.055x ? 0.04x = 0.015x
So, the percentage increase in fiscal deficit =
0.015?? 0.04?? ?100=37.5%

8. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can
empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is
opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is
_________.
A. 16.50 B. 14.50
C. 15.50 D. 13.50
Ans: option (B)
Sol: 1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(
1
6
? ?
1
12
? )=
1
3
?
Tank filled by when Q and R works for another 6 hours = 6(
1
9
? ?
1
12
? )=
1
6
?
Total tank filled in these 10 hours =
1
3
? +
1
6
? =0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in
9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours




4

9. While teaching a creative writing class in India, I was surprised at receiving stories from the
students that were all set in distant places: in the American West with cowboys and in
Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave
the writers in the once-colonised countries the confidence to see the shabby lives around them
as worthy of being ?told?.
The writer of this passage is surprised by the creative writing assignments of his students,
because __________.
A. Some of the students had written about ice cubes and cowboys
B. None of the students had written about ice cubes and cowboys
C. Some of the students had written stories set in foreign places
D. None of the students had written stories set in India
Ans: option (C)
Sol: option C is the most appropriate solution

10. Mola is a digital platform for taxis in a city. It offers three types of rides ? Pool, Mini and Prime.
The Table below presents the number of rides for the past four months. The platform earns one
US dollar per ride. What is the percentage share of revenue contributed by Prime to the total
revenues of Mola, for the entire duration?
Type
Month
January February March April
Pool 170 320 215 190
Mini 110 220 180 70
Prime 75 180 120 90

A. 38.74 B. 23.97
C. 25.86 D. 16.24

Ans: option (B)
Sol: Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580
Revenue contributed by Prime = 75 + 180 + 120 +90 = 465
Total revenue of Mola = 895 + 580 + 465 = 1940
So, the percentage share =
465
1940
?100=23.97%

MECHANICAL ENGINEERING
1. A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by
application of pure bending moments at its ends. The Young?s modulus of the material of the
wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.
Ans: 50
Sol: Tensile stress
?? =
?? ?? ?? =
100?10
3
1
(
1
1000?2
)=50 ??????





5

2. In an electrical discharge machining process, the breakdown voltage across inter electrode gap
(IEG) is 200 V and the capacitance of the RC circuit is 50 ?F. The energy (in J) released per
spark across the IEG is __________
Ans: 1
Sol:
?? =
1
2
??????????????????????? ????????????? ?? 2

?? =0.5?50?10
?6
?200
2
=1 ??


3. If x is the mean of data 3, x, 2 and 4, then the mode is _________
Ans: 3
Sol: ?? =
3+?? +2+4
4

4??? =3+?? +2+4
4??? ??? =3+2+4=9
?? =3
Mode is 3. (Maximum repeated value)

4. The cold forming process in which a hardened tool is pressed against a workpiece (when there is
relative motion between the tool and the workpiece) to produce a roughened surface with a
regular pattern is
A. Strip rolling B. Knurling
C. Roll forming D. Chamfering
Ans: option (B)
Sol: We provide special pattern to prevent the relative motion between contact surface. This special
pattern is known as Knurling.


5. Endurance limit of a beam subjected to pure bending decreases with
A. increase in the surface roughness and increase in the size of the beam
B. decrease in the surface roughness and decrease in the size of the beam
C. decrease in the surface roughness and increase in the size of the beam
D. increase in the surface roughness and decrease in the size of the beam
Ans: option (A)
Sol: Formula for endurance limit
?? ?? =?? ?? ??? ?? ??? ?? ??? ?? ??? ?? ?

?? ???????
?? ?? ????????? ????????????
?? ?? ??????????????? ????????????
?? ?? ????????? ????????????
?? ?? ??????????????????????? ????????????
?? ?? ?
??????????????????? ?????????????? ?
Form above formula it is clear that the Endurance limit increases with increase in size,
surface, load, temp and endurance strength.







6

6. In matrix equation [A] {X} = {R}.
? ?
4 8 4 2
8 16 4 , 1
4 4 15 4
AX
? ? ? ?
?? ??
= ? = ??
??
????
??
??
?
? ? ? ?
and ? ?
32
16 .
64
R
??
??
=
??
??
??

One of the eigenvalues of matrix [A] is
A. 4 B. 15
C. 8 D. 16
Ans: option (D)
Sol: [A] {X} = {R}.

We know ???? = ???? ;?? ??????? ?? ??????????? ??????????

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}={
32
16
64
}

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}=16{
2
1
4
}

Hence, ?? =????

7. Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number
ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit.
The Reynolds number at the exit of the pipe is___________.
Ans: 500
Sol: Reynold?s Number
???? =
?? ?? ????
?? ??
Where: -
?? ??????????? ??????????????
?? ????
??????????????? ????????????????
?? ??????????????? ???? ????????
?? ? Dynamic viscosity of Fluid
?? ?? =(
?? ?? ????
?? ?? )=
(

?? (
?? ???????? ?? ???????? ) ?? ?? )


From above expiration, Reynold?s Number is independent of flow profile. Hence, Reynold?s
Number for parabolic flow profile is 500.

8. For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure
and temperature, respectively. As per Maxwell?s relations,
p
v
s
? ??
??
?
??
is equal to
A.
T
p
v
? ??
??
?
??
B.
p
s
T
? ??
??
?
??
C.
s
T
p
?? ?
??
?
??
D.
p
T
v
? ??
?
??
?
??

Ans: option (C)
Sol: From mathematical relation expiration



7

???? = ?????? +??????
? (
????
????
)
?? = (
????
????
)
??
???????? ?????????????? ????????????????
?? ?= ?????? +??????
? (
????
????
)
?? = (
????
????
)
??

9. Hardenability of steel is a measure of
A. the ability to harden when it is cold worked
B. the maximum hardness that can be obtained when it is austenitized and then quenched
C. the ability to retain its hardness when it is heated to elevated temperatures
D. the depth to which required hardening is obtained when it is austenitized and then quenched
Ans: option (D)
Sol: The depth to which required hardening is obtained when it is austenitized and then quenched.

10. The directional derivative of the function f(x, y) = x
2
+ y
2
along a line directed from (0, 0) to (1,
1), evaluated at the point x = 1, y = 1 is
A. 2 B. ?2
C. 4?2 D. 2?2
Ans: option (D)
Sol: Directional derivative of function along the line is the scalar value of derivative along the line. i.e.
we have to calculate value of derivative of function in the direction of given line vector
? ?? = ??? (
????
????
)+ ??? (
????
????
)
? ?? = 2???+ 2???
Now, calculating the value of ? ?? in 1???+ 1???
D.D of given function is (2???+ 2??? ) ?
(??? + ?? ?)
|??? + ?? ?|
= 2 ?2

11. A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is
A.
2 D
T
?
B.
T
D

C.
D
T
?
D.
D
T

Ans: option (C)
Sol: circular pitch =
????
??

12. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the
instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of
points P and R are VP and VR, in the x and y directions, respectively. The magnitude of the
angular velocity of the body is

FirstRanker.com - FirstRanker's Choice



2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6




3

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of ?? =
8+6
2
=7

6. X is an online media provider. By offering unlimited and exclusive online content at attractive
prices for a loyalty membership, X is almost forcing its customers towards its loyalty
membership. If its loyalty membership continues to grow at its current rate, within the next
eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
A. Most households that subscribe to X?s loyalty membership discontinue watching cable
television
B. Non-members prefer to watch cable television
C. The X is cancelling accounts of non-members
D. Cable television operators don?t subscribe to X?s loyalty membership
Ans: option (A)
Sol: option A is the most appropriate solution

7. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased
by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.
A. 35.70 B. 10.00
C. 37.50 D. 25.00
Ans: option (C)
Sol: Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04??? =0.04??
And the fiscal deficit in 2016 = 0.05?1.1?? =0.055??
Increase in fiscal deficit = 0.055x ? 0.04x = 0.015x
So, the percentage increase in fiscal deficit =
0.015?? 0.04?? ?100=37.5%

8. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can
empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is
opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is
_________.
A. 16.50 B. 14.50
C. 15.50 D. 13.50
Ans: option (B)
Sol: 1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(
1
6
? ?
1
12
? )=
1
3
?
Tank filled by when Q and R works for another 6 hours = 6(
1
9
? ?
1
12
? )=
1
6
?
Total tank filled in these 10 hours =
1
3
? +
1
6
? =0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in
9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours




4

9. While teaching a creative writing class in India, I was surprised at receiving stories from the
students that were all set in distant places: in the American West with cowboys and in
Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave
the writers in the once-colonised countries the confidence to see the shabby lives around them
as worthy of being ?told?.
The writer of this passage is surprised by the creative writing assignments of his students,
because __________.
A. Some of the students had written about ice cubes and cowboys
B. None of the students had written about ice cubes and cowboys
C. Some of the students had written stories set in foreign places
D. None of the students had written stories set in India
Ans: option (C)
Sol: option C is the most appropriate solution

10. Mola is a digital platform for taxis in a city. It offers three types of rides ? Pool, Mini and Prime.
The Table below presents the number of rides for the past four months. The platform earns one
US dollar per ride. What is the percentage share of revenue contributed by Prime to the total
revenues of Mola, for the entire duration?
Type
Month
January February March April
Pool 170 320 215 190
Mini 110 220 180 70
Prime 75 180 120 90

A. 38.74 B. 23.97
C. 25.86 D. 16.24

Ans: option (B)
Sol: Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580
Revenue contributed by Prime = 75 + 180 + 120 +90 = 465
Total revenue of Mola = 895 + 580 + 465 = 1940
So, the percentage share =
465
1940
?100=23.97%

MECHANICAL ENGINEERING
1. A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by
application of pure bending moments at its ends. The Young?s modulus of the material of the
wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.
Ans: 50
Sol: Tensile stress
?? =
?? ?? ?? =
100?10
3
1
(
1
1000?2
)=50 ??????





5

2. In an electrical discharge machining process, the breakdown voltage across inter electrode gap
(IEG) is 200 V and the capacitance of the RC circuit is 50 ?F. The energy (in J) released per
spark across the IEG is __________
Ans: 1
Sol:
?? =
1
2
??????????????????????? ????????????? ?? 2

?? =0.5?50?10
?6
?200
2
=1 ??


3. If x is the mean of data 3, x, 2 and 4, then the mode is _________
Ans: 3
Sol: ?? =
3+?? +2+4
4

4??? =3+?? +2+4
4??? ??? =3+2+4=9
?? =3
Mode is 3. (Maximum repeated value)

4. The cold forming process in which a hardened tool is pressed against a workpiece (when there is
relative motion between the tool and the workpiece) to produce a roughened surface with a
regular pattern is
A. Strip rolling B. Knurling
C. Roll forming D. Chamfering
Ans: option (B)
Sol: We provide special pattern to prevent the relative motion between contact surface. This special
pattern is known as Knurling.


5. Endurance limit of a beam subjected to pure bending decreases with
A. increase in the surface roughness and increase in the size of the beam
B. decrease in the surface roughness and decrease in the size of the beam
C. decrease in the surface roughness and increase in the size of the beam
D. increase in the surface roughness and decrease in the size of the beam
Ans: option (A)
Sol: Formula for endurance limit
?? ?? =?? ?? ??? ?? ??? ?? ??? ?? ??? ?? ?

?? ???????
?? ?? ????????? ????????????
?? ?? ??????????????? ????????????
?? ?? ????????? ????????????
?? ?? ??????????????????????? ????????????
?? ?? ?
??????????????????? ?????????????? ?
Form above formula it is clear that the Endurance limit increases with increase in size,
surface, load, temp and endurance strength.







6

6. In matrix equation [A] {X} = {R}.
? ?
4 8 4 2
8 16 4 , 1
4 4 15 4
AX
? ? ? ?
?? ??
= ? = ??
??
????
??
??
?
? ? ? ?
and ? ?
32
16 .
64
R
??
??
=
??
??
??

One of the eigenvalues of matrix [A] is
A. 4 B. 15
C. 8 D. 16
Ans: option (D)
Sol: [A] {X} = {R}.

We know ???? = ???? ;?? ??????? ?? ??????????? ??????????

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}={
32
16
64
}

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}=16{
2
1
4
}

Hence, ?? =????

7. Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number
ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit.
The Reynolds number at the exit of the pipe is___________.
Ans: 500
Sol: Reynold?s Number
???? =
?? ?? ????
?? ??
Where: -
?? ??????????? ??????????????
?? ????
??????????????? ????????????????
?? ??????????????? ???? ????????
?? ? Dynamic viscosity of Fluid
?? ?? =(
?? ?? ????
?? ?? )=
(

?? (
?? ???????? ?? ???????? ) ?? ?? )


From above expiration, Reynold?s Number is independent of flow profile. Hence, Reynold?s
Number for parabolic flow profile is 500.

8. For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure
and temperature, respectively. As per Maxwell?s relations,
p
v
s
? ??
??
?
??
is equal to
A.
T
p
v
? ??
??
?
??
B.
p
s
T
? ??
??
?
??
C.
s
T
p
?? ?
??
?
??
D.
p
T
v
? ??
?
??
?
??

Ans: option (C)
Sol: From mathematical relation expiration



7

???? = ?????? +??????
? (
????
????
)
?? = (
????
????
)
??
???????? ?????????????? ????????????????
?? ?= ?????? +??????
? (
????
????
)
?? = (
????
????
)
??

9. Hardenability of steel is a measure of
A. the ability to harden when it is cold worked
B. the maximum hardness that can be obtained when it is austenitized and then quenched
C. the ability to retain its hardness when it is heated to elevated temperatures
D. the depth to which required hardening is obtained when it is austenitized and then quenched
Ans: option (D)
Sol: The depth to which required hardening is obtained when it is austenitized and then quenched.

10. The directional derivative of the function f(x, y) = x
2
+ y
2
along a line directed from (0, 0) to (1,
1), evaluated at the point x = 1, y = 1 is
A. 2 B. ?2
C. 4?2 D. 2?2
Ans: option (D)
Sol: Directional derivative of function along the line is the scalar value of derivative along the line. i.e.
we have to calculate value of derivative of function in the direction of given line vector
? ?? = ??? (
????
????
)+ ??? (
????
????
)
? ?? = 2???+ 2???
Now, calculating the value of ? ?? in 1???+ 1???
D.D of given function is (2???+ 2??? ) ?
(??? + ?? ?)
|??? + ?? ?|
= 2 ?2

11. A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is
A.
2 D
T
?
B.
T
D

C.
D
T
?
D.
D
T

Ans: option (C)
Sol: circular pitch =
????
??

12. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the
instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of
points P and R are VP and VR, in the x and y directions, respectively. The magnitude of the
angular velocity of the body is




8

A. /3
R
V B. /3
P
V
C. 2VR D. 2VP
Ans: option (C)
Sol: The given body is a rigid body; Hence the given body will not have any deformation, and the
possible motion is translation and angular motion. we know that the angular motion of the object is
always defined as the motion about the point. Hence, first we have to find a point parallel to both
velocity ?? ?? and ?? ?? .


? Angular velocity, ?? =
???????????????? ?????????????????????????? ????????????????
?? =
?? ?? ????
=
?? ?? ????

???? =
?3
2
????????? ???? ???????????????? =
?3
2
?1=
?3
2

???? =
1
2
????????? ???? ???????????????? =
1
2
?1=
1
2


?? =
2?? ?? ?3
=
2?? ?? 1


13. Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4
m. The view factor F12 is
A. 0.25 B. 0.0625
C. 1.0 D. 0.5
Ans: option (C)
Sol: ?? 12
=1

14. The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
A.
10
01
??
??
?
??
B.
01
10
? ??
??
?
??

C.
01
10
??
??
??
D.
10
01
???
??
??

Ans: option (C)
Sol: The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
01
10
??
??
??




S
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2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6




3

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of ?? =
8+6
2
=7

6. X is an online media provider. By offering unlimited and exclusive online content at attractive
prices for a loyalty membership, X is almost forcing its customers towards its loyalty
membership. If its loyalty membership continues to grow at its current rate, within the next
eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
A. Most households that subscribe to X?s loyalty membership discontinue watching cable
television
B. Non-members prefer to watch cable television
C. The X is cancelling accounts of non-members
D. Cable television operators don?t subscribe to X?s loyalty membership
Ans: option (A)
Sol: option A is the most appropriate solution

7. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased
by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.
A. 35.70 B. 10.00
C. 37.50 D. 25.00
Ans: option (C)
Sol: Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04??? =0.04??
And the fiscal deficit in 2016 = 0.05?1.1?? =0.055??
Increase in fiscal deficit = 0.055x ? 0.04x = 0.015x
So, the percentage increase in fiscal deficit =
0.015?? 0.04?? ?100=37.5%

8. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can
empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is
opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is
_________.
A. 16.50 B. 14.50
C. 15.50 D. 13.50
Ans: option (B)
Sol: 1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(
1
6
? ?
1
12
? )=
1
3
?
Tank filled by when Q and R works for another 6 hours = 6(
1
9
? ?
1
12
? )=
1
6
?
Total tank filled in these 10 hours =
1
3
? +
1
6
? =0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in
9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours




4

9. While teaching a creative writing class in India, I was surprised at receiving stories from the
students that were all set in distant places: in the American West with cowboys and in
Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave
the writers in the once-colonised countries the confidence to see the shabby lives around them
as worthy of being ?told?.
The writer of this passage is surprised by the creative writing assignments of his students,
because __________.
A. Some of the students had written about ice cubes and cowboys
B. None of the students had written about ice cubes and cowboys
C. Some of the students had written stories set in foreign places
D. None of the students had written stories set in India
Ans: option (C)
Sol: option C is the most appropriate solution

10. Mola is a digital platform for taxis in a city. It offers three types of rides ? Pool, Mini and Prime.
The Table below presents the number of rides for the past four months. The platform earns one
US dollar per ride. What is the percentage share of revenue contributed by Prime to the total
revenues of Mola, for the entire duration?
Type
Month
January February March April
Pool 170 320 215 190
Mini 110 220 180 70
Prime 75 180 120 90

A. 38.74 B. 23.97
C. 25.86 D. 16.24

Ans: option (B)
Sol: Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580
Revenue contributed by Prime = 75 + 180 + 120 +90 = 465
Total revenue of Mola = 895 + 580 + 465 = 1940
So, the percentage share =
465
1940
?100=23.97%

MECHANICAL ENGINEERING
1. A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by
application of pure bending moments at its ends. The Young?s modulus of the material of the
wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.
Ans: 50
Sol: Tensile stress
?? =
?? ?? ?? =
100?10
3
1
(
1
1000?2
)=50 ??????





5

2. In an electrical discharge machining process, the breakdown voltage across inter electrode gap
(IEG) is 200 V and the capacitance of the RC circuit is 50 ?F. The energy (in J) released per
spark across the IEG is __________
Ans: 1
Sol:
?? =
1
2
??????????????????????? ????????????? ?? 2

?? =0.5?50?10
?6
?200
2
=1 ??


3. If x is the mean of data 3, x, 2 and 4, then the mode is _________
Ans: 3
Sol: ?? =
3+?? +2+4
4

4??? =3+?? +2+4
4??? ??? =3+2+4=9
?? =3
Mode is 3. (Maximum repeated value)

4. The cold forming process in which a hardened tool is pressed against a workpiece (when there is
relative motion between the tool and the workpiece) to produce a roughened surface with a
regular pattern is
A. Strip rolling B. Knurling
C. Roll forming D. Chamfering
Ans: option (B)
Sol: We provide special pattern to prevent the relative motion between contact surface. This special
pattern is known as Knurling.


5. Endurance limit of a beam subjected to pure bending decreases with
A. increase in the surface roughness and increase in the size of the beam
B. decrease in the surface roughness and decrease in the size of the beam
C. decrease in the surface roughness and increase in the size of the beam
D. increase in the surface roughness and decrease in the size of the beam
Ans: option (A)
Sol: Formula for endurance limit
?? ?? =?? ?? ??? ?? ??? ?? ??? ?? ??? ?? ?

?? ???????
?? ?? ????????? ????????????
?? ?? ??????????????? ????????????
?? ?? ????????? ????????????
?? ?? ??????????????????????? ????????????
?? ?? ?
??????????????????? ?????????????? ?
Form above formula it is clear that the Endurance limit increases with increase in size,
surface, load, temp and endurance strength.







6

6. In matrix equation [A] {X} = {R}.
? ?
4 8 4 2
8 16 4 , 1
4 4 15 4
AX
? ? ? ?
?? ??
= ? = ??
??
????
??
??
?
? ? ? ?
and ? ?
32
16 .
64
R
??
??
=
??
??
??

One of the eigenvalues of matrix [A] is
A. 4 B. 15
C. 8 D. 16
Ans: option (D)
Sol: [A] {X} = {R}.

We know ???? = ???? ;?? ??????? ?? ??????????? ??????????

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}={
32
16
64
}

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}=16{
2
1
4
}

Hence, ?? =????

7. Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number
ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit.
The Reynolds number at the exit of the pipe is___________.
Ans: 500
Sol: Reynold?s Number
???? =
?? ?? ????
?? ??
Where: -
?? ??????????? ??????????????
?? ????
??????????????? ????????????????
?? ??????????????? ???? ????????
?? ? Dynamic viscosity of Fluid
?? ?? =(
?? ?? ????
?? ?? )=
(

?? (
?? ???????? ?? ???????? ) ?? ?? )


From above expiration, Reynold?s Number is independent of flow profile. Hence, Reynold?s
Number for parabolic flow profile is 500.

8. For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure
and temperature, respectively. As per Maxwell?s relations,
p
v
s
? ??
??
?
??
is equal to
A.
T
p
v
? ??
??
?
??
B.
p
s
T
? ??
??
?
??
C.
s
T
p
?? ?
??
?
??
D.
p
T
v
? ??
?
??
?
??

Ans: option (C)
Sol: From mathematical relation expiration



7

???? = ?????? +??????
? (
????
????
)
?? = (
????
????
)
??
???????? ?????????????? ????????????????
?? ?= ?????? +??????
? (
????
????
)
?? = (
????
????
)
??

9. Hardenability of steel is a measure of
A. the ability to harden when it is cold worked
B. the maximum hardness that can be obtained when it is austenitized and then quenched
C. the ability to retain its hardness when it is heated to elevated temperatures
D. the depth to which required hardening is obtained when it is austenitized and then quenched
Ans: option (D)
Sol: The depth to which required hardening is obtained when it is austenitized and then quenched.

10. The directional derivative of the function f(x, y) = x
2
+ y
2
along a line directed from (0, 0) to (1,
1), evaluated at the point x = 1, y = 1 is
A. 2 B. ?2
C. 4?2 D. 2?2
Ans: option (D)
Sol: Directional derivative of function along the line is the scalar value of derivative along the line. i.e.
we have to calculate value of derivative of function in the direction of given line vector
? ?? = ??? (
????
????
)+ ??? (
????
????
)
? ?? = 2???+ 2???
Now, calculating the value of ? ?? in 1???+ 1???
D.D of given function is (2???+ 2??? ) ?
(??? + ?? ?)
|??? + ?? ?|
= 2 ?2

11. A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is
A.
2 D
T
?
B.
T
D

C.
D
T
?
D.
D
T

Ans: option (C)
Sol: circular pitch =
????
??

12. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the
instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of
points P and R are VP and VR, in the x and y directions, respectively. The magnitude of the
angular velocity of the body is




8

A. /3
R
V B. /3
P
V
C. 2VR D. 2VP
Ans: option (C)
Sol: The given body is a rigid body; Hence the given body will not have any deformation, and the
possible motion is translation and angular motion. we know that the angular motion of the object is
always defined as the motion about the point. Hence, first we have to find a point parallel to both
velocity ?? ?? and ?? ?? .


? Angular velocity, ?? =
???????????????? ?????????????????????????? ????????????????
?? =
?? ?? ????
=
?? ?? ????

???? =
?3
2
????????? ???? ???????????????? =
?3
2
?1=
?3
2

???? =
1
2
????????? ???? ???????????????? =
1
2
?1=
1
2


?? =
2?? ?? ?3
=
2?? ?? 1


13. Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4
m. The view factor F12 is
A. 0.25 B. 0.0625
C. 1.0 D. 0.5
Ans: option (C)
Sol: ?? 12
=1

14. The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
A.
10
01
??
??
?
??
B.
01
10
? ??
??
?
??

C.
01
10
??
??
??
D.
10
01
???
??
??

Ans: option (C)
Sol: The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
01
10
??
??
??




S



9

15. The state of stress at a point in a component is represented by a Mohr?s circle of radius 100 MPa
centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the
normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same
point is ___________ MPa.
Ans: 80
Sol:


?? =?100
2
?60
2
=80 ??????

16. One-dimensional steady state heat conduction takes place through a solid whose cross-sectional
area varies linearly in the direction of heat transfer. Assume there is no heat generation in the
solid and the thermal conductivity of the material is constant and independent of temperature.
The temperature distribution in the solid is
A. Quadratic B. Exponential
C. Logarithmic D. Linear
Ans: option (C)
Sol: Let the given body cross-sectional area varies linearly, and heat is flowing from left to right.





If there is no heat generation,
?? ????
(?????
????
????
)=0

?
?? ????
(?????
????
????
)=?0

(?????
????
????
)=??

??? (?? 0
+?? ?? ?? )
????
????
=??
???? =
? ?? ????
?? (?? 0
+?? ?? ?? )


? ????
2
1
=?
? ?? ????
?? (?? 0
+?? ?? ?? )
2
1


?? 2
??? 1
= ?
?? ?? ln(
?? ?? ?? 2
+?? 0
?? ?? ?? 1
+?? 0
)
FirstRanker.com - FirstRanker's Choice



2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6




3

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of ?? =
8+6
2
=7

6. X is an online media provider. By offering unlimited and exclusive online content at attractive
prices for a loyalty membership, X is almost forcing its customers towards its loyalty
membership. If its loyalty membership continues to grow at its current rate, within the next
eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
A. Most households that subscribe to X?s loyalty membership discontinue watching cable
television
B. Non-members prefer to watch cable television
C. The X is cancelling accounts of non-members
D. Cable television operators don?t subscribe to X?s loyalty membership
Ans: option (A)
Sol: option A is the most appropriate solution

7. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased
by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.
A. 35.70 B. 10.00
C. 37.50 D. 25.00
Ans: option (C)
Sol: Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04??? =0.04??
And the fiscal deficit in 2016 = 0.05?1.1?? =0.055??
Increase in fiscal deficit = 0.055x ? 0.04x = 0.015x
So, the percentage increase in fiscal deficit =
0.015?? 0.04?? ?100=37.5%

8. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can
empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is
opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is
_________.
A. 16.50 B. 14.50
C. 15.50 D. 13.50
Ans: option (B)
Sol: 1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(
1
6
? ?
1
12
? )=
1
3
?
Tank filled by when Q and R works for another 6 hours = 6(
1
9
? ?
1
12
? )=
1
6
?
Total tank filled in these 10 hours =
1
3
? +
1
6
? =0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in
9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours




4

9. While teaching a creative writing class in India, I was surprised at receiving stories from the
students that were all set in distant places: in the American West with cowboys and in
Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave
the writers in the once-colonised countries the confidence to see the shabby lives around them
as worthy of being ?told?.
The writer of this passage is surprised by the creative writing assignments of his students,
because __________.
A. Some of the students had written about ice cubes and cowboys
B. None of the students had written about ice cubes and cowboys
C. Some of the students had written stories set in foreign places
D. None of the students had written stories set in India
Ans: option (C)
Sol: option C is the most appropriate solution

10. Mola is a digital platform for taxis in a city. It offers three types of rides ? Pool, Mini and Prime.
The Table below presents the number of rides for the past four months. The platform earns one
US dollar per ride. What is the percentage share of revenue contributed by Prime to the total
revenues of Mola, for the entire duration?
Type
Month
January February March April
Pool 170 320 215 190
Mini 110 220 180 70
Prime 75 180 120 90

A. 38.74 B. 23.97
C. 25.86 D. 16.24

Ans: option (B)
Sol: Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580
Revenue contributed by Prime = 75 + 180 + 120 +90 = 465
Total revenue of Mola = 895 + 580 + 465 = 1940
So, the percentage share =
465
1940
?100=23.97%

MECHANICAL ENGINEERING
1. A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by
application of pure bending moments at its ends. The Young?s modulus of the material of the
wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.
Ans: 50
Sol: Tensile stress
?? =
?? ?? ?? =
100?10
3
1
(
1
1000?2
)=50 ??????





5

2. In an electrical discharge machining process, the breakdown voltage across inter electrode gap
(IEG) is 200 V and the capacitance of the RC circuit is 50 ?F. The energy (in J) released per
spark across the IEG is __________
Ans: 1
Sol:
?? =
1
2
??????????????????????? ????????????? ?? 2

?? =0.5?50?10
?6
?200
2
=1 ??


3. If x is the mean of data 3, x, 2 and 4, then the mode is _________
Ans: 3
Sol: ?? =
3+?? +2+4
4

4??? =3+?? +2+4
4??? ??? =3+2+4=9
?? =3
Mode is 3. (Maximum repeated value)

4. The cold forming process in which a hardened tool is pressed against a workpiece (when there is
relative motion between the tool and the workpiece) to produce a roughened surface with a
regular pattern is
A. Strip rolling B. Knurling
C. Roll forming D. Chamfering
Ans: option (B)
Sol: We provide special pattern to prevent the relative motion between contact surface. This special
pattern is known as Knurling.


5. Endurance limit of a beam subjected to pure bending decreases with
A. increase in the surface roughness and increase in the size of the beam
B. decrease in the surface roughness and decrease in the size of the beam
C. decrease in the surface roughness and increase in the size of the beam
D. increase in the surface roughness and decrease in the size of the beam
Ans: option (A)
Sol: Formula for endurance limit
?? ?? =?? ?? ??? ?? ??? ?? ??? ?? ??? ?? ?

?? ???????
?? ?? ????????? ????????????
?? ?? ??????????????? ????????????
?? ?? ????????? ????????????
?? ?? ??????????????????????? ????????????
?? ?? ?
??????????????????? ?????????????? ?
Form above formula it is clear that the Endurance limit increases with increase in size,
surface, load, temp and endurance strength.







6

6. In matrix equation [A] {X} = {R}.
? ?
4 8 4 2
8 16 4 , 1
4 4 15 4
AX
? ? ? ?
?? ??
= ? = ??
??
????
??
??
?
? ? ? ?
and ? ?
32
16 .
64
R
??
??
=
??
??
??

One of the eigenvalues of matrix [A] is
A. 4 B. 15
C. 8 D. 16
Ans: option (D)
Sol: [A] {X} = {R}.

We know ???? = ???? ;?? ??????? ?? ??????????? ??????????

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}={
32
16
64
}

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}=16{
2
1
4
}

Hence, ?? =????

7. Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number
ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit.
The Reynolds number at the exit of the pipe is___________.
Ans: 500
Sol: Reynold?s Number
???? =
?? ?? ????
?? ??
Where: -
?? ??????????? ??????????????
?? ????
??????????????? ????????????????
?? ??????????????? ???? ????????
?? ? Dynamic viscosity of Fluid
?? ?? =(
?? ?? ????
?? ?? )=
(

?? (
?? ???????? ?? ???????? ) ?? ?? )


From above expiration, Reynold?s Number is independent of flow profile. Hence, Reynold?s
Number for parabolic flow profile is 500.

8. For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure
and temperature, respectively. As per Maxwell?s relations,
p
v
s
? ??
??
?
??
is equal to
A.
T
p
v
? ??
??
?
??
B.
p
s
T
? ??
??
?
??
C.
s
T
p
?? ?
??
?
??
D.
p
T
v
? ??
?
??
?
??

Ans: option (C)
Sol: From mathematical relation expiration



7

???? = ?????? +??????
? (
????
????
)
?? = (
????
????
)
??
???????? ?????????????? ????????????????
?? ?= ?????? +??????
? (
????
????
)
?? = (
????
????
)
??

9. Hardenability of steel is a measure of
A. the ability to harden when it is cold worked
B. the maximum hardness that can be obtained when it is austenitized and then quenched
C. the ability to retain its hardness when it is heated to elevated temperatures
D. the depth to which required hardening is obtained when it is austenitized and then quenched
Ans: option (D)
Sol: The depth to which required hardening is obtained when it is austenitized and then quenched.

10. The directional derivative of the function f(x, y) = x
2
+ y
2
along a line directed from (0, 0) to (1,
1), evaluated at the point x = 1, y = 1 is
A. 2 B. ?2
C. 4?2 D. 2?2
Ans: option (D)
Sol: Directional derivative of function along the line is the scalar value of derivative along the line. i.e.
we have to calculate value of derivative of function in the direction of given line vector
? ?? = ??? (
????
????
)+ ??? (
????
????
)
? ?? = 2???+ 2???
Now, calculating the value of ? ?? in 1???+ 1???
D.D of given function is (2???+ 2??? ) ?
(??? + ?? ?)
|??? + ?? ?|
= 2 ?2

11. A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is
A.
2 D
T
?
B.
T
D

C.
D
T
?
D.
D
T

Ans: option (C)
Sol: circular pitch =
????
??

12. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the
instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of
points P and R are VP and VR, in the x and y directions, respectively. The magnitude of the
angular velocity of the body is




8

A. /3
R
V B. /3
P
V
C. 2VR D. 2VP
Ans: option (C)
Sol: The given body is a rigid body; Hence the given body will not have any deformation, and the
possible motion is translation and angular motion. we know that the angular motion of the object is
always defined as the motion about the point. Hence, first we have to find a point parallel to both
velocity ?? ?? and ?? ?? .


? Angular velocity, ?? =
???????????????? ?????????????????????????? ????????????????
?? =
?? ?? ????
=
?? ?? ????

???? =
?3
2
????????? ???? ???????????????? =
?3
2
?1=
?3
2

???? =
1
2
????????? ???? ???????????????? =
1
2
?1=
1
2


?? =
2?? ?? ?3
=
2?? ?? 1


13. Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4
m. The view factor F12 is
A. 0.25 B. 0.0625
C. 1.0 D. 0.5
Ans: option (C)
Sol: ?? 12
=1

14. The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
A.
10
01
??
??
?
??
B.
01
10
? ??
??
?
??

C.
01
10
??
??
??
D.
10
01
???
??
??

Ans: option (C)
Sol: The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
01
10
??
??
??




S



9

15. The state of stress at a point in a component is represented by a Mohr?s circle of radius 100 MPa
centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the
normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same
point is ___________ MPa.
Ans: 80
Sol:


?? =?100
2
?60
2
=80 ??????

16. One-dimensional steady state heat conduction takes place through a solid whose cross-sectional
area varies linearly in the direction of heat transfer. Assume there is no heat generation in the
solid and the thermal conductivity of the material is constant and independent of temperature.
The temperature distribution in the solid is
A. Quadratic B. Exponential
C. Logarithmic D. Linear
Ans: option (C)
Sol: Let the given body cross-sectional area varies linearly, and heat is flowing from left to right.





If there is no heat generation,
?? ????
(?????
????
????
)=0

?
?? ????
(?????
????
????
)=?0

(?????
????
????
)=??

??? (?? 0
+?? ?? ?? )
????
????
=??
???? =
? ?? ????
?? (?? 0
+?? ?? ?? )


? ????
2
1
=?
? ?? ????
?? (?? 0
+?? ?? ?? )
2
1


?? 2
??? 1
= ?
?? ?? ln(
?? ?? ?? 2
+?? 0
?? ?? ?? 1
+?? 0
)



10

17. An analytic function f(z) of complex variable z = x + I y may be written as f(z) = u(x, y) + iv (x,
y). Then, u(x, y) and v(x, y) must satisfy
A.
uv
xy
??
=?
??
and
uv
yx
??
=
??

B.
uv
xy
??
=?
??
and
uv
yx
??
=?
??

C.
uv
xy
??
=
??
and
uv
yx
??
=?
??

D.
uv
xy
??
=
??
and
uv
yx
??
=
??

Ans: option (C)
Sol: If f(z) = u(x, y) + iv(x, y) is analytic function then it must satisfy the following relations.

????
????
=
????
????


????
????
=?
????
????


18. A thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is
losing heat to the surroundings by natural convection. The temperatures of the plate and the
surroundings, and the properties of the surrounding fluid, are constant. The relationship between
the average Nusselt and Rayleigh numbers is given as Nu = K Ra ?, where K is a constant. The
length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the
plate is increased to 16L keeping all other factors constant.

If the average heat transfer coefficient for the first plate is h1 and that for the second plate is h2,
the value of the ratio h1/h2 is____________.
Ans: 2
Sol: ?? ?? =?? (?? ?? )
1
4
We know that ?? ?? =?? ?? ?? ??
?? ?? =?? (?? ?? ?? ?? )
1
4
??? ?? ?(?? ?? )
1
4 ?(
???? ??? ?? 3
?? 2
)
1
4

??? ??? 3
4
???? ?
1
4
?
2
?
1
?(
?? 1
?? 2
)
1
4
=>
?
1
?
2
?(
?? 2
?? 1
)
1
4
=(16)
1
4=2
FirstRanker.com - FirstRanker's Choice



2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6




3

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of ?? =
8+6
2
=7

6. X is an online media provider. By offering unlimited and exclusive online content at attractive
prices for a loyalty membership, X is almost forcing its customers towards its loyalty
membership. If its loyalty membership continues to grow at its current rate, within the next
eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
A. Most households that subscribe to X?s loyalty membership discontinue watching cable
television
B. Non-members prefer to watch cable television
C. The X is cancelling accounts of non-members
D. Cable television operators don?t subscribe to X?s loyalty membership
Ans: option (A)
Sol: option A is the most appropriate solution

7. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased
by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.
A. 35.70 B. 10.00
C. 37.50 D. 25.00
Ans: option (C)
Sol: Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04??? =0.04??
And the fiscal deficit in 2016 = 0.05?1.1?? =0.055??
Increase in fiscal deficit = 0.055x ? 0.04x = 0.015x
So, the percentage increase in fiscal deficit =
0.015?? 0.04?? ?100=37.5%

8. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can
empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is
opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is
_________.
A. 16.50 B. 14.50
C. 15.50 D. 13.50
Ans: option (B)
Sol: 1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(
1
6
? ?
1
12
? )=
1
3
?
Tank filled by when Q and R works for another 6 hours = 6(
1
9
? ?
1
12
? )=
1
6
?
Total tank filled in these 10 hours =
1
3
? +
1
6
? =0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in
9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours




4

9. While teaching a creative writing class in India, I was surprised at receiving stories from the
students that were all set in distant places: in the American West with cowboys and in
Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave
the writers in the once-colonised countries the confidence to see the shabby lives around them
as worthy of being ?told?.
The writer of this passage is surprised by the creative writing assignments of his students,
because __________.
A. Some of the students had written about ice cubes and cowboys
B. None of the students had written about ice cubes and cowboys
C. Some of the students had written stories set in foreign places
D. None of the students had written stories set in India
Ans: option (C)
Sol: option C is the most appropriate solution

10. Mola is a digital platform for taxis in a city. It offers three types of rides ? Pool, Mini and Prime.
The Table below presents the number of rides for the past four months. The platform earns one
US dollar per ride. What is the percentage share of revenue contributed by Prime to the total
revenues of Mola, for the entire duration?
Type
Month
January February March April
Pool 170 320 215 190
Mini 110 220 180 70
Prime 75 180 120 90

A. 38.74 B. 23.97
C. 25.86 D. 16.24

Ans: option (B)
Sol: Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580
Revenue contributed by Prime = 75 + 180 + 120 +90 = 465
Total revenue of Mola = 895 + 580 + 465 = 1940
So, the percentage share =
465
1940
?100=23.97%

MECHANICAL ENGINEERING
1. A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by
application of pure bending moments at its ends. The Young?s modulus of the material of the
wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.
Ans: 50
Sol: Tensile stress
?? =
?? ?? ?? =
100?10
3
1
(
1
1000?2
)=50 ??????





5

2. In an electrical discharge machining process, the breakdown voltage across inter electrode gap
(IEG) is 200 V and the capacitance of the RC circuit is 50 ?F. The energy (in J) released per
spark across the IEG is __________
Ans: 1
Sol:
?? =
1
2
??????????????????????? ????????????? ?? 2

?? =0.5?50?10
?6
?200
2
=1 ??


3. If x is the mean of data 3, x, 2 and 4, then the mode is _________
Ans: 3
Sol: ?? =
3+?? +2+4
4

4??? =3+?? +2+4
4??? ??? =3+2+4=9
?? =3
Mode is 3. (Maximum repeated value)

4. The cold forming process in which a hardened tool is pressed against a workpiece (when there is
relative motion between the tool and the workpiece) to produce a roughened surface with a
regular pattern is
A. Strip rolling B. Knurling
C. Roll forming D. Chamfering
Ans: option (B)
Sol: We provide special pattern to prevent the relative motion between contact surface. This special
pattern is known as Knurling.


5. Endurance limit of a beam subjected to pure bending decreases with
A. increase in the surface roughness and increase in the size of the beam
B. decrease in the surface roughness and decrease in the size of the beam
C. decrease in the surface roughness and increase in the size of the beam
D. increase in the surface roughness and decrease in the size of the beam
Ans: option (A)
Sol: Formula for endurance limit
?? ?? =?? ?? ??? ?? ??? ?? ??? ?? ??? ?? ?

?? ???????
?? ?? ????????? ????????????
?? ?? ??????????????? ????????????
?? ?? ????????? ????????????
?? ?? ??????????????????????? ????????????
?? ?? ?
??????????????????? ?????????????? ?
Form above formula it is clear that the Endurance limit increases with increase in size,
surface, load, temp and endurance strength.







6

6. In matrix equation [A] {X} = {R}.
? ?
4 8 4 2
8 16 4 , 1
4 4 15 4
AX
? ? ? ?
?? ??
= ? = ??
??
????
??
??
?
? ? ? ?
and ? ?
32
16 .
64
R
??
??
=
??
??
??

One of the eigenvalues of matrix [A] is
A. 4 B. 15
C. 8 D. 16
Ans: option (D)
Sol: [A] {X} = {R}.

We know ???? = ???? ;?? ??????? ?? ??????????? ??????????

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}={
32
16
64
}

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}=16{
2
1
4
}

Hence, ?? =????

7. Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number
ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit.
The Reynolds number at the exit of the pipe is___________.
Ans: 500
Sol: Reynold?s Number
???? =
?? ?? ????
?? ??
Where: -
?? ??????????? ??????????????
?? ????
??????????????? ????????????????
?? ??????????????? ???? ????????
?? ? Dynamic viscosity of Fluid
?? ?? =(
?? ?? ????
?? ?? )=
(

?? (
?? ???????? ?? ???????? ) ?? ?? )


From above expiration, Reynold?s Number is independent of flow profile. Hence, Reynold?s
Number for parabolic flow profile is 500.

8. For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure
and temperature, respectively. As per Maxwell?s relations,
p
v
s
? ??
??
?
??
is equal to
A.
T
p
v
? ??
??
?
??
B.
p
s
T
? ??
??
?
??
C.
s
T
p
?? ?
??
?
??
D.
p
T
v
? ??
?
??
?
??

Ans: option (C)
Sol: From mathematical relation expiration



7

???? = ?????? +??????
? (
????
????
)
?? = (
????
????
)
??
???????? ?????????????? ????????????????
?? ?= ?????? +??????
? (
????
????
)
?? = (
????
????
)
??

9. Hardenability of steel is a measure of
A. the ability to harden when it is cold worked
B. the maximum hardness that can be obtained when it is austenitized and then quenched
C. the ability to retain its hardness when it is heated to elevated temperatures
D. the depth to which required hardening is obtained when it is austenitized and then quenched
Ans: option (D)
Sol: The depth to which required hardening is obtained when it is austenitized and then quenched.

10. The directional derivative of the function f(x, y) = x
2
+ y
2
along a line directed from (0, 0) to (1,
1), evaluated at the point x = 1, y = 1 is
A. 2 B. ?2
C. 4?2 D. 2?2
Ans: option (D)
Sol: Directional derivative of function along the line is the scalar value of derivative along the line. i.e.
we have to calculate value of derivative of function in the direction of given line vector
? ?? = ??? (
????
????
)+ ??? (
????
????
)
? ?? = 2???+ 2???
Now, calculating the value of ? ?? in 1???+ 1???
D.D of given function is (2???+ 2??? ) ?
(??? + ?? ?)
|??? + ?? ?|
= 2 ?2

11. A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is
A.
2 D
T
?
B.
T
D

C.
D
T
?
D.
D
T

Ans: option (C)
Sol: circular pitch =
????
??

12. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the
instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of
points P and R are VP and VR, in the x and y directions, respectively. The magnitude of the
angular velocity of the body is




8

A. /3
R
V B. /3
P
V
C. 2VR D. 2VP
Ans: option (C)
Sol: The given body is a rigid body; Hence the given body will not have any deformation, and the
possible motion is translation and angular motion. we know that the angular motion of the object is
always defined as the motion about the point. Hence, first we have to find a point parallel to both
velocity ?? ?? and ?? ?? .


? Angular velocity, ?? =
???????????????? ?????????????????????????? ????????????????
?? =
?? ?? ????
=
?? ?? ????

???? =
?3
2
????????? ???? ???????????????? =
?3
2
?1=
?3
2

???? =
1
2
????????? ???? ???????????????? =
1
2
?1=
1
2


?? =
2?? ?? ?3
=
2?? ?? 1


13. Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4
m. The view factor F12 is
A. 0.25 B. 0.0625
C. 1.0 D. 0.5
Ans: option (C)
Sol: ?? 12
=1

14. The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
A.
10
01
??
??
?
??
B.
01
10
? ??
??
?
??

C.
01
10
??
??
??
D.
10
01
???
??
??

Ans: option (C)
Sol: The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
01
10
??
??
??




S



9

15. The state of stress at a point in a component is represented by a Mohr?s circle of radius 100 MPa
centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the
normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same
point is ___________ MPa.
Ans: 80
Sol:


?? =?100
2
?60
2
=80 ??????

16. One-dimensional steady state heat conduction takes place through a solid whose cross-sectional
area varies linearly in the direction of heat transfer. Assume there is no heat generation in the
solid and the thermal conductivity of the material is constant and independent of temperature.
The temperature distribution in the solid is
A. Quadratic B. Exponential
C. Logarithmic D. Linear
Ans: option (C)
Sol: Let the given body cross-sectional area varies linearly, and heat is flowing from left to right.





If there is no heat generation,
?? ????
(?????
????
????
)=0

?
?? ????
(?????
????
????
)=?0

(?????
????
????
)=??

??? (?? 0
+?? ?? ?? )
????
????
=??
???? =
? ?? ????
?? (?? 0
+?? ?? ?? )


? ????
2
1
=?
? ?? ????
?? (?? 0
+?? ?? ?? )
2
1


?? 2
??? 1
= ?
?? ?? ln(
?? ?? ?? 2
+?? 0
?? ?? ?? 1
+?? 0
)



10

17. An analytic function f(z) of complex variable z = x + I y may be written as f(z) = u(x, y) + iv (x,
y). Then, u(x, y) and v(x, y) must satisfy
A.
uv
xy
??
=?
??
and
uv
yx
??
=
??

B.
uv
xy
??
=?
??
and
uv
yx
??
=?
??

C.
uv
xy
??
=
??
and
uv
yx
??
=?
??

D.
uv
xy
??
=
??
and
uv
yx
??
=
??

Ans: option (C)
Sol: If f(z) = u(x, y) + iv(x, y) is analytic function then it must satisfy the following relations.

????
????
=
????
????


????
????
=?
????
????


18. A thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is
losing heat to the surroundings by natural convection. The temperatures of the plate and the
surroundings, and the properties of the surrounding fluid, are constant. The relationship between
the average Nusselt and Rayleigh numbers is given as Nu = K Ra ?, where K is a constant. The
length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the
plate is increased to 16L keeping all other factors constant.

If the average heat transfer coefficient for the first plate is h1 and that for the second plate is h2,
the value of the ratio h1/h2 is____________.
Ans: 2
Sol: ?? ?? =?? (?? ?? )
1
4
We know that ?? ?? =?? ?? ?? ??
?? ?? =?? (?? ?? ?? ?? )
1
4
??? ?? ?(?? ?? )
1
4 ?(
???? ??? ?? 3
?? 2
)
1
4

??? ??? 3
4
???? ?
1
4
?
2
?
1
?(
?? 1
?? 2
)
1
4
=>
?
1
?
2
?(
?? 2
?? 1
)
1
4
=(16)
1
4=2



11


19. Which one of the following modifications of the simple ideal Rankine cycle increases the thermal
efficiency and reduces the moisture content of the steam at the turbine outlet?
A. Decreasing the condenser pressure.
B. Increasing the boiler pressure.
C. Decreasing the boiler pressure.
D. Increasing the turbine inlet temperature.
Ans: option (D)
Sol: Due to increase of the turbine inlet temperature, quality of the stream at outlet of the turbine
improves. Which increases the thermal efficiency and reduces the moisture content of the steam at the
turbine outlet.

20. Consider a linear rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of
100 MPa along the length direction. Assume plane stress conditions in the plane normal to the
thickness. The Young?s modulus E = 200 MPa and Poisson?s ratio v = 0.3 are given. The principal
strains in the plane of the sheet are
A. (0.5, 0.0) B. (0.35, -0.15)
C. (0.5, -0.5) D. (0.5, -0.15)
Ans: option (D)
Sol: ?
1
=
?? 1
?? ???
?? 2
?? =
100
200
?0.3?
0
200
=0.5

?
2
=
?? 2
?? ???
?? 1
?? =
0
200
?0.3?
100
200
=?0.15


21. The figure shows an idealized plane truss. If a horizontal force of 300 N is applied at point A,
then the magnitude of the force produced in member CD is ________N.

Ans: 0

Sol:
FirstRanker.com - FirstRanker's Choice



2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6




3

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of ?? =
8+6
2
=7

6. X is an online media provider. By offering unlimited and exclusive online content at attractive
prices for a loyalty membership, X is almost forcing its customers towards its loyalty
membership. If its loyalty membership continues to grow at its current rate, within the next
eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
A. Most households that subscribe to X?s loyalty membership discontinue watching cable
television
B. Non-members prefer to watch cable television
C. The X is cancelling accounts of non-members
D. Cable television operators don?t subscribe to X?s loyalty membership
Ans: option (A)
Sol: option A is the most appropriate solution

7. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased
by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.
A. 35.70 B. 10.00
C. 37.50 D. 25.00
Ans: option (C)
Sol: Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04??? =0.04??
And the fiscal deficit in 2016 = 0.05?1.1?? =0.055??
Increase in fiscal deficit = 0.055x ? 0.04x = 0.015x
So, the percentage increase in fiscal deficit =
0.015?? 0.04?? ?100=37.5%

8. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can
empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is
opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is
_________.
A. 16.50 B. 14.50
C. 15.50 D. 13.50
Ans: option (B)
Sol: 1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(
1
6
? ?
1
12
? )=
1
3
?
Tank filled by when Q and R works for another 6 hours = 6(
1
9
? ?
1
12
? )=
1
6
?
Total tank filled in these 10 hours =
1
3
? +
1
6
? =0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in
9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours




4

9. While teaching a creative writing class in India, I was surprised at receiving stories from the
students that were all set in distant places: in the American West with cowboys and in
Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave
the writers in the once-colonised countries the confidence to see the shabby lives around them
as worthy of being ?told?.
The writer of this passage is surprised by the creative writing assignments of his students,
because __________.
A. Some of the students had written about ice cubes and cowboys
B. None of the students had written about ice cubes and cowboys
C. Some of the students had written stories set in foreign places
D. None of the students had written stories set in India
Ans: option (C)
Sol: option C is the most appropriate solution

10. Mola is a digital platform for taxis in a city. It offers three types of rides ? Pool, Mini and Prime.
The Table below presents the number of rides for the past four months. The platform earns one
US dollar per ride. What is the percentage share of revenue contributed by Prime to the total
revenues of Mola, for the entire duration?
Type
Month
January February March April
Pool 170 320 215 190
Mini 110 220 180 70
Prime 75 180 120 90

A. 38.74 B. 23.97
C. 25.86 D. 16.24

Ans: option (B)
Sol: Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580
Revenue contributed by Prime = 75 + 180 + 120 +90 = 465
Total revenue of Mola = 895 + 580 + 465 = 1940
So, the percentage share =
465
1940
?100=23.97%

MECHANICAL ENGINEERING
1. A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by
application of pure bending moments at its ends. The Young?s modulus of the material of the
wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.
Ans: 50
Sol: Tensile stress
?? =
?? ?? ?? =
100?10
3
1
(
1
1000?2
)=50 ??????





5

2. In an electrical discharge machining process, the breakdown voltage across inter electrode gap
(IEG) is 200 V and the capacitance of the RC circuit is 50 ?F. The energy (in J) released per
spark across the IEG is __________
Ans: 1
Sol:
?? =
1
2
??????????????????????? ????????????? ?? 2

?? =0.5?50?10
?6
?200
2
=1 ??


3. If x is the mean of data 3, x, 2 and 4, then the mode is _________
Ans: 3
Sol: ?? =
3+?? +2+4
4

4??? =3+?? +2+4
4??? ??? =3+2+4=9
?? =3
Mode is 3. (Maximum repeated value)

4. The cold forming process in which a hardened tool is pressed against a workpiece (when there is
relative motion between the tool and the workpiece) to produce a roughened surface with a
regular pattern is
A. Strip rolling B. Knurling
C. Roll forming D. Chamfering
Ans: option (B)
Sol: We provide special pattern to prevent the relative motion between contact surface. This special
pattern is known as Knurling.


5. Endurance limit of a beam subjected to pure bending decreases with
A. increase in the surface roughness and increase in the size of the beam
B. decrease in the surface roughness and decrease in the size of the beam
C. decrease in the surface roughness and increase in the size of the beam
D. increase in the surface roughness and decrease in the size of the beam
Ans: option (A)
Sol: Formula for endurance limit
?? ?? =?? ?? ??? ?? ??? ?? ??? ?? ??? ?? ?

?? ???????
?? ?? ????????? ????????????
?? ?? ??????????????? ????????????
?? ?? ????????? ????????????
?? ?? ??????????????????????? ????????????
?? ?? ?
??????????????????? ?????????????? ?
Form above formula it is clear that the Endurance limit increases with increase in size,
surface, load, temp and endurance strength.







6

6. In matrix equation [A] {X} = {R}.
? ?
4 8 4 2
8 16 4 , 1
4 4 15 4
AX
? ? ? ?
?? ??
= ? = ??
??
????
??
??
?
? ? ? ?
and ? ?
32
16 .
64
R
??
??
=
??
??
??

One of the eigenvalues of matrix [A] is
A. 4 B. 15
C. 8 D. 16
Ans: option (D)
Sol: [A] {X} = {R}.

We know ???? = ???? ;?? ??????? ?? ??????????? ??????????

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}={
32
16
64
}

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}=16{
2
1
4
}

Hence, ?? =????

7. Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number
ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit.
The Reynolds number at the exit of the pipe is___________.
Ans: 500
Sol: Reynold?s Number
???? =
?? ?? ????
?? ??
Where: -
?? ??????????? ??????????????
?? ????
??????????????? ????????????????
?? ??????????????? ???? ????????
?? ? Dynamic viscosity of Fluid
?? ?? =(
?? ?? ????
?? ?? )=
(

?? (
?? ???????? ?? ???????? ) ?? ?? )


From above expiration, Reynold?s Number is independent of flow profile. Hence, Reynold?s
Number for parabolic flow profile is 500.

8. For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure
and temperature, respectively. As per Maxwell?s relations,
p
v
s
? ??
??
?
??
is equal to
A.
T
p
v
? ??
??
?
??
B.
p
s
T
? ??
??
?
??
C.
s
T
p
?? ?
??
?
??
D.
p
T
v
? ??
?
??
?
??

Ans: option (C)
Sol: From mathematical relation expiration



7

???? = ?????? +??????
? (
????
????
)
?? = (
????
????
)
??
???????? ?????????????? ????????????????
?? ?= ?????? +??????
? (
????
????
)
?? = (
????
????
)
??

9. Hardenability of steel is a measure of
A. the ability to harden when it is cold worked
B. the maximum hardness that can be obtained when it is austenitized and then quenched
C. the ability to retain its hardness when it is heated to elevated temperatures
D. the depth to which required hardening is obtained when it is austenitized and then quenched
Ans: option (D)
Sol: The depth to which required hardening is obtained when it is austenitized and then quenched.

10. The directional derivative of the function f(x, y) = x
2
+ y
2
along a line directed from (0, 0) to (1,
1), evaluated at the point x = 1, y = 1 is
A. 2 B. ?2
C. 4?2 D. 2?2
Ans: option (D)
Sol: Directional derivative of function along the line is the scalar value of derivative along the line. i.e.
we have to calculate value of derivative of function in the direction of given line vector
? ?? = ??? (
????
????
)+ ??? (
????
????
)
? ?? = 2???+ 2???
Now, calculating the value of ? ?? in 1???+ 1???
D.D of given function is (2???+ 2??? ) ?
(??? + ?? ?)
|??? + ?? ?|
= 2 ?2

11. A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is
A.
2 D
T
?
B.
T
D

C.
D
T
?
D.
D
T

Ans: option (C)
Sol: circular pitch =
????
??

12. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the
instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of
points P and R are VP and VR, in the x and y directions, respectively. The magnitude of the
angular velocity of the body is




8

A. /3
R
V B. /3
P
V
C. 2VR D. 2VP
Ans: option (C)
Sol: The given body is a rigid body; Hence the given body will not have any deformation, and the
possible motion is translation and angular motion. we know that the angular motion of the object is
always defined as the motion about the point. Hence, first we have to find a point parallel to both
velocity ?? ?? and ?? ?? .


? Angular velocity, ?? =
???????????????? ?????????????????????????? ????????????????
?? =
?? ?? ????
=
?? ?? ????

???? =
?3
2
????????? ???? ???????????????? =
?3
2
?1=
?3
2

???? =
1
2
????????? ???? ???????????????? =
1
2
?1=
1
2


?? =
2?? ?? ?3
=
2?? ?? 1


13. Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4
m. The view factor F12 is
A. 0.25 B. 0.0625
C. 1.0 D. 0.5
Ans: option (C)
Sol: ?? 12
=1

14. The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
A.
10
01
??
??
?
??
B.
01
10
? ??
??
?
??

C.
01
10
??
??
??
D.
10
01
???
??
??

Ans: option (C)
Sol: The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
01
10
??
??
??




S



9

15. The state of stress at a point in a component is represented by a Mohr?s circle of radius 100 MPa
centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the
normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same
point is ___________ MPa.
Ans: 80
Sol:


?? =?100
2
?60
2
=80 ??????

16. One-dimensional steady state heat conduction takes place through a solid whose cross-sectional
area varies linearly in the direction of heat transfer. Assume there is no heat generation in the
solid and the thermal conductivity of the material is constant and independent of temperature.
The temperature distribution in the solid is
A. Quadratic B. Exponential
C. Logarithmic D. Linear
Ans: option (C)
Sol: Let the given body cross-sectional area varies linearly, and heat is flowing from left to right.





If there is no heat generation,
?? ????
(?????
????
????
)=0

?
?? ????
(?????
????
????
)=?0

(?????
????
????
)=??

??? (?? 0
+?? ?? ?? )
????
????
=??
???? =
? ?? ????
?? (?? 0
+?? ?? ?? )


? ????
2
1
=?
? ?? ????
?? (?? 0
+?? ?? ?? )
2
1


?? 2
??? 1
= ?
?? ?? ln(
?? ?? ?? 2
+?? 0
?? ?? ?? 1
+?? 0
)



10

17. An analytic function f(z) of complex variable z = x + I y may be written as f(z) = u(x, y) + iv (x,
y). Then, u(x, y) and v(x, y) must satisfy
A.
uv
xy
??
=?
??
and
uv
yx
??
=
??

B.
uv
xy
??
=?
??
and
uv
yx
??
=?
??

C.
uv
xy
??
=
??
and
uv
yx
??
=?
??

D.
uv
xy
??
=
??
and
uv
yx
??
=
??

Ans: option (C)
Sol: If f(z) = u(x, y) + iv(x, y) is analytic function then it must satisfy the following relations.

????
????
=
????
????


????
????
=?
????
????


18. A thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is
losing heat to the surroundings by natural convection. The temperatures of the plate and the
surroundings, and the properties of the surrounding fluid, are constant. The relationship between
the average Nusselt and Rayleigh numbers is given as Nu = K Ra ?, where K is a constant. The
length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the
plate is increased to 16L keeping all other factors constant.

If the average heat transfer coefficient for the first plate is h1 and that for the second plate is h2,
the value of the ratio h1/h2 is____________.
Ans: 2
Sol: ?? ?? =?? (?? ?? )
1
4
We know that ?? ?? =?? ?? ?? ??
?? ?? =?? (?? ?? ?? ?? )
1
4
??? ?? ?(?? ?? )
1
4 ?(
???? ??? ?? 3
?? 2
)
1
4

??? ??? 3
4
???? ?
1
4
?
2
?
1
?(
?? 1
?? 2
)
1
4
=>
?
1
?
2
?(
?? 2
?? 1
)
1
4
=(16)
1
4=2



11


19. Which one of the following modifications of the simple ideal Rankine cycle increases the thermal
efficiency and reduces the moisture content of the steam at the turbine outlet?
A. Decreasing the condenser pressure.
B. Increasing the boiler pressure.
C. Decreasing the boiler pressure.
D. Increasing the turbine inlet temperature.
Ans: option (D)
Sol: Due to increase of the turbine inlet temperature, quality of the stream at outlet of the turbine
improves. Which increases the thermal efficiency and reduces the moisture content of the steam at the
turbine outlet.

20. Consider a linear rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of
100 MPa along the length direction. Assume plane stress conditions in the plane normal to the
thickness. The Young?s modulus E = 200 MPa and Poisson?s ratio v = 0.3 are given. The principal
strains in the plane of the sheet are
A. (0.5, 0.0) B. (0.35, -0.15)
C. (0.5, -0.5) D. (0.5, -0.15)
Ans: option (D)
Sol: ?
1
=
?? 1
?? ???
?? 2
?? =
100
200
?0.3?
0
200
=0.5

?
2
=
?? 2
?? ???
?? 1
?? =
0
200
?0.3?
100
200
=?0.15


21. The figure shows an idealized plane truss. If a horizontal force of 300 N is applied at point A,
then the magnitude of the force produced in member CD is ________N.

Ans: 0

Sol:



12



The momentum about the point A must be zero, because there is no deformation of any truss.
Hence, ?? ????
=0 [?? ????
is not passing through the point A]

22. The fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase
in
A. freezing range
B. surface tension
C. degree of superheat
D. viscosity
Ans: option (C)
Sol: Fluidity of molten metal of cast alloys increases with increase in degree of superheat.

23. The most common limit gage used for inspecting the hole diameter is
A. Ring gage B. Snap gage
C. Plug gage D. Master gage
Ans: option (C)
Sol: The most common limit gage used for inspecting the hole diameter is Plug gage.

24. The differential equation 45
dy
y
dx
+= is valid in the domain 0 ? x ? 1 with y(0) = 2.25. The
solution of the differential equation is
A. y = e
-4x
+ 1.25
B. y = e
4x
+ 5
C. y = e
4x
+ 1.25
D. y = e
-4x
+ 5
Ans: option (A)
Sol: The given equation is.
FirstRanker.com - FirstRanker's Choice



2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6




3

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of ?? =
8+6
2
=7

6. X is an online media provider. By offering unlimited and exclusive online content at attractive
prices for a loyalty membership, X is almost forcing its customers towards its loyalty
membership. If its loyalty membership continues to grow at its current rate, within the next
eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
A. Most households that subscribe to X?s loyalty membership discontinue watching cable
television
B. Non-members prefer to watch cable television
C. The X is cancelling accounts of non-members
D. Cable television operators don?t subscribe to X?s loyalty membership
Ans: option (A)
Sol: option A is the most appropriate solution

7. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased
by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.
A. 35.70 B. 10.00
C. 37.50 D. 25.00
Ans: option (C)
Sol: Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04??? =0.04??
And the fiscal deficit in 2016 = 0.05?1.1?? =0.055??
Increase in fiscal deficit = 0.055x ? 0.04x = 0.015x
So, the percentage increase in fiscal deficit =
0.015?? 0.04?? ?100=37.5%

8. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can
empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is
opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is
_________.
A. 16.50 B. 14.50
C. 15.50 D. 13.50
Ans: option (B)
Sol: 1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(
1
6
? ?
1
12
? )=
1
3
?
Tank filled by when Q and R works for another 6 hours = 6(
1
9
? ?
1
12
? )=
1
6
?
Total tank filled in these 10 hours =
1
3
? +
1
6
? =0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in
9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours




4

9. While teaching a creative writing class in India, I was surprised at receiving stories from the
students that were all set in distant places: in the American West with cowboys and in
Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave
the writers in the once-colonised countries the confidence to see the shabby lives around them
as worthy of being ?told?.
The writer of this passage is surprised by the creative writing assignments of his students,
because __________.
A. Some of the students had written about ice cubes and cowboys
B. None of the students had written about ice cubes and cowboys
C. Some of the students had written stories set in foreign places
D. None of the students had written stories set in India
Ans: option (C)
Sol: option C is the most appropriate solution

10. Mola is a digital platform for taxis in a city. It offers three types of rides ? Pool, Mini and Prime.
The Table below presents the number of rides for the past four months. The platform earns one
US dollar per ride. What is the percentage share of revenue contributed by Prime to the total
revenues of Mola, for the entire duration?
Type
Month
January February March April
Pool 170 320 215 190
Mini 110 220 180 70
Prime 75 180 120 90

A. 38.74 B. 23.97
C. 25.86 D. 16.24

Ans: option (B)
Sol: Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580
Revenue contributed by Prime = 75 + 180 + 120 +90 = 465
Total revenue of Mola = 895 + 580 + 465 = 1940
So, the percentage share =
465
1940
?100=23.97%

MECHANICAL ENGINEERING
1. A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by
application of pure bending moments at its ends. The Young?s modulus of the material of the
wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.
Ans: 50
Sol: Tensile stress
?? =
?? ?? ?? =
100?10
3
1
(
1
1000?2
)=50 ??????





5

2. In an electrical discharge machining process, the breakdown voltage across inter electrode gap
(IEG) is 200 V and the capacitance of the RC circuit is 50 ?F. The energy (in J) released per
spark across the IEG is __________
Ans: 1
Sol:
?? =
1
2
??????????????????????? ????????????? ?? 2

?? =0.5?50?10
?6
?200
2
=1 ??


3. If x is the mean of data 3, x, 2 and 4, then the mode is _________
Ans: 3
Sol: ?? =
3+?? +2+4
4

4??? =3+?? +2+4
4??? ??? =3+2+4=9
?? =3
Mode is 3. (Maximum repeated value)

4. The cold forming process in which a hardened tool is pressed against a workpiece (when there is
relative motion between the tool and the workpiece) to produce a roughened surface with a
regular pattern is
A. Strip rolling B. Knurling
C. Roll forming D. Chamfering
Ans: option (B)
Sol: We provide special pattern to prevent the relative motion between contact surface. This special
pattern is known as Knurling.


5. Endurance limit of a beam subjected to pure bending decreases with
A. increase in the surface roughness and increase in the size of the beam
B. decrease in the surface roughness and decrease in the size of the beam
C. decrease in the surface roughness and increase in the size of the beam
D. increase in the surface roughness and decrease in the size of the beam
Ans: option (A)
Sol: Formula for endurance limit
?? ?? =?? ?? ??? ?? ??? ?? ??? ?? ??? ?? ?

?? ???????
?? ?? ????????? ????????????
?? ?? ??????????????? ????????????
?? ?? ????????? ????????????
?? ?? ??????????????????????? ????????????
?? ?? ?
??????????????????? ?????????????? ?
Form above formula it is clear that the Endurance limit increases with increase in size,
surface, load, temp and endurance strength.







6

6. In matrix equation [A] {X} = {R}.
? ?
4 8 4 2
8 16 4 , 1
4 4 15 4
AX
? ? ? ?
?? ??
= ? = ??
??
????
??
??
?
? ? ? ?
and ? ?
32
16 .
64
R
??
??
=
??
??
??

One of the eigenvalues of matrix [A] is
A. 4 B. 15
C. 8 D. 16
Ans: option (D)
Sol: [A] {X} = {R}.

We know ???? = ???? ;?? ??????? ?? ??????????? ??????????

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}={
32
16
64
}

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}=16{
2
1
4
}

Hence, ?? =????

7. Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number
ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit.
The Reynolds number at the exit of the pipe is___________.
Ans: 500
Sol: Reynold?s Number
???? =
?? ?? ????
?? ??
Where: -
?? ??????????? ??????????????
?? ????
??????????????? ????????????????
?? ??????????????? ???? ????????
?? ? Dynamic viscosity of Fluid
?? ?? =(
?? ?? ????
?? ?? )=
(

?? (
?? ???????? ?? ???????? ) ?? ?? )


From above expiration, Reynold?s Number is independent of flow profile. Hence, Reynold?s
Number for parabolic flow profile is 500.

8. For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure
and temperature, respectively. As per Maxwell?s relations,
p
v
s
? ??
??
?
??
is equal to
A.
T
p
v
? ??
??
?
??
B.
p
s
T
? ??
??
?
??
C.
s
T
p
?? ?
??
?
??
D.
p
T
v
? ??
?
??
?
??

Ans: option (C)
Sol: From mathematical relation expiration



7

???? = ?????? +??????
? (
????
????
)
?? = (
????
????
)
??
???????? ?????????????? ????????????????
?? ?= ?????? +??????
? (
????
????
)
?? = (
????
????
)
??

9. Hardenability of steel is a measure of
A. the ability to harden when it is cold worked
B. the maximum hardness that can be obtained when it is austenitized and then quenched
C. the ability to retain its hardness when it is heated to elevated temperatures
D. the depth to which required hardening is obtained when it is austenitized and then quenched
Ans: option (D)
Sol: The depth to which required hardening is obtained when it is austenitized and then quenched.

10. The directional derivative of the function f(x, y) = x
2
+ y
2
along a line directed from (0, 0) to (1,
1), evaluated at the point x = 1, y = 1 is
A. 2 B. ?2
C. 4?2 D. 2?2
Ans: option (D)
Sol: Directional derivative of function along the line is the scalar value of derivative along the line. i.e.
we have to calculate value of derivative of function in the direction of given line vector
? ?? = ??? (
????
????
)+ ??? (
????
????
)
? ?? = 2???+ 2???
Now, calculating the value of ? ?? in 1???+ 1???
D.D of given function is (2???+ 2??? ) ?
(??? + ?? ?)
|??? + ?? ?|
= 2 ?2

11. A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is
A.
2 D
T
?
B.
T
D

C.
D
T
?
D.
D
T

Ans: option (C)
Sol: circular pitch =
????
??

12. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the
instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of
points P and R are VP and VR, in the x and y directions, respectively. The magnitude of the
angular velocity of the body is




8

A. /3
R
V B. /3
P
V
C. 2VR D. 2VP
Ans: option (C)
Sol: The given body is a rigid body; Hence the given body will not have any deformation, and the
possible motion is translation and angular motion. we know that the angular motion of the object is
always defined as the motion about the point. Hence, first we have to find a point parallel to both
velocity ?? ?? and ?? ?? .


? Angular velocity, ?? =
???????????????? ?????????????????????????? ????????????????
?? =
?? ?? ????
=
?? ?? ????

???? =
?3
2
????????? ???? ???????????????? =
?3
2
?1=
?3
2

???? =
1
2
????????? ???? ???????????????? =
1
2
?1=
1
2


?? =
2?? ?? ?3
=
2?? ?? 1


13. Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4
m. The view factor F12 is
A. 0.25 B. 0.0625
C. 1.0 D. 0.5
Ans: option (C)
Sol: ?? 12
=1

14. The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
A.
10
01
??
??
?
??
B.
01
10
? ??
??
?
??

C.
01
10
??
??
??
D.
10
01
???
??
??

Ans: option (C)
Sol: The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
01
10
??
??
??




S



9

15. The state of stress at a point in a component is represented by a Mohr?s circle of radius 100 MPa
centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the
normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same
point is ___________ MPa.
Ans: 80
Sol:


?? =?100
2
?60
2
=80 ??????

16. One-dimensional steady state heat conduction takes place through a solid whose cross-sectional
area varies linearly in the direction of heat transfer. Assume there is no heat generation in the
solid and the thermal conductivity of the material is constant and independent of temperature.
The temperature distribution in the solid is
A. Quadratic B. Exponential
C. Logarithmic D. Linear
Ans: option (C)
Sol: Let the given body cross-sectional area varies linearly, and heat is flowing from left to right.





If there is no heat generation,
?? ????
(?????
????
????
)=0

?
?? ????
(?????
????
????
)=?0

(?????
????
????
)=??

??? (?? 0
+?? ?? ?? )
????
????
=??
???? =
? ?? ????
?? (?? 0
+?? ?? ?? )


? ????
2
1
=?
? ?? ????
?? (?? 0
+?? ?? ?? )
2
1


?? 2
??? 1
= ?
?? ?? ln(
?? ?? ?? 2
+?? 0
?? ?? ?? 1
+?? 0
)



10

17. An analytic function f(z) of complex variable z = x + I y may be written as f(z) = u(x, y) + iv (x,
y). Then, u(x, y) and v(x, y) must satisfy
A.
uv
xy
??
=?
??
and
uv
yx
??
=
??

B.
uv
xy
??
=?
??
and
uv
yx
??
=?
??

C.
uv
xy
??
=
??
and
uv
yx
??
=?
??

D.
uv
xy
??
=
??
and
uv
yx
??
=
??

Ans: option (C)
Sol: If f(z) = u(x, y) + iv(x, y) is analytic function then it must satisfy the following relations.

????
????
=
????
????


????
????
=?
????
????


18. A thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is
losing heat to the surroundings by natural convection. The temperatures of the plate and the
surroundings, and the properties of the surrounding fluid, are constant. The relationship between
the average Nusselt and Rayleigh numbers is given as Nu = K Ra ?, where K is a constant. The
length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the
plate is increased to 16L keeping all other factors constant.

If the average heat transfer coefficient for the first plate is h1 and that for the second plate is h2,
the value of the ratio h1/h2 is____________.
Ans: 2
Sol: ?? ?? =?? (?? ?? )
1
4
We know that ?? ?? =?? ?? ?? ??
?? ?? =?? (?? ?? ?? ?? )
1
4
??? ?? ?(?? ?? )
1
4 ?(
???? ??? ?? 3
?? 2
)
1
4

??? ??? 3
4
???? ?
1
4
?
2
?
1
?(
?? 1
?? 2
)
1
4
=>
?
1
?
2
?(
?? 2
?? 1
)
1
4
=(16)
1
4=2



11


19. Which one of the following modifications of the simple ideal Rankine cycle increases the thermal
efficiency and reduces the moisture content of the steam at the turbine outlet?
A. Decreasing the condenser pressure.
B. Increasing the boiler pressure.
C. Decreasing the boiler pressure.
D. Increasing the turbine inlet temperature.
Ans: option (D)
Sol: Due to increase of the turbine inlet temperature, quality of the stream at outlet of the turbine
improves. Which increases the thermal efficiency and reduces the moisture content of the steam at the
turbine outlet.

20. Consider a linear rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of
100 MPa along the length direction. Assume plane stress conditions in the plane normal to the
thickness. The Young?s modulus E = 200 MPa and Poisson?s ratio v = 0.3 are given. The principal
strains in the plane of the sheet are
A. (0.5, 0.0) B. (0.35, -0.15)
C. (0.5, -0.5) D. (0.5, -0.15)
Ans: option (D)
Sol: ?
1
=
?? 1
?? ???
?? 2
?? =
100
200
?0.3?
0
200
=0.5

?
2
=
?? 2
?? ???
?? 1
?? =
0
200
?0.3?
100
200
=?0.15


21. The figure shows an idealized plane truss. If a horizontal force of 300 N is applied at point A,
then the magnitude of the force produced in member CD is ________N.

Ans: 0

Sol:



12



The momentum about the point A must be zero, because there is no deformation of any truss.
Hence, ?? ????
=0 [?? ????
is not passing through the point A]

22. The fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase
in
A. freezing range
B. surface tension
C. degree of superheat
D. viscosity
Ans: option (C)
Sol: Fluidity of molten metal of cast alloys increases with increase in degree of superheat.

23. The most common limit gage used for inspecting the hole diameter is
A. Ring gage B. Snap gage
C. Plug gage D. Master gage
Ans: option (C)
Sol: The most common limit gage used for inspecting the hole diameter is Plug gage.

24. The differential equation 45
dy
y
dx
+= is valid in the domain 0 ? x ? 1 with y(0) = 2.25. The
solution of the differential equation is
A. y = e
-4x
+ 1.25
B. y = e
4x
+ 5
C. y = e
4x
+ 1.25
D. y = e
-4x
+ 5
Ans: option (A)
Sol: The given equation is.



13

???? ???? +4?? =5
If Integration factor = ?? ?4????
=?? 4??
? ?? ????? =?5????? ???? +??
? ?? ??? 4?? =5?
?? 4?? 4
+??
? ?? ??? 4?? =5?
?? 4?? 4
+?? ?.( 1)
Now for at x=0,
? 2.25 =
5
4
+ ??
? ?? =1
? Using the value of C in equ (1)
? ?? ?
?? 4?? ?? 4?? =
5
?? 4?? ?
?? 4?? 4
+
?? ?? 4??
? ?? =1.25+ ?? ?4??

25. A two-dimensional incompressible frictionless flow field is given by
??
. u xi yj =? If ? is the density
of the fluid, the expression for pressure gradient vector at any point in the flow field is given as
A.
( )
22
??
x i y j ??+ B.
( )
??
xi yj ??+
C.
( )
??
xi yj ? + D.
( )
??
xi yj ? ?
Ans: option (B)
Sol: Euler?s Equation of motion in 2D.

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

As there is no extra force acting on the fluid.
?? ?? ?????? ?? ?? =0
Now form the given expiration, u=x & v=y
?
????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????


?0+ ?? ?1+0+0=0?
1
?? ????
????

0+ 0+?? ?1+0=0?
1
?? ????
????

??????????? ???????? ?????? =
????
????
???+
????
????
???= ??? (?? ???+?? ??? )

FirstRanker.com - FirstRanker's Choice



2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6




3

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of ?? =
8+6
2
=7

6. X is an online media provider. By offering unlimited and exclusive online content at attractive
prices for a loyalty membership, X is almost forcing its customers towards its loyalty
membership. If its loyalty membership continues to grow at its current rate, within the next
eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
A. Most households that subscribe to X?s loyalty membership discontinue watching cable
television
B. Non-members prefer to watch cable television
C. The X is cancelling accounts of non-members
D. Cable television operators don?t subscribe to X?s loyalty membership
Ans: option (A)
Sol: option A is the most appropriate solution

7. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased
by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.
A. 35.70 B. 10.00
C. 37.50 D. 25.00
Ans: option (C)
Sol: Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04??? =0.04??
And the fiscal deficit in 2016 = 0.05?1.1?? =0.055??
Increase in fiscal deficit = 0.055x ? 0.04x = 0.015x
So, the percentage increase in fiscal deficit =
0.015?? 0.04?? ?100=37.5%

8. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can
empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is
opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is
_________.
A. 16.50 B. 14.50
C. 15.50 D. 13.50
Ans: option (B)
Sol: 1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(
1
6
? ?
1
12
? )=
1
3
?
Tank filled by when Q and R works for another 6 hours = 6(
1
9
? ?
1
12
? )=
1
6
?
Total tank filled in these 10 hours =
1
3
? +
1
6
? =0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in
9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours




4

9. While teaching a creative writing class in India, I was surprised at receiving stories from the
students that were all set in distant places: in the American West with cowboys and in
Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave
the writers in the once-colonised countries the confidence to see the shabby lives around them
as worthy of being ?told?.
The writer of this passage is surprised by the creative writing assignments of his students,
because __________.
A. Some of the students had written about ice cubes and cowboys
B. None of the students had written about ice cubes and cowboys
C. Some of the students had written stories set in foreign places
D. None of the students had written stories set in India
Ans: option (C)
Sol: option C is the most appropriate solution

10. Mola is a digital platform for taxis in a city. It offers three types of rides ? Pool, Mini and Prime.
The Table below presents the number of rides for the past four months. The platform earns one
US dollar per ride. What is the percentage share of revenue contributed by Prime to the total
revenues of Mola, for the entire duration?
Type
Month
January February March April
Pool 170 320 215 190
Mini 110 220 180 70
Prime 75 180 120 90

A. 38.74 B. 23.97
C. 25.86 D. 16.24

Ans: option (B)
Sol: Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580
Revenue contributed by Prime = 75 + 180 + 120 +90 = 465
Total revenue of Mola = 895 + 580 + 465 = 1940
So, the percentage share =
465
1940
?100=23.97%

MECHANICAL ENGINEERING
1. A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by
application of pure bending moments at its ends. The Young?s modulus of the material of the
wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.
Ans: 50
Sol: Tensile stress
?? =
?? ?? ?? =
100?10
3
1
(
1
1000?2
)=50 ??????





5

2. In an electrical discharge machining process, the breakdown voltage across inter electrode gap
(IEG) is 200 V and the capacitance of the RC circuit is 50 ?F. The energy (in J) released per
spark across the IEG is __________
Ans: 1
Sol:
?? =
1
2
??????????????????????? ????????????? ?? 2

?? =0.5?50?10
?6
?200
2
=1 ??


3. If x is the mean of data 3, x, 2 and 4, then the mode is _________
Ans: 3
Sol: ?? =
3+?? +2+4
4

4??? =3+?? +2+4
4??? ??? =3+2+4=9
?? =3
Mode is 3. (Maximum repeated value)

4. The cold forming process in which a hardened tool is pressed against a workpiece (when there is
relative motion between the tool and the workpiece) to produce a roughened surface with a
regular pattern is
A. Strip rolling B. Knurling
C. Roll forming D. Chamfering
Ans: option (B)
Sol: We provide special pattern to prevent the relative motion between contact surface. This special
pattern is known as Knurling.


5. Endurance limit of a beam subjected to pure bending decreases with
A. increase in the surface roughness and increase in the size of the beam
B. decrease in the surface roughness and decrease in the size of the beam
C. decrease in the surface roughness and increase in the size of the beam
D. increase in the surface roughness and decrease in the size of the beam
Ans: option (A)
Sol: Formula for endurance limit
?? ?? =?? ?? ??? ?? ??? ?? ??? ?? ??? ?? ?

?? ???????
?? ?? ????????? ????????????
?? ?? ??????????????? ????????????
?? ?? ????????? ????????????
?? ?? ??????????????????????? ????????????
?? ?? ?
??????????????????? ?????????????? ?
Form above formula it is clear that the Endurance limit increases with increase in size,
surface, load, temp and endurance strength.







6

6. In matrix equation [A] {X} = {R}.
? ?
4 8 4 2
8 16 4 , 1
4 4 15 4
AX
? ? ? ?
?? ??
= ? = ??
??
????
??
??
?
? ? ? ?
and ? ?
32
16 .
64
R
??
??
=
??
??
??

One of the eigenvalues of matrix [A] is
A. 4 B. 15
C. 8 D. 16
Ans: option (D)
Sol: [A] {X} = {R}.

We know ???? = ???? ;?? ??????? ?? ??????????? ??????????

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}={
32
16
64
}

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}=16{
2
1
4
}

Hence, ?? =????

7. Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number
ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit.
The Reynolds number at the exit of the pipe is___________.
Ans: 500
Sol: Reynold?s Number
???? =
?? ?? ????
?? ??
Where: -
?? ??????????? ??????????????
?? ????
??????????????? ????????????????
?? ??????????????? ???? ????????
?? ? Dynamic viscosity of Fluid
?? ?? =(
?? ?? ????
?? ?? )=
(

?? (
?? ???????? ?? ???????? ) ?? ?? )


From above expiration, Reynold?s Number is independent of flow profile. Hence, Reynold?s
Number for parabolic flow profile is 500.

8. For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure
and temperature, respectively. As per Maxwell?s relations,
p
v
s
? ??
??
?
??
is equal to
A.
T
p
v
? ??
??
?
??
B.
p
s
T
? ??
??
?
??
C.
s
T
p
?? ?
??
?
??
D.
p
T
v
? ??
?
??
?
??

Ans: option (C)
Sol: From mathematical relation expiration



7

???? = ?????? +??????
? (
????
????
)
?? = (
????
????
)
??
???????? ?????????????? ????????????????
?? ?= ?????? +??????
? (
????
????
)
?? = (
????
????
)
??

9. Hardenability of steel is a measure of
A. the ability to harden when it is cold worked
B. the maximum hardness that can be obtained when it is austenitized and then quenched
C. the ability to retain its hardness when it is heated to elevated temperatures
D. the depth to which required hardening is obtained when it is austenitized and then quenched
Ans: option (D)
Sol: The depth to which required hardening is obtained when it is austenitized and then quenched.

10. The directional derivative of the function f(x, y) = x
2
+ y
2
along a line directed from (0, 0) to (1,
1), evaluated at the point x = 1, y = 1 is
A. 2 B. ?2
C. 4?2 D. 2?2
Ans: option (D)
Sol: Directional derivative of function along the line is the scalar value of derivative along the line. i.e.
we have to calculate value of derivative of function in the direction of given line vector
? ?? = ??? (
????
????
)+ ??? (
????
????
)
? ?? = 2???+ 2???
Now, calculating the value of ? ?? in 1???+ 1???
D.D of given function is (2???+ 2??? ) ?
(??? + ?? ?)
|??? + ?? ?|
= 2 ?2

11. A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is
A.
2 D
T
?
B.
T
D

C.
D
T
?
D.
D
T

Ans: option (C)
Sol: circular pitch =
????
??

12. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the
instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of
points P and R are VP and VR, in the x and y directions, respectively. The magnitude of the
angular velocity of the body is




8

A. /3
R
V B. /3
P
V
C. 2VR D. 2VP
Ans: option (C)
Sol: The given body is a rigid body; Hence the given body will not have any deformation, and the
possible motion is translation and angular motion. we know that the angular motion of the object is
always defined as the motion about the point. Hence, first we have to find a point parallel to both
velocity ?? ?? and ?? ?? .


? Angular velocity, ?? =
???????????????? ?????????????????????????? ????????????????
?? =
?? ?? ????
=
?? ?? ????

???? =
?3
2
????????? ???? ???????????????? =
?3
2
?1=
?3
2

???? =
1
2
????????? ???? ???????????????? =
1
2
?1=
1
2


?? =
2?? ?? ?3
=
2?? ?? 1


13. Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4
m. The view factor F12 is
A. 0.25 B. 0.0625
C. 1.0 D. 0.5
Ans: option (C)
Sol: ?? 12
=1

14. The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
A.
10
01
??
??
?
??
B.
01
10
? ??
??
?
??

C.
01
10
??
??
??
D.
10
01
???
??
??

Ans: option (C)
Sol: The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
01
10
??
??
??




S



9

15. The state of stress at a point in a component is represented by a Mohr?s circle of radius 100 MPa
centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the
normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same
point is ___________ MPa.
Ans: 80
Sol:


?? =?100
2
?60
2
=80 ??????

16. One-dimensional steady state heat conduction takes place through a solid whose cross-sectional
area varies linearly in the direction of heat transfer. Assume there is no heat generation in the
solid and the thermal conductivity of the material is constant and independent of temperature.
The temperature distribution in the solid is
A. Quadratic B. Exponential
C. Logarithmic D. Linear
Ans: option (C)
Sol: Let the given body cross-sectional area varies linearly, and heat is flowing from left to right.





If there is no heat generation,
?? ????
(?????
????
????
)=0

?
?? ????
(?????
????
????
)=?0

(?????
????
????
)=??

??? (?? 0
+?? ?? ?? )
????
????
=??
???? =
? ?? ????
?? (?? 0
+?? ?? ?? )


? ????
2
1
=?
? ?? ????
?? (?? 0
+?? ?? ?? )
2
1


?? 2
??? 1
= ?
?? ?? ln(
?? ?? ?? 2
+?? 0
?? ?? ?? 1
+?? 0
)



10

17. An analytic function f(z) of complex variable z = x + I y may be written as f(z) = u(x, y) + iv (x,
y). Then, u(x, y) and v(x, y) must satisfy
A.
uv
xy
??
=?
??
and
uv
yx
??
=
??

B.
uv
xy
??
=?
??
and
uv
yx
??
=?
??

C.
uv
xy
??
=
??
and
uv
yx
??
=?
??

D.
uv
xy
??
=
??
and
uv
yx
??
=
??

Ans: option (C)
Sol: If f(z) = u(x, y) + iv(x, y) is analytic function then it must satisfy the following relations.

????
????
=
????
????


????
????
=?
????
????


18. A thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is
losing heat to the surroundings by natural convection. The temperatures of the plate and the
surroundings, and the properties of the surrounding fluid, are constant. The relationship between
the average Nusselt and Rayleigh numbers is given as Nu = K Ra ?, where K is a constant. The
length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the
plate is increased to 16L keeping all other factors constant.

If the average heat transfer coefficient for the first plate is h1 and that for the second plate is h2,
the value of the ratio h1/h2 is____________.
Ans: 2
Sol: ?? ?? =?? (?? ?? )
1
4
We know that ?? ?? =?? ?? ?? ??
?? ?? =?? (?? ?? ?? ?? )
1
4
??? ?? ?(?? ?? )
1
4 ?(
???? ??? ?? 3
?? 2
)
1
4

??? ??? 3
4
???? ?
1
4
?
2
?
1
?(
?? 1
?? 2
)
1
4
=>
?
1
?
2
?(
?? 2
?? 1
)
1
4
=(16)
1
4=2



11


19. Which one of the following modifications of the simple ideal Rankine cycle increases the thermal
efficiency and reduces the moisture content of the steam at the turbine outlet?
A. Decreasing the condenser pressure.
B. Increasing the boiler pressure.
C. Decreasing the boiler pressure.
D. Increasing the turbine inlet temperature.
Ans: option (D)
Sol: Due to increase of the turbine inlet temperature, quality of the stream at outlet of the turbine
improves. Which increases the thermal efficiency and reduces the moisture content of the steam at the
turbine outlet.

20. Consider a linear rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of
100 MPa along the length direction. Assume plane stress conditions in the plane normal to the
thickness. The Young?s modulus E = 200 MPa and Poisson?s ratio v = 0.3 are given. The principal
strains in the plane of the sheet are
A. (0.5, 0.0) B. (0.35, -0.15)
C. (0.5, -0.5) D. (0.5, -0.15)
Ans: option (D)
Sol: ?
1
=
?? 1
?? ???
?? 2
?? =
100
200
?0.3?
0
200
=0.5

?
2
=
?? 2
?? ???
?? 1
?? =
0
200
?0.3?
100
200
=?0.15


21. The figure shows an idealized plane truss. If a horizontal force of 300 N is applied at point A,
then the magnitude of the force produced in member CD is ________N.

Ans: 0

Sol:



12



The momentum about the point A must be zero, because there is no deformation of any truss.
Hence, ?? ????
=0 [?? ????
is not passing through the point A]

22. The fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase
in
A. freezing range
B. surface tension
C. degree of superheat
D. viscosity
Ans: option (C)
Sol: Fluidity of molten metal of cast alloys increases with increase in degree of superheat.

23. The most common limit gage used for inspecting the hole diameter is
A. Ring gage B. Snap gage
C. Plug gage D. Master gage
Ans: option (C)
Sol: The most common limit gage used for inspecting the hole diameter is Plug gage.

24. The differential equation 45
dy
y
dx
+= is valid in the domain 0 ? x ? 1 with y(0) = 2.25. The
solution of the differential equation is
A. y = e
-4x
+ 1.25
B. y = e
4x
+ 5
C. y = e
4x
+ 1.25
D. y = e
-4x
+ 5
Ans: option (A)
Sol: The given equation is.



13

???? ???? +4?? =5
If Integration factor = ?? ?4????
=?? 4??
? ?? ????? =?5????? ???? +??
? ?? ??? 4?? =5?
?? 4?? 4
+??
? ?? ??? 4?? =5?
?? 4?? 4
+?? ?.( 1)
Now for at x=0,
? 2.25 =
5
4
+ ??
? ?? =1
? Using the value of C in equ (1)
? ?? ?
?? 4?? ?? 4?? =
5
?? 4?? ?
?? 4?? 4
+
?? ?? 4??
? ?? =1.25+ ?? ?4??

25. A two-dimensional incompressible frictionless flow field is given by
??
. u xi yj =? If ? is the density
of the fluid, the expression for pressure gradient vector at any point in the flow field is given as
A.
( )
22
??
x i y j ??+ B.
( )
??
xi yj ??+
C.
( )
??
xi yj ? + D.
( )
??
xi yj ? ?
Ans: option (B)
Sol: Euler?s Equation of motion in 2D.

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

As there is no extra force acting on the fluid.
?? ?? ?????? ?? ?? =0
Now form the given expiration, u=x & v=y
?
????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????


?0+ ?? ?1+0+0=0?
1
?? ????
????

0+ 0+?? ?1+0=0?
1
?? ????
????

??????????? ???????? ?????? =
????
????
???+
????
????
???= ??? (?? ???+?? ??? )




14

26. A short shoe external drum brake is shown in the figure. The diameter of the brake drum is 500
mm. The dimensions a = 1000 mm, b = 500 mm and c = 200 mm. The coefficient of friction
between the drum and the shoe is 0.35. The force applied on the lever F = 100 N as shown in
the figure. The drum is rotating anti-clockwise. The braking torque on the drum is _______N.m
(round off to two decimal places).

Ans: 20.34
Sol:

Applying momentum about point O.

??? ?? =0

?? ??? +?? ?? ?? ??? ??? ?? ??? =0
?? ?? =232.55
Breaking Torque = ?? ?? ?? ?? ?? = 20.34

27. A uniform disc with radius r and a mass of m kg is mounted centrally on a horizontal axle of
negligible mass and length of 1.5r. The disc spins counter-clockwise about the axle with angular
speed ?, when viewed from the right-hand side bearing, Q. The axle precesses about a vertical
axis at
?p = ?/10 in the clockwise direction when viewed from above. Let RP and RQ (positive upwards)
be the resultant reaction forces due to the mass and the gyroscopic effect, at bearings P and Q,
respectively. Assuming ?
2
r = 300 m/s
2
and g = 10 m/s
2
, the ratio of the larger to the smaller
bearing reaction force (considering appropriate signs) is __________.
FirstRanker.com - FirstRanker's Choice



2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6




3

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of ?? =
8+6
2
=7

6. X is an online media provider. By offering unlimited and exclusive online content at attractive
prices for a loyalty membership, X is almost forcing its customers towards its loyalty
membership. If its loyalty membership continues to grow at its current rate, within the next
eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
A. Most households that subscribe to X?s loyalty membership discontinue watching cable
television
B. Non-members prefer to watch cable television
C. The X is cancelling accounts of non-members
D. Cable television operators don?t subscribe to X?s loyalty membership
Ans: option (A)
Sol: option A is the most appropriate solution

7. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased
by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.
A. 35.70 B. 10.00
C. 37.50 D. 25.00
Ans: option (C)
Sol: Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04??? =0.04??
And the fiscal deficit in 2016 = 0.05?1.1?? =0.055??
Increase in fiscal deficit = 0.055x ? 0.04x = 0.015x
So, the percentage increase in fiscal deficit =
0.015?? 0.04?? ?100=37.5%

8. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can
empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is
opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is
_________.
A. 16.50 B. 14.50
C. 15.50 D. 13.50
Ans: option (B)
Sol: 1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(
1
6
? ?
1
12
? )=
1
3
?
Tank filled by when Q and R works for another 6 hours = 6(
1
9
? ?
1
12
? )=
1
6
?
Total tank filled in these 10 hours =
1
3
? +
1
6
? =0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in
9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours




4

9. While teaching a creative writing class in India, I was surprised at receiving stories from the
students that were all set in distant places: in the American West with cowboys and in
Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave
the writers in the once-colonised countries the confidence to see the shabby lives around them
as worthy of being ?told?.
The writer of this passage is surprised by the creative writing assignments of his students,
because __________.
A. Some of the students had written about ice cubes and cowboys
B. None of the students had written about ice cubes and cowboys
C. Some of the students had written stories set in foreign places
D. None of the students had written stories set in India
Ans: option (C)
Sol: option C is the most appropriate solution

10. Mola is a digital platform for taxis in a city. It offers three types of rides ? Pool, Mini and Prime.
The Table below presents the number of rides for the past four months. The platform earns one
US dollar per ride. What is the percentage share of revenue contributed by Prime to the total
revenues of Mola, for the entire duration?
Type
Month
January February March April
Pool 170 320 215 190
Mini 110 220 180 70
Prime 75 180 120 90

A. 38.74 B. 23.97
C. 25.86 D. 16.24

Ans: option (B)
Sol: Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580
Revenue contributed by Prime = 75 + 180 + 120 +90 = 465
Total revenue of Mola = 895 + 580 + 465 = 1940
So, the percentage share =
465
1940
?100=23.97%

MECHANICAL ENGINEERING
1. A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by
application of pure bending moments at its ends. The Young?s modulus of the material of the
wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.
Ans: 50
Sol: Tensile stress
?? =
?? ?? ?? =
100?10
3
1
(
1
1000?2
)=50 ??????





5

2. In an electrical discharge machining process, the breakdown voltage across inter electrode gap
(IEG) is 200 V and the capacitance of the RC circuit is 50 ?F. The energy (in J) released per
spark across the IEG is __________
Ans: 1
Sol:
?? =
1
2
??????????????????????? ????????????? ?? 2

?? =0.5?50?10
?6
?200
2
=1 ??


3. If x is the mean of data 3, x, 2 and 4, then the mode is _________
Ans: 3
Sol: ?? =
3+?? +2+4
4

4??? =3+?? +2+4
4??? ??? =3+2+4=9
?? =3
Mode is 3. (Maximum repeated value)

4. The cold forming process in which a hardened tool is pressed against a workpiece (when there is
relative motion between the tool and the workpiece) to produce a roughened surface with a
regular pattern is
A. Strip rolling B. Knurling
C. Roll forming D. Chamfering
Ans: option (B)
Sol: We provide special pattern to prevent the relative motion between contact surface. This special
pattern is known as Knurling.


5. Endurance limit of a beam subjected to pure bending decreases with
A. increase in the surface roughness and increase in the size of the beam
B. decrease in the surface roughness and decrease in the size of the beam
C. decrease in the surface roughness and increase in the size of the beam
D. increase in the surface roughness and decrease in the size of the beam
Ans: option (A)
Sol: Formula for endurance limit
?? ?? =?? ?? ??? ?? ??? ?? ??? ?? ??? ?? ?

?? ???????
?? ?? ????????? ????????????
?? ?? ??????????????? ????????????
?? ?? ????????? ????????????
?? ?? ??????????????????????? ????????????
?? ?? ?
??????????????????? ?????????????? ?
Form above formula it is clear that the Endurance limit increases with increase in size,
surface, load, temp and endurance strength.







6

6. In matrix equation [A] {X} = {R}.
? ?
4 8 4 2
8 16 4 , 1
4 4 15 4
AX
? ? ? ?
?? ??
= ? = ??
??
????
??
??
?
? ? ? ?
and ? ?
32
16 .
64
R
??
??
=
??
??
??

One of the eigenvalues of matrix [A] is
A. 4 B. 15
C. 8 D. 16
Ans: option (D)
Sol: [A] {X} = {R}.

We know ???? = ???? ;?? ??????? ?? ??????????? ??????????

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}={
32
16
64
}

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}=16{
2
1
4
}

Hence, ?? =????

7. Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number
ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit.
The Reynolds number at the exit of the pipe is___________.
Ans: 500
Sol: Reynold?s Number
???? =
?? ?? ????
?? ??
Where: -
?? ??????????? ??????????????
?? ????
??????????????? ????????????????
?? ??????????????? ???? ????????
?? ? Dynamic viscosity of Fluid
?? ?? =(
?? ?? ????
?? ?? )=
(

?? (
?? ???????? ?? ???????? ) ?? ?? )


From above expiration, Reynold?s Number is independent of flow profile. Hence, Reynold?s
Number for parabolic flow profile is 500.

8. For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure
and temperature, respectively. As per Maxwell?s relations,
p
v
s
? ??
??
?
??
is equal to
A.
T
p
v
? ??
??
?
??
B.
p
s
T
? ??
??
?
??
C.
s
T
p
?? ?
??
?
??
D.
p
T
v
? ??
?
??
?
??

Ans: option (C)
Sol: From mathematical relation expiration



7

???? = ?????? +??????
? (
????
????
)
?? = (
????
????
)
??
???????? ?????????????? ????????????????
?? ?= ?????? +??????
? (
????
????
)
?? = (
????
????
)
??

9. Hardenability of steel is a measure of
A. the ability to harden when it is cold worked
B. the maximum hardness that can be obtained when it is austenitized and then quenched
C. the ability to retain its hardness when it is heated to elevated temperatures
D. the depth to which required hardening is obtained when it is austenitized and then quenched
Ans: option (D)
Sol: The depth to which required hardening is obtained when it is austenitized and then quenched.

10. The directional derivative of the function f(x, y) = x
2
+ y
2
along a line directed from (0, 0) to (1,
1), evaluated at the point x = 1, y = 1 is
A. 2 B. ?2
C. 4?2 D. 2?2
Ans: option (D)
Sol: Directional derivative of function along the line is the scalar value of derivative along the line. i.e.
we have to calculate value of derivative of function in the direction of given line vector
? ?? = ??? (
????
????
)+ ??? (
????
????
)
? ?? = 2???+ 2???
Now, calculating the value of ? ?? in 1???+ 1???
D.D of given function is (2???+ 2??? ) ?
(??? + ?? ?)
|??? + ?? ?|
= 2 ?2

11. A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is
A.
2 D
T
?
B.
T
D

C.
D
T
?
D.
D
T

Ans: option (C)
Sol: circular pitch =
????
??

12. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the
instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of
points P and R are VP and VR, in the x and y directions, respectively. The magnitude of the
angular velocity of the body is




8

A. /3
R
V B. /3
P
V
C. 2VR D. 2VP
Ans: option (C)
Sol: The given body is a rigid body; Hence the given body will not have any deformation, and the
possible motion is translation and angular motion. we know that the angular motion of the object is
always defined as the motion about the point. Hence, first we have to find a point parallel to both
velocity ?? ?? and ?? ?? .


? Angular velocity, ?? =
???????????????? ?????????????????????????? ????????????????
?? =
?? ?? ????
=
?? ?? ????

???? =
?3
2
????????? ???? ???????????????? =
?3
2
?1=
?3
2

???? =
1
2
????????? ???? ???????????????? =
1
2
?1=
1
2


?? =
2?? ?? ?3
=
2?? ?? 1


13. Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4
m. The view factor F12 is
A. 0.25 B. 0.0625
C. 1.0 D. 0.5
Ans: option (C)
Sol: ?? 12
=1

14. The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
A.
10
01
??
??
?
??
B.
01
10
? ??
??
?
??

C.
01
10
??
??
??
D.
10
01
???
??
??

Ans: option (C)
Sol: The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
01
10
??
??
??




S



9

15. The state of stress at a point in a component is represented by a Mohr?s circle of radius 100 MPa
centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the
normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same
point is ___________ MPa.
Ans: 80
Sol:


?? =?100
2
?60
2
=80 ??????

16. One-dimensional steady state heat conduction takes place through a solid whose cross-sectional
area varies linearly in the direction of heat transfer. Assume there is no heat generation in the
solid and the thermal conductivity of the material is constant and independent of temperature.
The temperature distribution in the solid is
A. Quadratic B. Exponential
C. Logarithmic D. Linear
Ans: option (C)
Sol: Let the given body cross-sectional area varies linearly, and heat is flowing from left to right.





If there is no heat generation,
?? ????
(?????
????
????
)=0

?
?? ????
(?????
????
????
)=?0

(?????
????
????
)=??

??? (?? 0
+?? ?? ?? )
????
????
=??
???? =
? ?? ????
?? (?? 0
+?? ?? ?? )


? ????
2
1
=?
? ?? ????
?? (?? 0
+?? ?? ?? )
2
1


?? 2
??? 1
= ?
?? ?? ln(
?? ?? ?? 2
+?? 0
?? ?? ?? 1
+?? 0
)



10

17. An analytic function f(z) of complex variable z = x + I y may be written as f(z) = u(x, y) + iv (x,
y). Then, u(x, y) and v(x, y) must satisfy
A.
uv
xy
??
=?
??
and
uv
yx
??
=
??

B.
uv
xy
??
=?
??
and
uv
yx
??
=?
??

C.
uv
xy
??
=
??
and
uv
yx
??
=?
??

D.
uv
xy
??
=
??
and
uv
yx
??
=
??

Ans: option (C)
Sol: If f(z) = u(x, y) + iv(x, y) is analytic function then it must satisfy the following relations.

????
????
=
????
????


????
????
=?
????
????


18. A thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is
losing heat to the surroundings by natural convection. The temperatures of the plate and the
surroundings, and the properties of the surrounding fluid, are constant. The relationship between
the average Nusselt and Rayleigh numbers is given as Nu = K Ra ?, where K is a constant. The
length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the
plate is increased to 16L keeping all other factors constant.

If the average heat transfer coefficient for the first plate is h1 and that for the second plate is h2,
the value of the ratio h1/h2 is____________.
Ans: 2
Sol: ?? ?? =?? (?? ?? )
1
4
We know that ?? ?? =?? ?? ?? ??
?? ?? =?? (?? ?? ?? ?? )
1
4
??? ?? ?(?? ?? )
1
4 ?(
???? ??? ?? 3
?? 2
)
1
4

??? ??? 3
4
???? ?
1
4
?
2
?
1
?(
?? 1
?? 2
)
1
4
=>
?
1
?
2
?(
?? 2
?? 1
)
1
4
=(16)
1
4=2



11


19. Which one of the following modifications of the simple ideal Rankine cycle increases the thermal
efficiency and reduces the moisture content of the steam at the turbine outlet?
A. Decreasing the condenser pressure.
B. Increasing the boiler pressure.
C. Decreasing the boiler pressure.
D. Increasing the turbine inlet temperature.
Ans: option (D)
Sol: Due to increase of the turbine inlet temperature, quality of the stream at outlet of the turbine
improves. Which increases the thermal efficiency and reduces the moisture content of the steam at the
turbine outlet.

20. Consider a linear rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of
100 MPa along the length direction. Assume plane stress conditions in the plane normal to the
thickness. The Young?s modulus E = 200 MPa and Poisson?s ratio v = 0.3 are given. The principal
strains in the plane of the sheet are
A. (0.5, 0.0) B. (0.35, -0.15)
C. (0.5, -0.5) D. (0.5, -0.15)
Ans: option (D)
Sol: ?
1
=
?? 1
?? ???
?? 2
?? =
100
200
?0.3?
0
200
=0.5

?
2
=
?? 2
?? ???
?? 1
?? =
0
200
?0.3?
100
200
=?0.15


21. The figure shows an idealized plane truss. If a horizontal force of 300 N is applied at point A,
then the magnitude of the force produced in member CD is ________N.

Ans: 0

Sol:



12



The momentum about the point A must be zero, because there is no deformation of any truss.
Hence, ?? ????
=0 [?? ????
is not passing through the point A]

22. The fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase
in
A. freezing range
B. surface tension
C. degree of superheat
D. viscosity
Ans: option (C)
Sol: Fluidity of molten metal of cast alloys increases with increase in degree of superheat.

23. The most common limit gage used for inspecting the hole diameter is
A. Ring gage B. Snap gage
C. Plug gage D. Master gage
Ans: option (C)
Sol: The most common limit gage used for inspecting the hole diameter is Plug gage.

24. The differential equation 45
dy
y
dx
+= is valid in the domain 0 ? x ? 1 with y(0) = 2.25. The
solution of the differential equation is
A. y = e
-4x
+ 1.25
B. y = e
4x
+ 5
C. y = e
4x
+ 1.25
D. y = e
-4x
+ 5
Ans: option (A)
Sol: The given equation is.



13

???? ???? +4?? =5
If Integration factor = ?? ?4????
=?? 4??
? ?? ????? =?5????? ???? +??
? ?? ??? 4?? =5?
?? 4?? 4
+??
? ?? ??? 4?? =5?
?? 4?? 4
+?? ?.( 1)
Now for at x=0,
? 2.25 =
5
4
+ ??
? ?? =1
? Using the value of C in equ (1)
? ?? ?
?? 4?? ?? 4?? =
5
?? 4?? ?
?? 4?? 4
+
?? ?? 4??
? ?? =1.25+ ?? ?4??

25. A two-dimensional incompressible frictionless flow field is given by
??
. u xi yj =? If ? is the density
of the fluid, the expression for pressure gradient vector at any point in the flow field is given as
A.
( )
22
??
x i y j ??+ B.
( )
??
xi yj ??+
C.
( )
??
xi yj ? + D.
( )
??
xi yj ? ?
Ans: option (B)
Sol: Euler?s Equation of motion in 2D.

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

As there is no extra force acting on the fluid.
?? ?? ?????? ?? ?? =0
Now form the given expiration, u=x & v=y
?
????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????


?0+ ?? ?1+0+0=0?
1
?? ????
????

0+ 0+?? ?1+0=0?
1
?? ????
????

??????????? ???????? ?????? =
????
????
???+
????
????
???= ??? (?? ???+?? ??? )




14

26. A short shoe external drum brake is shown in the figure. The diameter of the brake drum is 500
mm. The dimensions a = 1000 mm, b = 500 mm and c = 200 mm. The coefficient of friction
between the drum and the shoe is 0.35. The force applied on the lever F = 100 N as shown in
the figure. The drum is rotating anti-clockwise. The braking torque on the drum is _______N.m
(round off to two decimal places).

Ans: 20.34
Sol:

Applying momentum about point O.

??? ?? =0

?? ??? +?? ?? ?? ??? ??? ?? ??? =0
?? ?? =232.55
Breaking Torque = ?? ?? ?? ?? ?? = 20.34

27. A uniform disc with radius r and a mass of m kg is mounted centrally on a horizontal axle of
negligible mass and length of 1.5r. The disc spins counter-clockwise about the axle with angular
speed ?, when viewed from the right-hand side bearing, Q. The axle precesses about a vertical
axis at
?p = ?/10 in the clockwise direction when viewed from above. Let RP and RQ (positive upwards)
be the resultant reaction forces due to the mass and the gyroscopic effect, at bearings P and Q,
respectively. Assuming ?
2
r = 300 m/s
2
and g = 10 m/s
2
, the ratio of the larger to the smaller
bearing reaction force (considering appropriate signs) is __________.



15


Ans: -3
Sol: ?????????????????? ???????????? (???? )=???? ?? ??

Using: ?? ?? =
?? 10
and ?? 2
?? =300

???? =
?? ?? 2
2
?? 2
10
=15????

Reaction at P and Q due to gravity

?? ?? 1
+?? ?? 1
=???? =10??
?? ?? 1
=5??
??? ?? 1
= 5 ??

Reaction at P and Q due to GC

Taking momentum about point p.
?? ?? 2
?1.5?? ?15???? =0
?? ?? 2
=
15????
1.5?? =10 ??
??? ?? 2
= ?10 ??
?????? ,
?? ?? ?? ?? =
?? ?? 1
+?? ?? 2

?? ?? 1
+?? ?? 2
=
5+10
5?10
= ?3

28. The figure shows a pouring arrangement for casting of a metal block. Frictional losses are
negligible. The acceleration due to gravity is 9.81 m/s
2
. The time (in s, round off to two decimal
places) to fill up the mold cavity (of size 40 cm ? 30 cm ? 15 cm) is ____________
FirstRanker.com - FirstRanker's Choice



2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6




3

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of ?? =
8+6
2
=7

6. X is an online media provider. By offering unlimited and exclusive online content at attractive
prices for a loyalty membership, X is almost forcing its customers towards its loyalty
membership. If its loyalty membership continues to grow at its current rate, within the next
eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
A. Most households that subscribe to X?s loyalty membership discontinue watching cable
television
B. Non-members prefer to watch cable television
C. The X is cancelling accounts of non-members
D. Cable television operators don?t subscribe to X?s loyalty membership
Ans: option (A)
Sol: option A is the most appropriate solution

7. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased
by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.
A. 35.70 B. 10.00
C. 37.50 D. 25.00
Ans: option (C)
Sol: Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04??? =0.04??
And the fiscal deficit in 2016 = 0.05?1.1?? =0.055??
Increase in fiscal deficit = 0.055x ? 0.04x = 0.015x
So, the percentage increase in fiscal deficit =
0.015?? 0.04?? ?100=37.5%

8. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can
empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is
opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is
_________.
A. 16.50 B. 14.50
C. 15.50 D. 13.50
Ans: option (B)
Sol: 1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(
1
6
? ?
1
12
? )=
1
3
?
Tank filled by when Q and R works for another 6 hours = 6(
1
9
? ?
1
12
? )=
1
6
?
Total tank filled in these 10 hours =
1
3
? +
1
6
? =0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in
9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours




4

9. While teaching a creative writing class in India, I was surprised at receiving stories from the
students that were all set in distant places: in the American West with cowboys and in
Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave
the writers in the once-colonised countries the confidence to see the shabby lives around them
as worthy of being ?told?.
The writer of this passage is surprised by the creative writing assignments of his students,
because __________.
A. Some of the students had written about ice cubes and cowboys
B. None of the students had written about ice cubes and cowboys
C. Some of the students had written stories set in foreign places
D. None of the students had written stories set in India
Ans: option (C)
Sol: option C is the most appropriate solution

10. Mola is a digital platform for taxis in a city. It offers three types of rides ? Pool, Mini and Prime.
The Table below presents the number of rides for the past four months. The platform earns one
US dollar per ride. What is the percentage share of revenue contributed by Prime to the total
revenues of Mola, for the entire duration?
Type
Month
January February March April
Pool 170 320 215 190
Mini 110 220 180 70
Prime 75 180 120 90

A. 38.74 B. 23.97
C. 25.86 D. 16.24

Ans: option (B)
Sol: Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580
Revenue contributed by Prime = 75 + 180 + 120 +90 = 465
Total revenue of Mola = 895 + 580 + 465 = 1940
So, the percentage share =
465
1940
?100=23.97%

MECHANICAL ENGINEERING
1. A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by
application of pure bending moments at its ends. The Young?s modulus of the material of the
wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.
Ans: 50
Sol: Tensile stress
?? =
?? ?? ?? =
100?10
3
1
(
1
1000?2
)=50 ??????





5

2. In an electrical discharge machining process, the breakdown voltage across inter electrode gap
(IEG) is 200 V and the capacitance of the RC circuit is 50 ?F. The energy (in J) released per
spark across the IEG is __________
Ans: 1
Sol:
?? =
1
2
??????????????????????? ????????????? ?? 2

?? =0.5?50?10
?6
?200
2
=1 ??


3. If x is the mean of data 3, x, 2 and 4, then the mode is _________
Ans: 3
Sol: ?? =
3+?? +2+4
4

4??? =3+?? +2+4
4??? ??? =3+2+4=9
?? =3
Mode is 3. (Maximum repeated value)

4. The cold forming process in which a hardened tool is pressed against a workpiece (when there is
relative motion between the tool and the workpiece) to produce a roughened surface with a
regular pattern is
A. Strip rolling B. Knurling
C. Roll forming D. Chamfering
Ans: option (B)
Sol: We provide special pattern to prevent the relative motion between contact surface. This special
pattern is known as Knurling.


5. Endurance limit of a beam subjected to pure bending decreases with
A. increase in the surface roughness and increase in the size of the beam
B. decrease in the surface roughness and decrease in the size of the beam
C. decrease in the surface roughness and increase in the size of the beam
D. increase in the surface roughness and decrease in the size of the beam
Ans: option (A)
Sol: Formula for endurance limit
?? ?? =?? ?? ??? ?? ??? ?? ??? ?? ??? ?? ?

?? ???????
?? ?? ????????? ????????????
?? ?? ??????????????? ????????????
?? ?? ????????? ????????????
?? ?? ??????????????????????? ????????????
?? ?? ?
??????????????????? ?????????????? ?
Form above formula it is clear that the Endurance limit increases with increase in size,
surface, load, temp and endurance strength.







6

6. In matrix equation [A] {X} = {R}.
? ?
4 8 4 2
8 16 4 , 1
4 4 15 4
AX
? ? ? ?
?? ??
= ? = ??
??
????
??
??
?
? ? ? ?
and ? ?
32
16 .
64
R
??
??
=
??
??
??

One of the eigenvalues of matrix [A] is
A. 4 B. 15
C. 8 D. 16
Ans: option (D)
Sol: [A] {X} = {R}.

We know ???? = ???? ;?? ??????? ?? ??????????? ??????????

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}={
32
16
64
}

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}=16{
2
1
4
}

Hence, ?? =????

7. Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number
ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit.
The Reynolds number at the exit of the pipe is___________.
Ans: 500
Sol: Reynold?s Number
???? =
?? ?? ????
?? ??
Where: -
?? ??????????? ??????????????
?? ????
??????????????? ????????????????
?? ??????????????? ???? ????????
?? ? Dynamic viscosity of Fluid
?? ?? =(
?? ?? ????
?? ?? )=
(

?? (
?? ???????? ?? ???????? ) ?? ?? )


From above expiration, Reynold?s Number is independent of flow profile. Hence, Reynold?s
Number for parabolic flow profile is 500.

8. For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure
and temperature, respectively. As per Maxwell?s relations,
p
v
s
? ??
??
?
??
is equal to
A.
T
p
v
? ??
??
?
??
B.
p
s
T
? ??
??
?
??
C.
s
T
p
?? ?
??
?
??
D.
p
T
v
? ??
?
??
?
??

Ans: option (C)
Sol: From mathematical relation expiration



7

???? = ?????? +??????
? (
????
????
)
?? = (
????
????
)
??
???????? ?????????????? ????????????????
?? ?= ?????? +??????
? (
????
????
)
?? = (
????
????
)
??

9. Hardenability of steel is a measure of
A. the ability to harden when it is cold worked
B. the maximum hardness that can be obtained when it is austenitized and then quenched
C. the ability to retain its hardness when it is heated to elevated temperatures
D. the depth to which required hardening is obtained when it is austenitized and then quenched
Ans: option (D)
Sol: The depth to which required hardening is obtained when it is austenitized and then quenched.

10. The directional derivative of the function f(x, y) = x
2
+ y
2
along a line directed from (0, 0) to (1,
1), evaluated at the point x = 1, y = 1 is
A. 2 B. ?2
C. 4?2 D. 2?2
Ans: option (D)
Sol: Directional derivative of function along the line is the scalar value of derivative along the line. i.e.
we have to calculate value of derivative of function in the direction of given line vector
? ?? = ??? (
????
????
)+ ??? (
????
????
)
? ?? = 2???+ 2???
Now, calculating the value of ? ?? in 1???+ 1???
D.D of given function is (2???+ 2??? ) ?
(??? + ?? ?)
|??? + ?? ?|
= 2 ?2

11. A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is
A.
2 D
T
?
B.
T
D

C.
D
T
?
D.
D
T

Ans: option (C)
Sol: circular pitch =
????
??

12. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the
instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of
points P and R are VP and VR, in the x and y directions, respectively. The magnitude of the
angular velocity of the body is




8

A. /3
R
V B. /3
P
V
C. 2VR D. 2VP
Ans: option (C)
Sol: The given body is a rigid body; Hence the given body will not have any deformation, and the
possible motion is translation and angular motion. we know that the angular motion of the object is
always defined as the motion about the point. Hence, first we have to find a point parallel to both
velocity ?? ?? and ?? ?? .


? Angular velocity, ?? =
???????????????? ?????????????????????????? ????????????????
?? =
?? ?? ????
=
?? ?? ????

???? =
?3
2
????????? ???? ???????????????? =
?3
2
?1=
?3
2

???? =
1
2
????????? ???? ???????????????? =
1
2
?1=
1
2


?? =
2?? ?? ?3
=
2?? ?? 1


13. Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4
m. The view factor F12 is
A. 0.25 B. 0.0625
C. 1.0 D. 0.5
Ans: option (C)
Sol: ?? 12
=1

14. The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
A.
10
01
??
??
?
??
B.
01
10
? ??
??
?
??

C.
01
10
??
??
??
D.
10
01
???
??
??

Ans: option (C)
Sol: The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
01
10
??
??
??




S



9

15. The state of stress at a point in a component is represented by a Mohr?s circle of radius 100 MPa
centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the
normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same
point is ___________ MPa.
Ans: 80
Sol:


?? =?100
2
?60
2
=80 ??????

16. One-dimensional steady state heat conduction takes place through a solid whose cross-sectional
area varies linearly in the direction of heat transfer. Assume there is no heat generation in the
solid and the thermal conductivity of the material is constant and independent of temperature.
The temperature distribution in the solid is
A. Quadratic B. Exponential
C. Logarithmic D. Linear
Ans: option (C)
Sol: Let the given body cross-sectional area varies linearly, and heat is flowing from left to right.





If there is no heat generation,
?? ????
(?????
????
????
)=0

?
?? ????
(?????
????
????
)=?0

(?????
????
????
)=??

??? (?? 0
+?? ?? ?? )
????
????
=??
???? =
? ?? ????
?? (?? 0
+?? ?? ?? )


? ????
2
1
=?
? ?? ????
?? (?? 0
+?? ?? ?? )
2
1


?? 2
??? 1
= ?
?? ?? ln(
?? ?? ?? 2
+?? 0
?? ?? ?? 1
+?? 0
)



10

17. An analytic function f(z) of complex variable z = x + I y may be written as f(z) = u(x, y) + iv (x,
y). Then, u(x, y) and v(x, y) must satisfy
A.
uv
xy
??
=?
??
and
uv
yx
??
=
??

B.
uv
xy
??
=?
??
and
uv
yx
??
=?
??

C.
uv
xy
??
=
??
and
uv
yx
??
=?
??

D.
uv
xy
??
=
??
and
uv
yx
??
=
??

Ans: option (C)
Sol: If f(z) = u(x, y) + iv(x, y) is analytic function then it must satisfy the following relations.

????
????
=
????
????


????
????
=?
????
????


18. A thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is
losing heat to the surroundings by natural convection. The temperatures of the plate and the
surroundings, and the properties of the surrounding fluid, are constant. The relationship between
the average Nusselt and Rayleigh numbers is given as Nu = K Ra ?, where K is a constant. The
length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the
plate is increased to 16L keeping all other factors constant.

If the average heat transfer coefficient for the first plate is h1 and that for the second plate is h2,
the value of the ratio h1/h2 is____________.
Ans: 2
Sol: ?? ?? =?? (?? ?? )
1
4
We know that ?? ?? =?? ?? ?? ??
?? ?? =?? (?? ?? ?? ?? )
1
4
??? ?? ?(?? ?? )
1
4 ?(
???? ??? ?? 3
?? 2
)
1
4

??? ??? 3
4
???? ?
1
4
?
2
?
1
?(
?? 1
?? 2
)
1
4
=>
?
1
?
2
?(
?? 2
?? 1
)
1
4
=(16)
1
4=2



11


19. Which one of the following modifications of the simple ideal Rankine cycle increases the thermal
efficiency and reduces the moisture content of the steam at the turbine outlet?
A. Decreasing the condenser pressure.
B. Increasing the boiler pressure.
C. Decreasing the boiler pressure.
D. Increasing the turbine inlet temperature.
Ans: option (D)
Sol: Due to increase of the turbine inlet temperature, quality of the stream at outlet of the turbine
improves. Which increases the thermal efficiency and reduces the moisture content of the steam at the
turbine outlet.

20. Consider a linear rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of
100 MPa along the length direction. Assume plane stress conditions in the plane normal to the
thickness. The Young?s modulus E = 200 MPa and Poisson?s ratio v = 0.3 are given. The principal
strains in the plane of the sheet are
A. (0.5, 0.0) B. (0.35, -0.15)
C. (0.5, -0.5) D. (0.5, -0.15)
Ans: option (D)
Sol: ?
1
=
?? 1
?? ???
?? 2
?? =
100
200
?0.3?
0
200
=0.5

?
2
=
?? 2
?? ???
?? 1
?? =
0
200
?0.3?
100
200
=?0.15


21. The figure shows an idealized plane truss. If a horizontal force of 300 N is applied at point A,
then the magnitude of the force produced in member CD is ________N.

Ans: 0

Sol:



12



The momentum about the point A must be zero, because there is no deformation of any truss.
Hence, ?? ????
=0 [?? ????
is not passing through the point A]

22. The fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase
in
A. freezing range
B. surface tension
C. degree of superheat
D. viscosity
Ans: option (C)
Sol: Fluidity of molten metal of cast alloys increases with increase in degree of superheat.

23. The most common limit gage used for inspecting the hole diameter is
A. Ring gage B. Snap gage
C. Plug gage D. Master gage
Ans: option (C)
Sol: The most common limit gage used for inspecting the hole diameter is Plug gage.

24. The differential equation 45
dy
y
dx
+= is valid in the domain 0 ? x ? 1 with y(0) = 2.25. The
solution of the differential equation is
A. y = e
-4x
+ 1.25
B. y = e
4x
+ 5
C. y = e
4x
+ 1.25
D. y = e
-4x
+ 5
Ans: option (A)
Sol: The given equation is.



13

???? ???? +4?? =5
If Integration factor = ?? ?4????
=?? 4??
? ?? ????? =?5????? ???? +??
? ?? ??? 4?? =5?
?? 4?? 4
+??
? ?? ??? 4?? =5?
?? 4?? 4
+?? ?.( 1)
Now for at x=0,
? 2.25 =
5
4
+ ??
? ?? =1
? Using the value of C in equ (1)
? ?? ?
?? 4?? ?? 4?? =
5
?? 4?? ?
?? 4?? 4
+
?? ?? 4??
? ?? =1.25+ ?? ?4??

25. A two-dimensional incompressible frictionless flow field is given by
??
. u xi yj =? If ? is the density
of the fluid, the expression for pressure gradient vector at any point in the flow field is given as
A.
( )
22
??
x i y j ??+ B.
( )
??
xi yj ??+
C.
( )
??
xi yj ? + D.
( )
??
xi yj ? ?
Ans: option (B)
Sol: Euler?s Equation of motion in 2D.

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

As there is no extra force acting on the fluid.
?? ?? ?????? ?? ?? =0
Now form the given expiration, u=x & v=y
?
????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????


?0+ ?? ?1+0+0=0?
1
?? ????
????

0+ 0+?? ?1+0=0?
1
?? ????
????

??????????? ???????? ?????? =
????
????
???+
????
????
???= ??? (?? ???+?? ??? )




14

26. A short shoe external drum brake is shown in the figure. The diameter of the brake drum is 500
mm. The dimensions a = 1000 mm, b = 500 mm and c = 200 mm. The coefficient of friction
between the drum and the shoe is 0.35. The force applied on the lever F = 100 N as shown in
the figure. The drum is rotating anti-clockwise. The braking torque on the drum is _______N.m
(round off to two decimal places).

Ans: 20.34
Sol:

Applying momentum about point O.

??? ?? =0

?? ??? +?? ?? ?? ??? ??? ?? ??? =0
?? ?? =232.55
Breaking Torque = ?? ?? ?? ?? ?? = 20.34

27. A uniform disc with radius r and a mass of m kg is mounted centrally on a horizontal axle of
negligible mass and length of 1.5r. The disc spins counter-clockwise about the axle with angular
speed ?, when viewed from the right-hand side bearing, Q. The axle precesses about a vertical
axis at
?p = ?/10 in the clockwise direction when viewed from above. Let RP and RQ (positive upwards)
be the resultant reaction forces due to the mass and the gyroscopic effect, at bearings P and Q,
respectively. Assuming ?
2
r = 300 m/s
2
and g = 10 m/s
2
, the ratio of the larger to the smaller
bearing reaction force (considering appropriate signs) is __________.



15


Ans: -3
Sol: ?????????????????? ???????????? (???? )=???? ?? ??

Using: ?? ?? =
?? 10
and ?? 2
?? =300

???? =
?? ?? 2
2
?? 2
10
=15????

Reaction at P and Q due to gravity

?? ?? 1
+?? ?? 1
=???? =10??
?? ?? 1
=5??
??? ?? 1
= 5 ??

Reaction at P and Q due to GC

Taking momentum about point p.
?? ?? 2
?1.5?? ?15???? =0
?? ?? 2
=
15????
1.5?? =10 ??
??? ?? 2
= ?10 ??
?????? ,
?? ?? ?? ?? =
?? ?? 1
+?? ?? 2

?? ?? 1
+?? ?? 2
=
5+10
5?10
= ?3

28. The figure shows a pouring arrangement for casting of a metal block. Frictional losses are
negligible. The acceleration due to gravity is 9.81 m/s
2
. The time (in s, round off to two decimal
places) to fill up the mold cavity (of size 40 cm ? 30 cm ? 15 cm) is ____________



16


Ans: 29.84
Sol: ???????? ?????????????? ???????? =
?? ?? ?? ?? .?2?? ?

???????? =
0.40?0.30?0.15
?? 0.02
2
4
.?2?9.81?0.20
28.94 ??????

29. The activities of a project, their duration and the precedence relationships are given in the table.
For example, in a precedence relationship ?X < Y, Z? means that X is predecessor of activities Y
and Z. The time to complete the activities along the critical path is ____________ weeks.
Activity Duration
(Weeks)
Precedence
Relationship
A 5 A < B, C, D
B 7 B < E, F, G
C 10 C < I
D 6 D < G
E 3 E < H
F 9 F < I
G 7 G < I
H 4 H < I
I 2 ---
A. 21 B. 25
C. 23 D. 17
Ans: option (C)
Sol:
FirstRanker.com - FirstRanker's Choice



2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6




3

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of ?? =
8+6
2
=7

6. X is an online media provider. By offering unlimited and exclusive online content at attractive
prices for a loyalty membership, X is almost forcing its customers towards its loyalty
membership. If its loyalty membership continues to grow at its current rate, within the next
eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
A. Most households that subscribe to X?s loyalty membership discontinue watching cable
television
B. Non-members prefer to watch cable television
C. The X is cancelling accounts of non-members
D. Cable television operators don?t subscribe to X?s loyalty membership
Ans: option (A)
Sol: option A is the most appropriate solution

7. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased
by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.
A. 35.70 B. 10.00
C. 37.50 D. 25.00
Ans: option (C)
Sol: Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04??? =0.04??
And the fiscal deficit in 2016 = 0.05?1.1?? =0.055??
Increase in fiscal deficit = 0.055x ? 0.04x = 0.015x
So, the percentage increase in fiscal deficit =
0.015?? 0.04?? ?100=37.5%

8. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can
empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is
opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is
_________.
A. 16.50 B. 14.50
C. 15.50 D. 13.50
Ans: option (B)
Sol: 1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(
1
6
? ?
1
12
? )=
1
3
?
Tank filled by when Q and R works for another 6 hours = 6(
1
9
? ?
1
12
? )=
1
6
?
Total tank filled in these 10 hours =
1
3
? +
1
6
? =0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in
9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours




4

9. While teaching a creative writing class in India, I was surprised at receiving stories from the
students that were all set in distant places: in the American West with cowboys and in
Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave
the writers in the once-colonised countries the confidence to see the shabby lives around them
as worthy of being ?told?.
The writer of this passage is surprised by the creative writing assignments of his students,
because __________.
A. Some of the students had written about ice cubes and cowboys
B. None of the students had written about ice cubes and cowboys
C. Some of the students had written stories set in foreign places
D. None of the students had written stories set in India
Ans: option (C)
Sol: option C is the most appropriate solution

10. Mola is a digital platform for taxis in a city. It offers three types of rides ? Pool, Mini and Prime.
The Table below presents the number of rides for the past four months. The platform earns one
US dollar per ride. What is the percentage share of revenue contributed by Prime to the total
revenues of Mola, for the entire duration?
Type
Month
January February March April
Pool 170 320 215 190
Mini 110 220 180 70
Prime 75 180 120 90

A. 38.74 B. 23.97
C. 25.86 D. 16.24

Ans: option (B)
Sol: Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580
Revenue contributed by Prime = 75 + 180 + 120 +90 = 465
Total revenue of Mola = 895 + 580 + 465 = 1940
So, the percentage share =
465
1940
?100=23.97%

MECHANICAL ENGINEERING
1. A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by
application of pure bending moments at its ends. The Young?s modulus of the material of the
wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.
Ans: 50
Sol: Tensile stress
?? =
?? ?? ?? =
100?10
3
1
(
1
1000?2
)=50 ??????





5

2. In an electrical discharge machining process, the breakdown voltage across inter electrode gap
(IEG) is 200 V and the capacitance of the RC circuit is 50 ?F. The energy (in J) released per
spark across the IEG is __________
Ans: 1
Sol:
?? =
1
2
??????????????????????? ????????????? ?? 2

?? =0.5?50?10
?6
?200
2
=1 ??


3. If x is the mean of data 3, x, 2 and 4, then the mode is _________
Ans: 3
Sol: ?? =
3+?? +2+4
4

4??? =3+?? +2+4
4??? ??? =3+2+4=9
?? =3
Mode is 3. (Maximum repeated value)

4. The cold forming process in which a hardened tool is pressed against a workpiece (when there is
relative motion between the tool and the workpiece) to produce a roughened surface with a
regular pattern is
A. Strip rolling B. Knurling
C. Roll forming D. Chamfering
Ans: option (B)
Sol: We provide special pattern to prevent the relative motion between contact surface. This special
pattern is known as Knurling.


5. Endurance limit of a beam subjected to pure bending decreases with
A. increase in the surface roughness and increase in the size of the beam
B. decrease in the surface roughness and decrease in the size of the beam
C. decrease in the surface roughness and increase in the size of the beam
D. increase in the surface roughness and decrease in the size of the beam
Ans: option (A)
Sol: Formula for endurance limit
?? ?? =?? ?? ??? ?? ??? ?? ??? ?? ??? ?? ?

?? ???????
?? ?? ????????? ????????????
?? ?? ??????????????? ????????????
?? ?? ????????? ????????????
?? ?? ??????????????????????? ????????????
?? ?? ?
??????????????????? ?????????????? ?
Form above formula it is clear that the Endurance limit increases with increase in size,
surface, load, temp and endurance strength.







6

6. In matrix equation [A] {X} = {R}.
? ?
4 8 4 2
8 16 4 , 1
4 4 15 4
AX
? ? ? ?
?? ??
= ? = ??
??
????
??
??
?
? ? ? ?
and ? ?
32
16 .
64
R
??
??
=
??
??
??

One of the eigenvalues of matrix [A] is
A. 4 B. 15
C. 8 D. 16
Ans: option (D)
Sol: [A] {X} = {R}.

We know ???? = ???? ;?? ??????? ?? ??????????? ??????????

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}={
32
16
64
}

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}=16{
2
1
4
}

Hence, ?? =????

7. Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number
ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit.
The Reynolds number at the exit of the pipe is___________.
Ans: 500
Sol: Reynold?s Number
???? =
?? ?? ????
?? ??
Where: -
?? ??????????? ??????????????
?? ????
??????????????? ????????????????
?? ??????????????? ???? ????????
?? ? Dynamic viscosity of Fluid
?? ?? =(
?? ?? ????
?? ?? )=
(

?? (
?? ???????? ?? ???????? ) ?? ?? )


From above expiration, Reynold?s Number is independent of flow profile. Hence, Reynold?s
Number for parabolic flow profile is 500.

8. For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure
and temperature, respectively. As per Maxwell?s relations,
p
v
s
? ??
??
?
??
is equal to
A.
T
p
v
? ??
??
?
??
B.
p
s
T
? ??
??
?
??
C.
s
T
p
?? ?
??
?
??
D.
p
T
v
? ??
?
??
?
??

Ans: option (C)
Sol: From mathematical relation expiration



7

???? = ?????? +??????
? (
????
????
)
?? = (
????
????
)
??
???????? ?????????????? ????????????????
?? ?= ?????? +??????
? (
????
????
)
?? = (
????
????
)
??

9. Hardenability of steel is a measure of
A. the ability to harden when it is cold worked
B. the maximum hardness that can be obtained when it is austenitized and then quenched
C. the ability to retain its hardness when it is heated to elevated temperatures
D. the depth to which required hardening is obtained when it is austenitized and then quenched
Ans: option (D)
Sol: The depth to which required hardening is obtained when it is austenitized and then quenched.

10. The directional derivative of the function f(x, y) = x
2
+ y
2
along a line directed from (0, 0) to (1,
1), evaluated at the point x = 1, y = 1 is
A. 2 B. ?2
C. 4?2 D. 2?2
Ans: option (D)
Sol: Directional derivative of function along the line is the scalar value of derivative along the line. i.e.
we have to calculate value of derivative of function in the direction of given line vector
? ?? = ??? (
????
????
)+ ??? (
????
????
)
? ?? = 2???+ 2???
Now, calculating the value of ? ?? in 1???+ 1???
D.D of given function is (2???+ 2??? ) ?
(??? + ?? ?)
|??? + ?? ?|
= 2 ?2

11. A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is
A.
2 D
T
?
B.
T
D

C.
D
T
?
D.
D
T

Ans: option (C)
Sol: circular pitch =
????
??

12. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the
instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of
points P and R are VP and VR, in the x and y directions, respectively. The magnitude of the
angular velocity of the body is




8

A. /3
R
V B. /3
P
V
C. 2VR D. 2VP
Ans: option (C)
Sol: The given body is a rigid body; Hence the given body will not have any deformation, and the
possible motion is translation and angular motion. we know that the angular motion of the object is
always defined as the motion about the point. Hence, first we have to find a point parallel to both
velocity ?? ?? and ?? ?? .


? Angular velocity, ?? =
???????????????? ?????????????????????????? ????????????????
?? =
?? ?? ????
=
?? ?? ????

???? =
?3
2
????????? ???? ???????????????? =
?3
2
?1=
?3
2

???? =
1
2
????????? ???? ???????????????? =
1
2
?1=
1
2


?? =
2?? ?? ?3
=
2?? ?? 1


13. Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4
m. The view factor F12 is
A. 0.25 B. 0.0625
C. 1.0 D. 0.5
Ans: option (C)
Sol: ?? 12
=1

14. The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
A.
10
01
??
??
?
??
B.
01
10
? ??
??
?
??

C.
01
10
??
??
??
D.
10
01
???
??
??

Ans: option (C)
Sol: The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
01
10
??
??
??




S



9

15. The state of stress at a point in a component is represented by a Mohr?s circle of radius 100 MPa
centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the
normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same
point is ___________ MPa.
Ans: 80
Sol:


?? =?100
2
?60
2
=80 ??????

16. One-dimensional steady state heat conduction takes place through a solid whose cross-sectional
area varies linearly in the direction of heat transfer. Assume there is no heat generation in the
solid and the thermal conductivity of the material is constant and independent of temperature.
The temperature distribution in the solid is
A. Quadratic B. Exponential
C. Logarithmic D. Linear
Ans: option (C)
Sol: Let the given body cross-sectional area varies linearly, and heat is flowing from left to right.





If there is no heat generation,
?? ????
(?????
????
????
)=0

?
?? ????
(?????
????
????
)=?0

(?????
????
????
)=??

??? (?? 0
+?? ?? ?? )
????
????
=??
???? =
? ?? ????
?? (?? 0
+?? ?? ?? )


? ????
2
1
=?
? ?? ????
?? (?? 0
+?? ?? ?? )
2
1


?? 2
??? 1
= ?
?? ?? ln(
?? ?? ?? 2
+?? 0
?? ?? ?? 1
+?? 0
)



10

17. An analytic function f(z) of complex variable z = x + I y may be written as f(z) = u(x, y) + iv (x,
y). Then, u(x, y) and v(x, y) must satisfy
A.
uv
xy
??
=?
??
and
uv
yx
??
=
??

B.
uv
xy
??
=?
??
and
uv
yx
??
=?
??

C.
uv
xy
??
=
??
and
uv
yx
??
=?
??

D.
uv
xy
??
=
??
and
uv
yx
??
=
??

Ans: option (C)
Sol: If f(z) = u(x, y) + iv(x, y) is analytic function then it must satisfy the following relations.

????
????
=
????
????


????
????
=?
????
????


18. A thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is
losing heat to the surroundings by natural convection. The temperatures of the plate and the
surroundings, and the properties of the surrounding fluid, are constant. The relationship between
the average Nusselt and Rayleigh numbers is given as Nu = K Ra ?, where K is a constant. The
length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the
plate is increased to 16L keeping all other factors constant.

If the average heat transfer coefficient for the first plate is h1 and that for the second plate is h2,
the value of the ratio h1/h2 is____________.
Ans: 2
Sol: ?? ?? =?? (?? ?? )
1
4
We know that ?? ?? =?? ?? ?? ??
?? ?? =?? (?? ?? ?? ?? )
1
4
??? ?? ?(?? ?? )
1
4 ?(
???? ??? ?? 3
?? 2
)
1
4

??? ??? 3
4
???? ?
1
4
?
2
?
1
?(
?? 1
?? 2
)
1
4
=>
?
1
?
2
?(
?? 2
?? 1
)
1
4
=(16)
1
4=2



11


19. Which one of the following modifications of the simple ideal Rankine cycle increases the thermal
efficiency and reduces the moisture content of the steam at the turbine outlet?
A. Decreasing the condenser pressure.
B. Increasing the boiler pressure.
C. Decreasing the boiler pressure.
D. Increasing the turbine inlet temperature.
Ans: option (D)
Sol: Due to increase of the turbine inlet temperature, quality of the stream at outlet of the turbine
improves. Which increases the thermal efficiency and reduces the moisture content of the steam at the
turbine outlet.

20. Consider a linear rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of
100 MPa along the length direction. Assume plane stress conditions in the plane normal to the
thickness. The Young?s modulus E = 200 MPa and Poisson?s ratio v = 0.3 are given. The principal
strains in the plane of the sheet are
A. (0.5, 0.0) B. (0.35, -0.15)
C. (0.5, -0.5) D. (0.5, -0.15)
Ans: option (D)
Sol: ?
1
=
?? 1
?? ???
?? 2
?? =
100
200
?0.3?
0
200
=0.5

?
2
=
?? 2
?? ???
?? 1
?? =
0
200
?0.3?
100
200
=?0.15


21. The figure shows an idealized plane truss. If a horizontal force of 300 N is applied at point A,
then the magnitude of the force produced in member CD is ________N.

Ans: 0

Sol:



12



The momentum about the point A must be zero, because there is no deformation of any truss.
Hence, ?? ????
=0 [?? ????
is not passing through the point A]

22. The fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase
in
A. freezing range
B. surface tension
C. degree of superheat
D. viscosity
Ans: option (C)
Sol: Fluidity of molten metal of cast alloys increases with increase in degree of superheat.

23. The most common limit gage used for inspecting the hole diameter is
A. Ring gage B. Snap gage
C. Plug gage D. Master gage
Ans: option (C)
Sol: The most common limit gage used for inspecting the hole diameter is Plug gage.

24. The differential equation 45
dy
y
dx
+= is valid in the domain 0 ? x ? 1 with y(0) = 2.25. The
solution of the differential equation is
A. y = e
-4x
+ 1.25
B. y = e
4x
+ 5
C. y = e
4x
+ 1.25
D. y = e
-4x
+ 5
Ans: option (A)
Sol: The given equation is.



13

???? ???? +4?? =5
If Integration factor = ?? ?4????
=?? 4??
? ?? ????? =?5????? ???? +??
? ?? ??? 4?? =5?
?? 4?? 4
+??
? ?? ??? 4?? =5?
?? 4?? 4
+?? ?.( 1)
Now for at x=0,
? 2.25 =
5
4
+ ??
? ?? =1
? Using the value of C in equ (1)
? ?? ?
?? 4?? ?? 4?? =
5
?? 4?? ?
?? 4?? 4
+
?? ?? 4??
? ?? =1.25+ ?? ?4??

25. A two-dimensional incompressible frictionless flow field is given by
??
. u xi yj =? If ? is the density
of the fluid, the expression for pressure gradient vector at any point in the flow field is given as
A.
( )
22
??
x i y j ??+ B.
( )
??
xi yj ??+
C.
( )
??
xi yj ? + D.
( )
??
xi yj ? ?
Ans: option (B)
Sol: Euler?s Equation of motion in 2D.

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

As there is no extra force acting on the fluid.
?? ?? ?????? ?? ?? =0
Now form the given expiration, u=x & v=y
?
????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????


?0+ ?? ?1+0+0=0?
1
?? ????
????

0+ 0+?? ?1+0=0?
1
?? ????
????

??????????? ???????? ?????? =
????
????
???+
????
????
???= ??? (?? ???+?? ??? )




14

26. A short shoe external drum brake is shown in the figure. The diameter of the brake drum is 500
mm. The dimensions a = 1000 mm, b = 500 mm and c = 200 mm. The coefficient of friction
between the drum and the shoe is 0.35. The force applied on the lever F = 100 N as shown in
the figure. The drum is rotating anti-clockwise. The braking torque on the drum is _______N.m
(round off to two decimal places).

Ans: 20.34
Sol:

Applying momentum about point O.

??? ?? =0

?? ??? +?? ?? ?? ??? ??? ?? ??? =0
?? ?? =232.55
Breaking Torque = ?? ?? ?? ?? ?? = 20.34

27. A uniform disc with radius r and a mass of m kg is mounted centrally on a horizontal axle of
negligible mass and length of 1.5r. The disc spins counter-clockwise about the axle with angular
speed ?, when viewed from the right-hand side bearing, Q. The axle precesses about a vertical
axis at
?p = ?/10 in the clockwise direction when viewed from above. Let RP and RQ (positive upwards)
be the resultant reaction forces due to the mass and the gyroscopic effect, at bearings P and Q,
respectively. Assuming ?
2
r = 300 m/s
2
and g = 10 m/s
2
, the ratio of the larger to the smaller
bearing reaction force (considering appropriate signs) is __________.



15


Ans: -3
Sol: ?????????????????? ???????????? (???? )=???? ?? ??

Using: ?? ?? =
?? 10
and ?? 2
?? =300

???? =
?? ?? 2
2
?? 2
10
=15????

Reaction at P and Q due to gravity

?? ?? 1
+?? ?? 1
=???? =10??
?? ?? 1
=5??
??? ?? 1
= 5 ??

Reaction at P and Q due to GC

Taking momentum about point p.
?? ?? 2
?1.5?? ?15???? =0
?? ?? 2
=
15????
1.5?? =10 ??
??? ?? 2
= ?10 ??
?????? ,
?? ?? ?? ?? =
?? ?? 1
+?? ?? 2

?? ?? 1
+?? ?? 2
=
5+10
5?10
= ?3

28. The figure shows a pouring arrangement for casting of a metal block. Frictional losses are
negligible. The acceleration due to gravity is 9.81 m/s
2
. The time (in s, round off to two decimal
places) to fill up the mold cavity (of size 40 cm ? 30 cm ? 15 cm) is ____________



16


Ans: 29.84
Sol: ???????? ?????????????? ???????? =
?? ?? ?? ?? .?2?? ?

???????? =
0.40?0.30?0.15
?? 0.02
2
4
.?2?9.81?0.20
28.94 ??????

29. The activities of a project, their duration and the precedence relationships are given in the table.
For example, in a precedence relationship ?X < Y, Z? means that X is predecessor of activities Y
and Z. The time to complete the activities along the critical path is ____________ weeks.
Activity Duration
(Weeks)
Precedence
Relationship
A 5 A < B, C, D
B 7 B < E, F, G
C 10 C < I
D 6 D < G
E 3 E < H
F 9 F < I
G 7 G < I
H 4 H < I
I 2 ---
A. 21 B. 25
C. 23 D. 17
Ans: option (C)
Sol:



17


30. The crank of a slider-crank mechanism rotates counter-clockwise (CCW) with a constant angular
velocity ?, as shown. Assume the length of the crank to be r.

Using exact analysis, the acceleration of the slider in the y-direction, at the instant shown, where
the crank is parallel to x-axis, is given by
A. -?
2
r B. 2?
2
r
C. ?
2
r D. -2?
2
r
Ans: option (C)
Sol:


Velocity of point A, ?? ?? = ?? ???
The radial acceleration of point A, ?? ????
=?? ?? 2

Since, the inclination of line AB is 45 degree, the acceleration of the point B will be equal to the
acceleration of point A. i.e. ?? ?? 2


31. A gas tungsten arc welding operation is performed using a current of 250 A and an arc voltage of
20 V at a welding speed of 5 mm/s. Assuming that the arc efficiency is 70%, the net heat input
per unit length of the weld will be ________ kJ/mm (round off to one decimal place).
Ans: 0.7
Sol: ???????? ?????????? =??Power
elec

???????? ?????????? =0.7?250?20=3500 ????????

???????? ?????????? per unit length=
3500
5
=700
?? ????

=0.7 KJ/mm

32. Water flows through two different pipes A and B of the same circular cross-section but at
different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both
the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes
is same, the ratio of volume flow rates QB/QA is ______ (round off to two decimal places).
A
O
B
FirstRanker.com - FirstRanker's Choice



2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6




3

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of ?? =
8+6
2
=7

6. X is an online media provider. By offering unlimited and exclusive online content at attractive
prices for a loyalty membership, X is almost forcing its customers towards its loyalty
membership. If its loyalty membership continues to grow at its current rate, within the next
eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
A. Most households that subscribe to X?s loyalty membership discontinue watching cable
television
B. Non-members prefer to watch cable television
C. The X is cancelling accounts of non-members
D. Cable television operators don?t subscribe to X?s loyalty membership
Ans: option (A)
Sol: option A is the most appropriate solution

7. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased
by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.
A. 35.70 B. 10.00
C. 37.50 D. 25.00
Ans: option (C)
Sol: Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04??? =0.04??
And the fiscal deficit in 2016 = 0.05?1.1?? =0.055??
Increase in fiscal deficit = 0.055x ? 0.04x = 0.015x
So, the percentage increase in fiscal deficit =
0.015?? 0.04?? ?100=37.5%

8. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can
empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is
opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is
_________.
A. 16.50 B. 14.50
C. 15.50 D. 13.50
Ans: option (B)
Sol: 1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(
1
6
? ?
1
12
? )=
1
3
?
Tank filled by when Q and R works for another 6 hours = 6(
1
9
? ?
1
12
? )=
1
6
?
Total tank filled in these 10 hours =
1
3
? +
1
6
? =0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in
9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours




4

9. While teaching a creative writing class in India, I was surprised at receiving stories from the
students that were all set in distant places: in the American West with cowboys and in
Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave
the writers in the once-colonised countries the confidence to see the shabby lives around them
as worthy of being ?told?.
The writer of this passage is surprised by the creative writing assignments of his students,
because __________.
A. Some of the students had written about ice cubes and cowboys
B. None of the students had written about ice cubes and cowboys
C. Some of the students had written stories set in foreign places
D. None of the students had written stories set in India
Ans: option (C)
Sol: option C is the most appropriate solution

10. Mola is a digital platform for taxis in a city. It offers three types of rides ? Pool, Mini and Prime.
The Table below presents the number of rides for the past four months. The platform earns one
US dollar per ride. What is the percentage share of revenue contributed by Prime to the total
revenues of Mola, for the entire duration?
Type
Month
January February March April
Pool 170 320 215 190
Mini 110 220 180 70
Prime 75 180 120 90

A. 38.74 B. 23.97
C. 25.86 D. 16.24

Ans: option (B)
Sol: Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580
Revenue contributed by Prime = 75 + 180 + 120 +90 = 465
Total revenue of Mola = 895 + 580 + 465 = 1940
So, the percentage share =
465
1940
?100=23.97%

MECHANICAL ENGINEERING
1. A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by
application of pure bending moments at its ends. The Young?s modulus of the material of the
wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.
Ans: 50
Sol: Tensile stress
?? =
?? ?? ?? =
100?10
3
1
(
1
1000?2
)=50 ??????





5

2. In an electrical discharge machining process, the breakdown voltage across inter electrode gap
(IEG) is 200 V and the capacitance of the RC circuit is 50 ?F. The energy (in J) released per
spark across the IEG is __________
Ans: 1
Sol:
?? =
1
2
??????????????????????? ????????????? ?? 2

?? =0.5?50?10
?6
?200
2
=1 ??


3. If x is the mean of data 3, x, 2 and 4, then the mode is _________
Ans: 3
Sol: ?? =
3+?? +2+4
4

4??? =3+?? +2+4
4??? ??? =3+2+4=9
?? =3
Mode is 3. (Maximum repeated value)

4. The cold forming process in which a hardened tool is pressed against a workpiece (when there is
relative motion between the tool and the workpiece) to produce a roughened surface with a
regular pattern is
A. Strip rolling B. Knurling
C. Roll forming D. Chamfering
Ans: option (B)
Sol: We provide special pattern to prevent the relative motion between contact surface. This special
pattern is known as Knurling.


5. Endurance limit of a beam subjected to pure bending decreases with
A. increase in the surface roughness and increase in the size of the beam
B. decrease in the surface roughness and decrease in the size of the beam
C. decrease in the surface roughness and increase in the size of the beam
D. increase in the surface roughness and decrease in the size of the beam
Ans: option (A)
Sol: Formula for endurance limit
?? ?? =?? ?? ??? ?? ??? ?? ??? ?? ??? ?? ?

?? ???????
?? ?? ????????? ????????????
?? ?? ??????????????? ????????????
?? ?? ????????? ????????????
?? ?? ??????????????????????? ????????????
?? ?? ?
??????????????????? ?????????????? ?
Form above formula it is clear that the Endurance limit increases with increase in size,
surface, load, temp and endurance strength.







6

6. In matrix equation [A] {X} = {R}.
? ?
4 8 4 2
8 16 4 , 1
4 4 15 4
AX
? ? ? ?
?? ??
= ? = ??
??
????
??
??
?
? ? ? ?
and ? ?
32
16 .
64
R
??
??
=
??
??
??

One of the eigenvalues of matrix [A] is
A. 4 B. 15
C. 8 D. 16
Ans: option (D)
Sol: [A] {X} = {R}.

We know ???? = ???? ;?? ??????? ?? ??????????? ??????????

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}={
32
16
64
}

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}=16{
2
1
4
}

Hence, ?? =????

7. Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number
ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit.
The Reynolds number at the exit of the pipe is___________.
Ans: 500
Sol: Reynold?s Number
???? =
?? ?? ????
?? ??
Where: -
?? ??????????? ??????????????
?? ????
??????????????? ????????????????
?? ??????????????? ???? ????????
?? ? Dynamic viscosity of Fluid
?? ?? =(
?? ?? ????
?? ?? )=
(

?? (
?? ???????? ?? ???????? ) ?? ?? )


From above expiration, Reynold?s Number is independent of flow profile. Hence, Reynold?s
Number for parabolic flow profile is 500.

8. For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure
and temperature, respectively. As per Maxwell?s relations,
p
v
s
? ??
??
?
??
is equal to
A.
T
p
v
? ??
??
?
??
B.
p
s
T
? ??
??
?
??
C.
s
T
p
?? ?
??
?
??
D.
p
T
v
? ??
?
??
?
??

Ans: option (C)
Sol: From mathematical relation expiration



7

???? = ?????? +??????
? (
????
????
)
?? = (
????
????
)
??
???????? ?????????????? ????????????????
?? ?= ?????? +??????
? (
????
????
)
?? = (
????
????
)
??

9. Hardenability of steel is a measure of
A. the ability to harden when it is cold worked
B. the maximum hardness that can be obtained when it is austenitized and then quenched
C. the ability to retain its hardness when it is heated to elevated temperatures
D. the depth to which required hardening is obtained when it is austenitized and then quenched
Ans: option (D)
Sol: The depth to which required hardening is obtained when it is austenitized and then quenched.

10. The directional derivative of the function f(x, y) = x
2
+ y
2
along a line directed from (0, 0) to (1,
1), evaluated at the point x = 1, y = 1 is
A. 2 B. ?2
C. 4?2 D. 2?2
Ans: option (D)
Sol: Directional derivative of function along the line is the scalar value of derivative along the line. i.e.
we have to calculate value of derivative of function in the direction of given line vector
? ?? = ??? (
????
????
)+ ??? (
????
????
)
? ?? = 2???+ 2???
Now, calculating the value of ? ?? in 1???+ 1???
D.D of given function is (2???+ 2??? ) ?
(??? + ?? ?)
|??? + ?? ?|
= 2 ?2

11. A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is
A.
2 D
T
?
B.
T
D

C.
D
T
?
D.
D
T

Ans: option (C)
Sol: circular pitch =
????
??

12. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the
instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of
points P and R are VP and VR, in the x and y directions, respectively. The magnitude of the
angular velocity of the body is




8

A. /3
R
V B. /3
P
V
C. 2VR D. 2VP
Ans: option (C)
Sol: The given body is a rigid body; Hence the given body will not have any deformation, and the
possible motion is translation and angular motion. we know that the angular motion of the object is
always defined as the motion about the point. Hence, first we have to find a point parallel to both
velocity ?? ?? and ?? ?? .


? Angular velocity, ?? =
???????????????? ?????????????????????????? ????????????????
?? =
?? ?? ????
=
?? ?? ????

???? =
?3
2
????????? ???? ???????????????? =
?3
2
?1=
?3
2

???? =
1
2
????????? ???? ???????????????? =
1
2
?1=
1
2


?? =
2?? ?? ?3
=
2?? ?? 1


13. Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4
m. The view factor F12 is
A. 0.25 B. 0.0625
C. 1.0 D. 0.5
Ans: option (C)
Sol: ?? 12
=1

14. The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
A.
10
01
??
??
?
??
B.
01
10
? ??
??
?
??

C.
01
10
??
??
??
D.
10
01
???
??
??

Ans: option (C)
Sol: The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
01
10
??
??
??




S



9

15. The state of stress at a point in a component is represented by a Mohr?s circle of radius 100 MPa
centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the
normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same
point is ___________ MPa.
Ans: 80
Sol:


?? =?100
2
?60
2
=80 ??????

16. One-dimensional steady state heat conduction takes place through a solid whose cross-sectional
area varies linearly in the direction of heat transfer. Assume there is no heat generation in the
solid and the thermal conductivity of the material is constant and independent of temperature.
The temperature distribution in the solid is
A. Quadratic B. Exponential
C. Logarithmic D. Linear
Ans: option (C)
Sol: Let the given body cross-sectional area varies linearly, and heat is flowing from left to right.





If there is no heat generation,
?? ????
(?????
????
????
)=0

?
?? ????
(?????
????
????
)=?0

(?????
????
????
)=??

??? (?? 0
+?? ?? ?? )
????
????
=??
???? =
? ?? ????
?? (?? 0
+?? ?? ?? )


? ????
2
1
=?
? ?? ????
?? (?? 0
+?? ?? ?? )
2
1


?? 2
??? 1
= ?
?? ?? ln(
?? ?? ?? 2
+?? 0
?? ?? ?? 1
+?? 0
)



10

17. An analytic function f(z) of complex variable z = x + I y may be written as f(z) = u(x, y) + iv (x,
y). Then, u(x, y) and v(x, y) must satisfy
A.
uv
xy
??
=?
??
and
uv
yx
??
=
??

B.
uv
xy
??
=?
??
and
uv
yx
??
=?
??

C.
uv
xy
??
=
??
and
uv
yx
??
=?
??

D.
uv
xy
??
=
??
and
uv
yx
??
=
??

Ans: option (C)
Sol: If f(z) = u(x, y) + iv(x, y) is analytic function then it must satisfy the following relations.

????
????
=
????
????


????
????
=?
????
????


18. A thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is
losing heat to the surroundings by natural convection. The temperatures of the plate and the
surroundings, and the properties of the surrounding fluid, are constant. The relationship between
the average Nusselt and Rayleigh numbers is given as Nu = K Ra ?, where K is a constant. The
length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the
plate is increased to 16L keeping all other factors constant.

If the average heat transfer coefficient for the first plate is h1 and that for the second plate is h2,
the value of the ratio h1/h2 is____________.
Ans: 2
Sol: ?? ?? =?? (?? ?? )
1
4
We know that ?? ?? =?? ?? ?? ??
?? ?? =?? (?? ?? ?? ?? )
1
4
??? ?? ?(?? ?? )
1
4 ?(
???? ??? ?? 3
?? 2
)
1
4

??? ??? 3
4
???? ?
1
4
?
2
?
1
?(
?? 1
?? 2
)
1
4
=>
?
1
?
2
?(
?? 2
?? 1
)
1
4
=(16)
1
4=2



11


19. Which one of the following modifications of the simple ideal Rankine cycle increases the thermal
efficiency and reduces the moisture content of the steam at the turbine outlet?
A. Decreasing the condenser pressure.
B. Increasing the boiler pressure.
C. Decreasing the boiler pressure.
D. Increasing the turbine inlet temperature.
Ans: option (D)
Sol: Due to increase of the turbine inlet temperature, quality of the stream at outlet of the turbine
improves. Which increases the thermal efficiency and reduces the moisture content of the steam at the
turbine outlet.

20. Consider a linear rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of
100 MPa along the length direction. Assume plane stress conditions in the plane normal to the
thickness. The Young?s modulus E = 200 MPa and Poisson?s ratio v = 0.3 are given. The principal
strains in the plane of the sheet are
A. (0.5, 0.0) B. (0.35, -0.15)
C. (0.5, -0.5) D. (0.5, -0.15)
Ans: option (D)
Sol: ?
1
=
?? 1
?? ???
?? 2
?? =
100
200
?0.3?
0
200
=0.5

?
2
=
?? 2
?? ???
?? 1
?? =
0
200
?0.3?
100
200
=?0.15


21. The figure shows an idealized plane truss. If a horizontal force of 300 N is applied at point A,
then the magnitude of the force produced in member CD is ________N.

Ans: 0

Sol:



12



The momentum about the point A must be zero, because there is no deformation of any truss.
Hence, ?? ????
=0 [?? ????
is not passing through the point A]

22. The fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase
in
A. freezing range
B. surface tension
C. degree of superheat
D. viscosity
Ans: option (C)
Sol: Fluidity of molten metal of cast alloys increases with increase in degree of superheat.

23. The most common limit gage used for inspecting the hole diameter is
A. Ring gage B. Snap gage
C. Plug gage D. Master gage
Ans: option (C)
Sol: The most common limit gage used for inspecting the hole diameter is Plug gage.

24. The differential equation 45
dy
y
dx
+= is valid in the domain 0 ? x ? 1 with y(0) = 2.25. The
solution of the differential equation is
A. y = e
-4x
+ 1.25
B. y = e
4x
+ 5
C. y = e
4x
+ 1.25
D. y = e
-4x
+ 5
Ans: option (A)
Sol: The given equation is.



13

???? ???? +4?? =5
If Integration factor = ?? ?4????
=?? 4??
? ?? ????? =?5????? ???? +??
? ?? ??? 4?? =5?
?? 4?? 4
+??
? ?? ??? 4?? =5?
?? 4?? 4
+?? ?.( 1)
Now for at x=0,
? 2.25 =
5
4
+ ??
? ?? =1
? Using the value of C in equ (1)
? ?? ?
?? 4?? ?? 4?? =
5
?? 4?? ?
?? 4?? 4
+
?? ?? 4??
? ?? =1.25+ ?? ?4??

25. A two-dimensional incompressible frictionless flow field is given by
??
. u xi yj =? If ? is the density
of the fluid, the expression for pressure gradient vector at any point in the flow field is given as
A.
( )
22
??
x i y j ??+ B.
( )
??
xi yj ??+
C.
( )
??
xi yj ? + D.
( )
??
xi yj ? ?
Ans: option (B)
Sol: Euler?s Equation of motion in 2D.

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

As there is no extra force acting on the fluid.
?? ?? ?????? ?? ?? =0
Now form the given expiration, u=x & v=y
?
????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????


?0+ ?? ?1+0+0=0?
1
?? ????
????

0+ 0+?? ?1+0=0?
1
?? ????
????

??????????? ???????? ?????? =
????
????
???+
????
????
???= ??? (?? ???+?? ??? )




14

26. A short shoe external drum brake is shown in the figure. The diameter of the brake drum is 500
mm. The dimensions a = 1000 mm, b = 500 mm and c = 200 mm. The coefficient of friction
between the drum and the shoe is 0.35. The force applied on the lever F = 100 N as shown in
the figure. The drum is rotating anti-clockwise. The braking torque on the drum is _______N.m
(round off to two decimal places).

Ans: 20.34
Sol:

Applying momentum about point O.

??? ?? =0

?? ??? +?? ?? ?? ??? ??? ?? ??? =0
?? ?? =232.55
Breaking Torque = ?? ?? ?? ?? ?? = 20.34

27. A uniform disc with radius r and a mass of m kg is mounted centrally on a horizontal axle of
negligible mass and length of 1.5r. The disc spins counter-clockwise about the axle with angular
speed ?, when viewed from the right-hand side bearing, Q. The axle precesses about a vertical
axis at
?p = ?/10 in the clockwise direction when viewed from above. Let RP and RQ (positive upwards)
be the resultant reaction forces due to the mass and the gyroscopic effect, at bearings P and Q,
respectively. Assuming ?
2
r = 300 m/s
2
and g = 10 m/s
2
, the ratio of the larger to the smaller
bearing reaction force (considering appropriate signs) is __________.



15


Ans: -3
Sol: ?????????????????? ???????????? (???? )=???? ?? ??

Using: ?? ?? =
?? 10
and ?? 2
?? =300

???? =
?? ?? 2
2
?? 2
10
=15????

Reaction at P and Q due to gravity

?? ?? 1
+?? ?? 1
=???? =10??
?? ?? 1
=5??
??? ?? 1
= 5 ??

Reaction at P and Q due to GC

Taking momentum about point p.
?? ?? 2
?1.5?? ?15???? =0
?? ?? 2
=
15????
1.5?? =10 ??
??? ?? 2
= ?10 ??
?????? ,
?? ?? ?? ?? =
?? ?? 1
+?? ?? 2

?? ?? 1
+?? ?? 2
=
5+10
5?10
= ?3

28. The figure shows a pouring arrangement for casting of a metal block. Frictional losses are
negligible. The acceleration due to gravity is 9.81 m/s
2
. The time (in s, round off to two decimal
places) to fill up the mold cavity (of size 40 cm ? 30 cm ? 15 cm) is ____________



16


Ans: 29.84
Sol: ???????? ?????????????? ???????? =
?? ?? ?? ?? .?2?? ?

???????? =
0.40?0.30?0.15
?? 0.02
2
4
.?2?9.81?0.20
28.94 ??????

29. The activities of a project, their duration and the precedence relationships are given in the table.
For example, in a precedence relationship ?X < Y, Z? means that X is predecessor of activities Y
and Z. The time to complete the activities along the critical path is ____________ weeks.
Activity Duration
(Weeks)
Precedence
Relationship
A 5 A < B, C, D
B 7 B < E, F, G
C 10 C < I
D 6 D < G
E 3 E < H
F 9 F < I
G 7 G < I
H 4 H < I
I 2 ---
A. 21 B. 25
C. 23 D. 17
Ans: option (C)
Sol:



17


30. The crank of a slider-crank mechanism rotates counter-clockwise (CCW) with a constant angular
velocity ?, as shown. Assume the length of the crank to be r.

Using exact analysis, the acceleration of the slider in the y-direction, at the instant shown, where
the crank is parallel to x-axis, is given by
A. -?
2
r B. 2?
2
r
C. ?
2
r D. -2?
2
r
Ans: option (C)
Sol:


Velocity of point A, ?? ?? = ?? ???
The radial acceleration of point A, ?? ????
=?? ?? 2

Since, the inclination of line AB is 45 degree, the acceleration of the point B will be equal to the
acceleration of point A. i.e. ?? ?? 2


31. A gas tungsten arc welding operation is performed using a current of 250 A and an arc voltage of
20 V at a welding speed of 5 mm/s. Assuming that the arc efficiency is 70%, the net heat input
per unit length of the weld will be ________ kJ/mm (round off to one decimal place).
Ans: 0.7
Sol: ???????? ?????????? =??Power
elec

???????? ?????????? =0.7?250?20=3500 ????????

???????? ?????????? per unit length=
3500
5
=700
?? ????

=0.7 KJ/mm

32. Water flows through two different pipes A and B of the same circular cross-section but at
different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both
the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes
is same, the ratio of volume flow rates QB/QA is ______ (round off to two decimal places).
A
O
B



18

Ans: 0.5
Sol: Frictional losses of pipe

??? ? ????
?? ?? ?? ? ????
(
?? ?? )
?? ?? ?????
?? ?? ?? ??

?
????
?????
=
?? ?? ?? ?? ?? ?? 2
?? ?? ?? ?? ?? ?? 2
;?? ??????? ?? =
64
????



?? ?? 2
?? ?? 2
=
?
????
?? ?? ?? ?? ??? ?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? ?? ??

?? ?? ?? ?? =
?? ?? ?? ?? =0.5

33. Consider two concentric circular cylinders of different materials M and N in contact with each
other at r = b, as shown below. The interface at r = b is frictionless. The composite cylinder
system is subjected to internal pressure P. Let
( )
,
MM
r
uu
?
and
( )
,
MM
rr ??
?? denote the radial and
tangential displacement and stress components, respectively, in material M Similarly,
( )
,
NN
r
uu
?

and
( )
,
NN
rr ??
?? denote the radial and tangential displacement and stress components, respectively,
in material N. The boundary conditions that need to be satisfied at the frictionless interface
between the two cylinders are :

A.
MN
rr
uu = and
MN
rr rr
?? = and
MN
uu
??
= and
MN
? ? ? ?
?? =
B.
MN
rr rr
?? = and
MN
? ? ? ?
?? = only
C.
MN
uu
??
= and
MN
? ? ? ?
?? = only
D.
MN
rr
uu = and
MN
rr rr
?? = only
Ans: option (D)
Sol:
FirstRanker.com - FirstRanker's Choice



2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6




3

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of ?? =
8+6
2
=7

6. X is an online media provider. By offering unlimited and exclusive online content at attractive
prices for a loyalty membership, X is almost forcing its customers towards its loyalty
membership. If its loyalty membership continues to grow at its current rate, within the next
eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
A. Most households that subscribe to X?s loyalty membership discontinue watching cable
television
B. Non-members prefer to watch cable television
C. The X is cancelling accounts of non-members
D. Cable television operators don?t subscribe to X?s loyalty membership
Ans: option (A)
Sol: option A is the most appropriate solution

7. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased
by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.
A. 35.70 B. 10.00
C. 37.50 D. 25.00
Ans: option (C)
Sol: Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04??? =0.04??
And the fiscal deficit in 2016 = 0.05?1.1?? =0.055??
Increase in fiscal deficit = 0.055x ? 0.04x = 0.015x
So, the percentage increase in fiscal deficit =
0.015?? 0.04?? ?100=37.5%

8. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can
empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is
opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is
_________.
A. 16.50 B. 14.50
C. 15.50 D. 13.50
Ans: option (B)
Sol: 1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(
1
6
? ?
1
12
? )=
1
3
?
Tank filled by when Q and R works for another 6 hours = 6(
1
9
? ?
1
12
? )=
1
6
?
Total tank filled in these 10 hours =
1
3
? +
1
6
? =0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in
9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours




4

9. While teaching a creative writing class in India, I was surprised at receiving stories from the
students that were all set in distant places: in the American West with cowboys and in
Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave
the writers in the once-colonised countries the confidence to see the shabby lives around them
as worthy of being ?told?.
The writer of this passage is surprised by the creative writing assignments of his students,
because __________.
A. Some of the students had written about ice cubes and cowboys
B. None of the students had written about ice cubes and cowboys
C. Some of the students had written stories set in foreign places
D. None of the students had written stories set in India
Ans: option (C)
Sol: option C is the most appropriate solution

10. Mola is a digital platform for taxis in a city. It offers three types of rides ? Pool, Mini and Prime.
The Table below presents the number of rides for the past four months. The platform earns one
US dollar per ride. What is the percentage share of revenue contributed by Prime to the total
revenues of Mola, for the entire duration?
Type
Month
January February March April
Pool 170 320 215 190
Mini 110 220 180 70
Prime 75 180 120 90

A. 38.74 B. 23.97
C. 25.86 D. 16.24

Ans: option (B)
Sol: Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580
Revenue contributed by Prime = 75 + 180 + 120 +90 = 465
Total revenue of Mola = 895 + 580 + 465 = 1940
So, the percentage share =
465
1940
?100=23.97%

MECHANICAL ENGINEERING
1. A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by
application of pure bending moments at its ends. The Young?s modulus of the material of the
wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.
Ans: 50
Sol: Tensile stress
?? =
?? ?? ?? =
100?10
3
1
(
1
1000?2
)=50 ??????





5

2. In an electrical discharge machining process, the breakdown voltage across inter electrode gap
(IEG) is 200 V and the capacitance of the RC circuit is 50 ?F. The energy (in J) released per
spark across the IEG is __________
Ans: 1
Sol:
?? =
1
2
??????????????????????? ????????????? ?? 2

?? =0.5?50?10
?6
?200
2
=1 ??


3. If x is the mean of data 3, x, 2 and 4, then the mode is _________
Ans: 3
Sol: ?? =
3+?? +2+4
4

4??? =3+?? +2+4
4??? ??? =3+2+4=9
?? =3
Mode is 3. (Maximum repeated value)

4. The cold forming process in which a hardened tool is pressed against a workpiece (when there is
relative motion between the tool and the workpiece) to produce a roughened surface with a
regular pattern is
A. Strip rolling B. Knurling
C. Roll forming D. Chamfering
Ans: option (B)
Sol: We provide special pattern to prevent the relative motion between contact surface. This special
pattern is known as Knurling.


5. Endurance limit of a beam subjected to pure bending decreases with
A. increase in the surface roughness and increase in the size of the beam
B. decrease in the surface roughness and decrease in the size of the beam
C. decrease in the surface roughness and increase in the size of the beam
D. increase in the surface roughness and decrease in the size of the beam
Ans: option (A)
Sol: Formula for endurance limit
?? ?? =?? ?? ??? ?? ??? ?? ??? ?? ??? ?? ?

?? ???????
?? ?? ????????? ????????????
?? ?? ??????????????? ????????????
?? ?? ????????? ????????????
?? ?? ??????????????????????? ????????????
?? ?? ?
??????????????????? ?????????????? ?
Form above formula it is clear that the Endurance limit increases with increase in size,
surface, load, temp and endurance strength.







6

6. In matrix equation [A] {X} = {R}.
? ?
4 8 4 2
8 16 4 , 1
4 4 15 4
AX
? ? ? ?
?? ??
= ? = ??
??
????
??
??
?
? ? ? ?
and ? ?
32
16 .
64
R
??
??
=
??
??
??

One of the eigenvalues of matrix [A] is
A. 4 B. 15
C. 8 D. 16
Ans: option (D)
Sol: [A] {X} = {R}.

We know ???? = ???? ;?? ??????? ?? ??????????? ??????????

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}={
32
16
64
}

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}=16{
2
1
4
}

Hence, ?? =????

7. Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number
ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit.
The Reynolds number at the exit of the pipe is___________.
Ans: 500
Sol: Reynold?s Number
???? =
?? ?? ????
?? ??
Where: -
?? ??????????? ??????????????
?? ????
??????????????? ????????????????
?? ??????????????? ???? ????????
?? ? Dynamic viscosity of Fluid
?? ?? =(
?? ?? ????
?? ?? )=
(

?? (
?? ???????? ?? ???????? ) ?? ?? )


From above expiration, Reynold?s Number is independent of flow profile. Hence, Reynold?s
Number for parabolic flow profile is 500.

8. For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure
and temperature, respectively. As per Maxwell?s relations,
p
v
s
? ??
??
?
??
is equal to
A.
T
p
v
? ??
??
?
??
B.
p
s
T
? ??
??
?
??
C.
s
T
p
?? ?
??
?
??
D.
p
T
v
? ??
?
??
?
??

Ans: option (C)
Sol: From mathematical relation expiration



7

???? = ?????? +??????
? (
????
????
)
?? = (
????
????
)
??
???????? ?????????????? ????????????????
?? ?= ?????? +??????
? (
????
????
)
?? = (
????
????
)
??

9. Hardenability of steel is a measure of
A. the ability to harden when it is cold worked
B. the maximum hardness that can be obtained when it is austenitized and then quenched
C. the ability to retain its hardness when it is heated to elevated temperatures
D. the depth to which required hardening is obtained when it is austenitized and then quenched
Ans: option (D)
Sol: The depth to which required hardening is obtained when it is austenitized and then quenched.

10. The directional derivative of the function f(x, y) = x
2
+ y
2
along a line directed from (0, 0) to (1,
1), evaluated at the point x = 1, y = 1 is
A. 2 B. ?2
C. 4?2 D. 2?2
Ans: option (D)
Sol: Directional derivative of function along the line is the scalar value of derivative along the line. i.e.
we have to calculate value of derivative of function in the direction of given line vector
? ?? = ??? (
????
????
)+ ??? (
????
????
)
? ?? = 2???+ 2???
Now, calculating the value of ? ?? in 1???+ 1???
D.D of given function is (2???+ 2??? ) ?
(??? + ?? ?)
|??? + ?? ?|
= 2 ?2

11. A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is
A.
2 D
T
?
B.
T
D

C.
D
T
?
D.
D
T

Ans: option (C)
Sol: circular pitch =
????
??

12. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the
instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of
points P and R are VP and VR, in the x and y directions, respectively. The magnitude of the
angular velocity of the body is




8

A. /3
R
V B. /3
P
V
C. 2VR D. 2VP
Ans: option (C)
Sol: The given body is a rigid body; Hence the given body will not have any deformation, and the
possible motion is translation and angular motion. we know that the angular motion of the object is
always defined as the motion about the point. Hence, first we have to find a point parallel to both
velocity ?? ?? and ?? ?? .


? Angular velocity, ?? =
???????????????? ?????????????????????????? ????????????????
?? =
?? ?? ????
=
?? ?? ????

???? =
?3
2
????????? ???? ???????????????? =
?3
2
?1=
?3
2

???? =
1
2
????????? ???? ???????????????? =
1
2
?1=
1
2


?? =
2?? ?? ?3
=
2?? ?? 1


13. Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4
m. The view factor F12 is
A. 0.25 B. 0.0625
C. 1.0 D. 0.5
Ans: option (C)
Sol: ?? 12
=1

14. The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
A.
10
01
??
??
?
??
B.
01
10
? ??
??
?
??

C.
01
10
??
??
??
D.
10
01
???
??
??

Ans: option (C)
Sol: The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
01
10
??
??
??




S



9

15. The state of stress at a point in a component is represented by a Mohr?s circle of radius 100 MPa
centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the
normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same
point is ___________ MPa.
Ans: 80
Sol:


?? =?100
2
?60
2
=80 ??????

16. One-dimensional steady state heat conduction takes place through a solid whose cross-sectional
area varies linearly in the direction of heat transfer. Assume there is no heat generation in the
solid and the thermal conductivity of the material is constant and independent of temperature.
The temperature distribution in the solid is
A. Quadratic B. Exponential
C. Logarithmic D. Linear
Ans: option (C)
Sol: Let the given body cross-sectional area varies linearly, and heat is flowing from left to right.





If there is no heat generation,
?? ????
(?????
????
????
)=0

?
?? ????
(?????
????
????
)=?0

(?????
????
????
)=??

??? (?? 0
+?? ?? ?? )
????
????
=??
???? =
? ?? ????
?? (?? 0
+?? ?? ?? )


? ????
2
1
=?
? ?? ????
?? (?? 0
+?? ?? ?? )
2
1


?? 2
??? 1
= ?
?? ?? ln(
?? ?? ?? 2
+?? 0
?? ?? ?? 1
+?? 0
)



10

17. An analytic function f(z) of complex variable z = x + I y may be written as f(z) = u(x, y) + iv (x,
y). Then, u(x, y) and v(x, y) must satisfy
A.
uv
xy
??
=?
??
and
uv
yx
??
=
??

B.
uv
xy
??
=?
??
and
uv
yx
??
=?
??

C.
uv
xy
??
=
??
and
uv
yx
??
=?
??

D.
uv
xy
??
=
??
and
uv
yx
??
=
??

Ans: option (C)
Sol: If f(z) = u(x, y) + iv(x, y) is analytic function then it must satisfy the following relations.

????
????
=
????
????


????
????
=?
????
????


18. A thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is
losing heat to the surroundings by natural convection. The temperatures of the plate and the
surroundings, and the properties of the surrounding fluid, are constant. The relationship between
the average Nusselt and Rayleigh numbers is given as Nu = K Ra ?, where K is a constant. The
length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the
plate is increased to 16L keeping all other factors constant.

If the average heat transfer coefficient for the first plate is h1 and that for the second plate is h2,
the value of the ratio h1/h2 is____________.
Ans: 2
Sol: ?? ?? =?? (?? ?? )
1
4
We know that ?? ?? =?? ?? ?? ??
?? ?? =?? (?? ?? ?? ?? )
1
4
??? ?? ?(?? ?? )
1
4 ?(
???? ??? ?? 3
?? 2
)
1
4

??? ??? 3
4
???? ?
1
4
?
2
?
1
?(
?? 1
?? 2
)
1
4
=>
?
1
?
2
?(
?? 2
?? 1
)
1
4
=(16)
1
4=2



11


19. Which one of the following modifications of the simple ideal Rankine cycle increases the thermal
efficiency and reduces the moisture content of the steam at the turbine outlet?
A. Decreasing the condenser pressure.
B. Increasing the boiler pressure.
C. Decreasing the boiler pressure.
D. Increasing the turbine inlet temperature.
Ans: option (D)
Sol: Due to increase of the turbine inlet temperature, quality of the stream at outlet of the turbine
improves. Which increases the thermal efficiency and reduces the moisture content of the steam at the
turbine outlet.

20. Consider a linear rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of
100 MPa along the length direction. Assume plane stress conditions in the plane normal to the
thickness. The Young?s modulus E = 200 MPa and Poisson?s ratio v = 0.3 are given. The principal
strains in the plane of the sheet are
A. (0.5, 0.0) B. (0.35, -0.15)
C. (0.5, -0.5) D. (0.5, -0.15)
Ans: option (D)
Sol: ?
1
=
?? 1
?? ???
?? 2
?? =
100
200
?0.3?
0
200
=0.5

?
2
=
?? 2
?? ???
?? 1
?? =
0
200
?0.3?
100
200
=?0.15


21. The figure shows an idealized plane truss. If a horizontal force of 300 N is applied at point A,
then the magnitude of the force produced in member CD is ________N.

Ans: 0

Sol:



12



The momentum about the point A must be zero, because there is no deformation of any truss.
Hence, ?? ????
=0 [?? ????
is not passing through the point A]

22. The fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase
in
A. freezing range
B. surface tension
C. degree of superheat
D. viscosity
Ans: option (C)
Sol: Fluidity of molten metal of cast alloys increases with increase in degree of superheat.

23. The most common limit gage used for inspecting the hole diameter is
A. Ring gage B. Snap gage
C. Plug gage D. Master gage
Ans: option (C)
Sol: The most common limit gage used for inspecting the hole diameter is Plug gage.

24. The differential equation 45
dy
y
dx
+= is valid in the domain 0 ? x ? 1 with y(0) = 2.25. The
solution of the differential equation is
A. y = e
-4x
+ 1.25
B. y = e
4x
+ 5
C. y = e
4x
+ 1.25
D. y = e
-4x
+ 5
Ans: option (A)
Sol: The given equation is.



13

???? ???? +4?? =5
If Integration factor = ?? ?4????
=?? 4??
? ?? ????? =?5????? ???? +??
? ?? ??? 4?? =5?
?? 4?? 4
+??
? ?? ??? 4?? =5?
?? 4?? 4
+?? ?.( 1)
Now for at x=0,
? 2.25 =
5
4
+ ??
? ?? =1
? Using the value of C in equ (1)
? ?? ?
?? 4?? ?? 4?? =
5
?? 4?? ?
?? 4?? 4
+
?? ?? 4??
? ?? =1.25+ ?? ?4??

25. A two-dimensional incompressible frictionless flow field is given by
??
. u xi yj =? If ? is the density
of the fluid, the expression for pressure gradient vector at any point in the flow field is given as
A.
( )
22
??
x i y j ??+ B.
( )
??
xi yj ??+
C.
( )
??
xi yj ? + D.
( )
??
xi yj ? ?
Ans: option (B)
Sol: Euler?s Equation of motion in 2D.

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

As there is no extra force acting on the fluid.
?? ?? ?????? ?? ?? =0
Now form the given expiration, u=x & v=y
?
????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????


?0+ ?? ?1+0+0=0?
1
?? ????
????

0+ 0+?? ?1+0=0?
1
?? ????
????

??????????? ???????? ?????? =
????
????
???+
????
????
???= ??? (?? ???+?? ??? )




14

26. A short shoe external drum brake is shown in the figure. The diameter of the brake drum is 500
mm. The dimensions a = 1000 mm, b = 500 mm and c = 200 mm. The coefficient of friction
between the drum and the shoe is 0.35. The force applied on the lever F = 100 N as shown in
the figure. The drum is rotating anti-clockwise. The braking torque on the drum is _______N.m
(round off to two decimal places).

Ans: 20.34
Sol:

Applying momentum about point O.

??? ?? =0

?? ??? +?? ?? ?? ??? ??? ?? ??? =0
?? ?? =232.55
Breaking Torque = ?? ?? ?? ?? ?? = 20.34

27. A uniform disc with radius r and a mass of m kg is mounted centrally on a horizontal axle of
negligible mass and length of 1.5r. The disc spins counter-clockwise about the axle with angular
speed ?, when viewed from the right-hand side bearing, Q. The axle precesses about a vertical
axis at
?p = ?/10 in the clockwise direction when viewed from above. Let RP and RQ (positive upwards)
be the resultant reaction forces due to the mass and the gyroscopic effect, at bearings P and Q,
respectively. Assuming ?
2
r = 300 m/s
2
and g = 10 m/s
2
, the ratio of the larger to the smaller
bearing reaction force (considering appropriate signs) is __________.



15


Ans: -3
Sol: ?????????????????? ???????????? (???? )=???? ?? ??

Using: ?? ?? =
?? 10
and ?? 2
?? =300

???? =
?? ?? 2
2
?? 2
10
=15????

Reaction at P and Q due to gravity

?? ?? 1
+?? ?? 1
=???? =10??
?? ?? 1
=5??
??? ?? 1
= 5 ??

Reaction at P and Q due to GC

Taking momentum about point p.
?? ?? 2
?1.5?? ?15???? =0
?? ?? 2
=
15????
1.5?? =10 ??
??? ?? 2
= ?10 ??
?????? ,
?? ?? ?? ?? =
?? ?? 1
+?? ?? 2

?? ?? 1
+?? ?? 2
=
5+10
5?10
= ?3

28. The figure shows a pouring arrangement for casting of a metal block. Frictional losses are
negligible. The acceleration due to gravity is 9.81 m/s
2
. The time (in s, round off to two decimal
places) to fill up the mold cavity (of size 40 cm ? 30 cm ? 15 cm) is ____________



16


Ans: 29.84
Sol: ???????? ?????????????? ???????? =
?? ?? ?? ?? .?2?? ?

???????? =
0.40?0.30?0.15
?? 0.02
2
4
.?2?9.81?0.20
28.94 ??????

29. The activities of a project, their duration and the precedence relationships are given in the table.
For example, in a precedence relationship ?X < Y, Z? means that X is predecessor of activities Y
and Z. The time to complete the activities along the critical path is ____________ weeks.
Activity Duration
(Weeks)
Precedence
Relationship
A 5 A < B, C, D
B 7 B < E, F, G
C 10 C < I
D 6 D < G
E 3 E < H
F 9 F < I
G 7 G < I
H 4 H < I
I 2 ---
A. 21 B. 25
C. 23 D. 17
Ans: option (C)
Sol:



17


30. The crank of a slider-crank mechanism rotates counter-clockwise (CCW) with a constant angular
velocity ?, as shown. Assume the length of the crank to be r.

Using exact analysis, the acceleration of the slider in the y-direction, at the instant shown, where
the crank is parallel to x-axis, is given by
A. -?
2
r B. 2?
2
r
C. ?
2
r D. -2?
2
r
Ans: option (C)
Sol:


Velocity of point A, ?? ?? = ?? ???
The radial acceleration of point A, ?? ????
=?? ?? 2

Since, the inclination of line AB is 45 degree, the acceleration of the point B will be equal to the
acceleration of point A. i.e. ?? ?? 2


31. A gas tungsten arc welding operation is performed using a current of 250 A and an arc voltage of
20 V at a welding speed of 5 mm/s. Assuming that the arc efficiency is 70%, the net heat input
per unit length of the weld will be ________ kJ/mm (round off to one decimal place).
Ans: 0.7
Sol: ???????? ?????????? =??Power
elec

???????? ?????????? =0.7?250?20=3500 ????????

???????? ?????????? per unit length=
3500
5
=700
?? ????

=0.7 KJ/mm

32. Water flows through two different pipes A and B of the same circular cross-section but at
different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both
the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes
is same, the ratio of volume flow rates QB/QA is ______ (round off to two decimal places).
A
O
B



18

Ans: 0.5
Sol: Frictional losses of pipe

??? ? ????
?? ?? ?? ? ????
(
?? ?? )
?? ?? ?????
?? ?? ?? ??

?
????
?????
=
?? ?? ?? ?? ?? ?? 2
?? ?? ?? ?? ?? ?? 2
;?? ??????? ?? =
64
????



?? ?? 2
?? ?? 2
=
?
????
?? ?? ?? ?? ??? ?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? ?? ??

?? ?? ?? ?? =
?? ?? ?? ?? =0.5

33. Consider two concentric circular cylinders of different materials M and N in contact with each
other at r = b, as shown below. The interface at r = b is frictionless. The composite cylinder
system is subjected to internal pressure P. Let
( )
,
MM
r
uu
?
and
( )
,
MM
rr ??
?? denote the radial and
tangential displacement and stress components, respectively, in material M Similarly,
( )
,
NN
r
uu
?

and
( )
,
NN
rr ??
?? denote the radial and tangential displacement and stress components, respectively,
in material N. The boundary conditions that need to be satisfied at the frictionless interface
between the two cylinders are :

A.
MN
rr
uu = and
MN
rr rr
?? = and
MN
uu
??
= and
MN
? ? ? ?
?? =
B.
MN
rr rr
?? = and
MN
? ? ? ?
?? = only
C.
MN
uu
??
= and
MN
? ? ? ?
?? = only
D.
MN
rr
uu = and
MN
rr rr
?? = only
Ans: option (D)
Sol:



19



Internal pressure causes the stress in radial as well as circumferential direction.

At r=b i.e. interference of the cylinder can be frictionless if Stress in radial direction must be equal.
Velocity in radial direction must be equal. (This condition will make the normal force Zero)
As radius of the cylinder increases due to inside pressure, there will be relative velocity between
the contact surfaces in the circumferential direction.

34. The binary phase diagram of metals P and Q is shown in the figure. An alloy X containing 60% P
and 40% Q (by weight) is cooled from liquid to solid state. The fractions of solid and liquid (in
weight percent) at 1250
o
C, respectively, will be

A. 22.2% and 77.8%
B. 68.0% and 32.0%
C. 77.8% and 22.2%
D. 32.0% and 68.0%
Ans: option (A)
Sol: Mass fraction of liquid =
?? ?? ??? 0
?? ?? ??? ??
?? ?? =
68?40
68?32
= 0.778=77.8%
?? ?? =1??? ?? =0.222=22.2%

35. The annual demand of valves per year in a company is 10,000 units. The current order quantity
is 400 valves per order. The holding cost is Rs. 24 per valve per year and the ordering cost is Rs.
400 per order. If the current order quantity is changed to Economic Order Quantity, then the
saving in the total cost of inventory per year will be Rs. __________ (round off to two decimal
places).
Ans: 943.59
Sol:
Annual Demand (D) = 10000 nos
FirstRanker.com - FirstRanker's Choice



2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6




3

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of ?? =
8+6
2
=7

6. X is an online media provider. By offering unlimited and exclusive online content at attractive
prices for a loyalty membership, X is almost forcing its customers towards its loyalty
membership. If its loyalty membership continues to grow at its current rate, within the next
eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
A. Most households that subscribe to X?s loyalty membership discontinue watching cable
television
B. Non-members prefer to watch cable television
C. The X is cancelling accounts of non-members
D. Cable television operators don?t subscribe to X?s loyalty membership
Ans: option (A)
Sol: option A is the most appropriate solution

7. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased
by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.
A. 35.70 B. 10.00
C. 37.50 D. 25.00
Ans: option (C)
Sol: Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04??? =0.04??
And the fiscal deficit in 2016 = 0.05?1.1?? =0.055??
Increase in fiscal deficit = 0.055x ? 0.04x = 0.015x
So, the percentage increase in fiscal deficit =
0.015?? 0.04?? ?100=37.5%

8. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can
empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is
opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is
_________.
A. 16.50 B. 14.50
C. 15.50 D. 13.50
Ans: option (B)
Sol: 1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(
1
6
? ?
1
12
? )=
1
3
?
Tank filled by when Q and R works for another 6 hours = 6(
1
9
? ?
1
12
? )=
1
6
?
Total tank filled in these 10 hours =
1
3
? +
1
6
? =0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in
9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours




4

9. While teaching a creative writing class in India, I was surprised at receiving stories from the
students that were all set in distant places: in the American West with cowboys and in
Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave
the writers in the once-colonised countries the confidence to see the shabby lives around them
as worthy of being ?told?.
The writer of this passage is surprised by the creative writing assignments of his students,
because __________.
A. Some of the students had written about ice cubes and cowboys
B. None of the students had written about ice cubes and cowboys
C. Some of the students had written stories set in foreign places
D. None of the students had written stories set in India
Ans: option (C)
Sol: option C is the most appropriate solution

10. Mola is a digital platform for taxis in a city. It offers three types of rides ? Pool, Mini and Prime.
The Table below presents the number of rides for the past four months. The platform earns one
US dollar per ride. What is the percentage share of revenue contributed by Prime to the total
revenues of Mola, for the entire duration?
Type
Month
January February March April
Pool 170 320 215 190
Mini 110 220 180 70
Prime 75 180 120 90

A. 38.74 B. 23.97
C. 25.86 D. 16.24

Ans: option (B)
Sol: Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580
Revenue contributed by Prime = 75 + 180 + 120 +90 = 465
Total revenue of Mola = 895 + 580 + 465 = 1940
So, the percentage share =
465
1940
?100=23.97%

MECHANICAL ENGINEERING
1. A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by
application of pure bending moments at its ends. The Young?s modulus of the material of the
wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.
Ans: 50
Sol: Tensile stress
?? =
?? ?? ?? =
100?10
3
1
(
1
1000?2
)=50 ??????





5

2. In an electrical discharge machining process, the breakdown voltage across inter electrode gap
(IEG) is 200 V and the capacitance of the RC circuit is 50 ?F. The energy (in J) released per
spark across the IEG is __________
Ans: 1
Sol:
?? =
1
2
??????????????????????? ????????????? ?? 2

?? =0.5?50?10
?6
?200
2
=1 ??


3. If x is the mean of data 3, x, 2 and 4, then the mode is _________
Ans: 3
Sol: ?? =
3+?? +2+4
4

4??? =3+?? +2+4
4??? ??? =3+2+4=9
?? =3
Mode is 3. (Maximum repeated value)

4. The cold forming process in which a hardened tool is pressed against a workpiece (when there is
relative motion between the tool and the workpiece) to produce a roughened surface with a
regular pattern is
A. Strip rolling B. Knurling
C. Roll forming D. Chamfering
Ans: option (B)
Sol: We provide special pattern to prevent the relative motion between contact surface. This special
pattern is known as Knurling.


5. Endurance limit of a beam subjected to pure bending decreases with
A. increase in the surface roughness and increase in the size of the beam
B. decrease in the surface roughness and decrease in the size of the beam
C. decrease in the surface roughness and increase in the size of the beam
D. increase in the surface roughness and decrease in the size of the beam
Ans: option (A)
Sol: Formula for endurance limit
?? ?? =?? ?? ??? ?? ??? ?? ??? ?? ??? ?? ?

?? ???????
?? ?? ????????? ????????????
?? ?? ??????????????? ????????????
?? ?? ????????? ????????????
?? ?? ??????????????????????? ????????????
?? ?? ?
??????????????????? ?????????????? ?
Form above formula it is clear that the Endurance limit increases with increase in size,
surface, load, temp and endurance strength.







6

6. In matrix equation [A] {X} = {R}.
? ?
4 8 4 2
8 16 4 , 1
4 4 15 4
AX
? ? ? ?
?? ??
= ? = ??
??
????
??
??
?
? ? ? ?
and ? ?
32
16 .
64
R
??
??
=
??
??
??

One of the eigenvalues of matrix [A] is
A. 4 B. 15
C. 8 D. 16
Ans: option (D)
Sol: [A] {X} = {R}.

We know ???? = ???? ;?? ??????? ?? ??????????? ??????????

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}={
32
16
64
}

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}=16{
2
1
4
}

Hence, ?? =????

7. Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number
ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit.
The Reynolds number at the exit of the pipe is___________.
Ans: 500
Sol: Reynold?s Number
???? =
?? ?? ????
?? ??
Where: -
?? ??????????? ??????????????
?? ????
??????????????? ????????????????
?? ??????????????? ???? ????????
?? ? Dynamic viscosity of Fluid
?? ?? =(
?? ?? ????
?? ?? )=
(

?? (
?? ???????? ?? ???????? ) ?? ?? )


From above expiration, Reynold?s Number is independent of flow profile. Hence, Reynold?s
Number for parabolic flow profile is 500.

8. For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure
and temperature, respectively. As per Maxwell?s relations,
p
v
s
? ??
??
?
??
is equal to
A.
T
p
v
? ??
??
?
??
B.
p
s
T
? ??
??
?
??
C.
s
T
p
?? ?
??
?
??
D.
p
T
v
? ??
?
??
?
??

Ans: option (C)
Sol: From mathematical relation expiration



7

???? = ?????? +??????
? (
????
????
)
?? = (
????
????
)
??
???????? ?????????????? ????????????????
?? ?= ?????? +??????
? (
????
????
)
?? = (
????
????
)
??

9. Hardenability of steel is a measure of
A. the ability to harden when it is cold worked
B. the maximum hardness that can be obtained when it is austenitized and then quenched
C. the ability to retain its hardness when it is heated to elevated temperatures
D. the depth to which required hardening is obtained when it is austenitized and then quenched
Ans: option (D)
Sol: The depth to which required hardening is obtained when it is austenitized and then quenched.

10. The directional derivative of the function f(x, y) = x
2
+ y
2
along a line directed from (0, 0) to (1,
1), evaluated at the point x = 1, y = 1 is
A. 2 B. ?2
C. 4?2 D. 2?2
Ans: option (D)
Sol: Directional derivative of function along the line is the scalar value of derivative along the line. i.e.
we have to calculate value of derivative of function in the direction of given line vector
? ?? = ??? (
????
????
)+ ??? (
????
????
)
? ?? = 2???+ 2???
Now, calculating the value of ? ?? in 1???+ 1???
D.D of given function is (2???+ 2??? ) ?
(??? + ?? ?)
|??? + ?? ?|
= 2 ?2

11. A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is
A.
2 D
T
?
B.
T
D

C.
D
T
?
D.
D
T

Ans: option (C)
Sol: circular pitch =
????
??

12. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the
instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of
points P and R are VP and VR, in the x and y directions, respectively. The magnitude of the
angular velocity of the body is




8

A. /3
R
V B. /3
P
V
C. 2VR D. 2VP
Ans: option (C)
Sol: The given body is a rigid body; Hence the given body will not have any deformation, and the
possible motion is translation and angular motion. we know that the angular motion of the object is
always defined as the motion about the point. Hence, first we have to find a point parallel to both
velocity ?? ?? and ?? ?? .


? Angular velocity, ?? =
???????????????? ?????????????????????????? ????????????????
?? =
?? ?? ????
=
?? ?? ????

???? =
?3
2
????????? ???? ???????????????? =
?3
2
?1=
?3
2

???? =
1
2
????????? ???? ???????????????? =
1
2
?1=
1
2


?? =
2?? ?? ?3
=
2?? ?? 1


13. Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4
m. The view factor F12 is
A. 0.25 B. 0.0625
C. 1.0 D. 0.5
Ans: option (C)
Sol: ?? 12
=1

14. The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
A.
10
01
??
??
?
??
B.
01
10
? ??
??
?
??

C.
01
10
??
??
??
D.
10
01
???
??
??

Ans: option (C)
Sol: The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
01
10
??
??
??




S



9

15. The state of stress at a point in a component is represented by a Mohr?s circle of radius 100 MPa
centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the
normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same
point is ___________ MPa.
Ans: 80
Sol:


?? =?100
2
?60
2
=80 ??????

16. One-dimensional steady state heat conduction takes place through a solid whose cross-sectional
area varies linearly in the direction of heat transfer. Assume there is no heat generation in the
solid and the thermal conductivity of the material is constant and independent of temperature.
The temperature distribution in the solid is
A. Quadratic B. Exponential
C. Logarithmic D. Linear
Ans: option (C)
Sol: Let the given body cross-sectional area varies linearly, and heat is flowing from left to right.





If there is no heat generation,
?? ????
(?????
????
????
)=0

?
?? ????
(?????
????
????
)=?0

(?????
????
????
)=??

??? (?? 0
+?? ?? ?? )
????
????
=??
???? =
? ?? ????
?? (?? 0
+?? ?? ?? )


? ????
2
1
=?
? ?? ????
?? (?? 0
+?? ?? ?? )
2
1


?? 2
??? 1
= ?
?? ?? ln(
?? ?? ?? 2
+?? 0
?? ?? ?? 1
+?? 0
)



10

17. An analytic function f(z) of complex variable z = x + I y may be written as f(z) = u(x, y) + iv (x,
y). Then, u(x, y) and v(x, y) must satisfy
A.
uv
xy
??
=?
??
and
uv
yx
??
=
??

B.
uv
xy
??
=?
??
and
uv
yx
??
=?
??

C.
uv
xy
??
=
??
and
uv
yx
??
=?
??

D.
uv
xy
??
=
??
and
uv
yx
??
=
??

Ans: option (C)
Sol: If f(z) = u(x, y) + iv(x, y) is analytic function then it must satisfy the following relations.

????
????
=
????
????


????
????
=?
????
????


18. A thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is
losing heat to the surroundings by natural convection. The temperatures of the plate and the
surroundings, and the properties of the surrounding fluid, are constant. The relationship between
the average Nusselt and Rayleigh numbers is given as Nu = K Ra ?, where K is a constant. The
length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the
plate is increased to 16L keeping all other factors constant.

If the average heat transfer coefficient for the first plate is h1 and that for the second plate is h2,
the value of the ratio h1/h2 is____________.
Ans: 2
Sol: ?? ?? =?? (?? ?? )
1
4
We know that ?? ?? =?? ?? ?? ??
?? ?? =?? (?? ?? ?? ?? )
1
4
??? ?? ?(?? ?? )
1
4 ?(
???? ??? ?? 3
?? 2
)
1
4

??? ??? 3
4
???? ?
1
4
?
2
?
1
?(
?? 1
?? 2
)
1
4
=>
?
1
?
2
?(
?? 2
?? 1
)
1
4
=(16)
1
4=2



11


19. Which one of the following modifications of the simple ideal Rankine cycle increases the thermal
efficiency and reduces the moisture content of the steam at the turbine outlet?
A. Decreasing the condenser pressure.
B. Increasing the boiler pressure.
C. Decreasing the boiler pressure.
D. Increasing the turbine inlet temperature.
Ans: option (D)
Sol: Due to increase of the turbine inlet temperature, quality of the stream at outlet of the turbine
improves. Which increases the thermal efficiency and reduces the moisture content of the steam at the
turbine outlet.

20. Consider a linear rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of
100 MPa along the length direction. Assume plane stress conditions in the plane normal to the
thickness. The Young?s modulus E = 200 MPa and Poisson?s ratio v = 0.3 are given. The principal
strains in the plane of the sheet are
A. (0.5, 0.0) B. (0.35, -0.15)
C. (0.5, -0.5) D. (0.5, -0.15)
Ans: option (D)
Sol: ?
1
=
?? 1
?? ???
?? 2
?? =
100
200
?0.3?
0
200
=0.5

?
2
=
?? 2
?? ???
?? 1
?? =
0
200
?0.3?
100
200
=?0.15


21. The figure shows an idealized plane truss. If a horizontal force of 300 N is applied at point A,
then the magnitude of the force produced in member CD is ________N.

Ans: 0

Sol:



12



The momentum about the point A must be zero, because there is no deformation of any truss.
Hence, ?? ????
=0 [?? ????
is not passing through the point A]

22. The fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase
in
A. freezing range
B. surface tension
C. degree of superheat
D. viscosity
Ans: option (C)
Sol: Fluidity of molten metal of cast alloys increases with increase in degree of superheat.

23. The most common limit gage used for inspecting the hole diameter is
A. Ring gage B. Snap gage
C. Plug gage D. Master gage
Ans: option (C)
Sol: The most common limit gage used for inspecting the hole diameter is Plug gage.

24. The differential equation 45
dy
y
dx
+= is valid in the domain 0 ? x ? 1 with y(0) = 2.25. The
solution of the differential equation is
A. y = e
-4x
+ 1.25
B. y = e
4x
+ 5
C. y = e
4x
+ 1.25
D. y = e
-4x
+ 5
Ans: option (A)
Sol: The given equation is.



13

???? ???? +4?? =5
If Integration factor = ?? ?4????
=?? 4??
? ?? ????? =?5????? ???? +??
? ?? ??? 4?? =5?
?? 4?? 4
+??
? ?? ??? 4?? =5?
?? 4?? 4
+?? ?.( 1)
Now for at x=0,
? 2.25 =
5
4
+ ??
? ?? =1
? Using the value of C in equ (1)
? ?? ?
?? 4?? ?? 4?? =
5
?? 4?? ?
?? 4?? 4
+
?? ?? 4??
? ?? =1.25+ ?? ?4??

25. A two-dimensional incompressible frictionless flow field is given by
??
. u xi yj =? If ? is the density
of the fluid, the expression for pressure gradient vector at any point in the flow field is given as
A.
( )
22
??
x i y j ??+ B.
( )
??
xi yj ??+
C.
( )
??
xi yj ? + D.
( )
??
xi yj ? ?
Ans: option (B)
Sol: Euler?s Equation of motion in 2D.

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

As there is no extra force acting on the fluid.
?? ?? ?????? ?? ?? =0
Now form the given expiration, u=x & v=y
?
????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????


?0+ ?? ?1+0+0=0?
1
?? ????
????

0+ 0+?? ?1+0=0?
1
?? ????
????

??????????? ???????? ?????? =
????
????
???+
????
????
???= ??? (?? ???+?? ??? )




14

26. A short shoe external drum brake is shown in the figure. The diameter of the brake drum is 500
mm. The dimensions a = 1000 mm, b = 500 mm and c = 200 mm. The coefficient of friction
between the drum and the shoe is 0.35. The force applied on the lever F = 100 N as shown in
the figure. The drum is rotating anti-clockwise. The braking torque on the drum is _______N.m
(round off to two decimal places).

Ans: 20.34
Sol:

Applying momentum about point O.

??? ?? =0

?? ??? +?? ?? ?? ??? ??? ?? ??? =0
?? ?? =232.55
Breaking Torque = ?? ?? ?? ?? ?? = 20.34

27. A uniform disc with radius r and a mass of m kg is mounted centrally on a horizontal axle of
negligible mass and length of 1.5r. The disc spins counter-clockwise about the axle with angular
speed ?, when viewed from the right-hand side bearing, Q. The axle precesses about a vertical
axis at
?p = ?/10 in the clockwise direction when viewed from above. Let RP and RQ (positive upwards)
be the resultant reaction forces due to the mass and the gyroscopic effect, at bearings P and Q,
respectively. Assuming ?
2
r = 300 m/s
2
and g = 10 m/s
2
, the ratio of the larger to the smaller
bearing reaction force (considering appropriate signs) is __________.



15


Ans: -3
Sol: ?????????????????? ???????????? (???? )=???? ?? ??

Using: ?? ?? =
?? 10
and ?? 2
?? =300

???? =
?? ?? 2
2
?? 2
10
=15????

Reaction at P and Q due to gravity

?? ?? 1
+?? ?? 1
=???? =10??
?? ?? 1
=5??
??? ?? 1
= 5 ??

Reaction at P and Q due to GC

Taking momentum about point p.
?? ?? 2
?1.5?? ?15???? =0
?? ?? 2
=
15????
1.5?? =10 ??
??? ?? 2
= ?10 ??
?????? ,
?? ?? ?? ?? =
?? ?? 1
+?? ?? 2

?? ?? 1
+?? ?? 2
=
5+10
5?10
= ?3

28. The figure shows a pouring arrangement for casting of a metal block. Frictional losses are
negligible. The acceleration due to gravity is 9.81 m/s
2
. The time (in s, round off to two decimal
places) to fill up the mold cavity (of size 40 cm ? 30 cm ? 15 cm) is ____________



16


Ans: 29.84
Sol: ???????? ?????????????? ???????? =
?? ?? ?? ?? .?2?? ?

???????? =
0.40?0.30?0.15
?? 0.02
2
4
.?2?9.81?0.20
28.94 ??????

29. The activities of a project, their duration and the precedence relationships are given in the table.
For example, in a precedence relationship ?X < Y, Z? means that X is predecessor of activities Y
and Z. The time to complete the activities along the critical path is ____________ weeks.
Activity Duration
(Weeks)
Precedence
Relationship
A 5 A < B, C, D
B 7 B < E, F, G
C 10 C < I
D 6 D < G
E 3 E < H
F 9 F < I
G 7 G < I
H 4 H < I
I 2 ---
A. 21 B. 25
C. 23 D. 17
Ans: option (C)
Sol:



17


30. The crank of a slider-crank mechanism rotates counter-clockwise (CCW) with a constant angular
velocity ?, as shown. Assume the length of the crank to be r.

Using exact analysis, the acceleration of the slider in the y-direction, at the instant shown, where
the crank is parallel to x-axis, is given by
A. -?
2
r B. 2?
2
r
C. ?
2
r D. -2?
2
r
Ans: option (C)
Sol:


Velocity of point A, ?? ?? = ?? ???
The radial acceleration of point A, ?? ????
=?? ?? 2

Since, the inclination of line AB is 45 degree, the acceleration of the point B will be equal to the
acceleration of point A. i.e. ?? ?? 2


31. A gas tungsten arc welding operation is performed using a current of 250 A and an arc voltage of
20 V at a welding speed of 5 mm/s. Assuming that the arc efficiency is 70%, the net heat input
per unit length of the weld will be ________ kJ/mm (round off to one decimal place).
Ans: 0.7
Sol: ???????? ?????????? =??Power
elec

???????? ?????????? =0.7?250?20=3500 ????????

???????? ?????????? per unit length=
3500
5
=700
?? ????

=0.7 KJ/mm

32. Water flows through two different pipes A and B of the same circular cross-section but at
different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both
the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes
is same, the ratio of volume flow rates QB/QA is ______ (round off to two decimal places).
A
O
B



18

Ans: 0.5
Sol: Frictional losses of pipe

??? ? ????
?? ?? ?? ? ????
(
?? ?? )
?? ?? ?????
?? ?? ?? ??

?
????
?????
=
?? ?? ?? ?? ?? ?? 2
?? ?? ?? ?? ?? ?? 2
;?? ??????? ?? =
64
????



?? ?? 2
?? ?? 2
=
?
????
?? ?? ?? ?? ??? ?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? ?? ??

?? ?? ?? ?? =
?? ?? ?? ?? =0.5

33. Consider two concentric circular cylinders of different materials M and N in contact with each
other at r = b, as shown below. The interface at r = b is frictionless. The composite cylinder
system is subjected to internal pressure P. Let
( )
,
MM
r
uu
?
and
( )
,
MM
rr ??
?? denote the radial and
tangential displacement and stress components, respectively, in material M Similarly,
( )
,
NN
r
uu
?

and
( )
,
NN
rr ??
?? denote the radial and tangential displacement and stress components, respectively,
in material N. The boundary conditions that need to be satisfied at the frictionless interface
between the two cylinders are :

A.
MN
rr
uu = and
MN
rr rr
?? = and
MN
uu
??
= and
MN
? ? ? ?
?? =
B.
MN
rr rr
?? = and
MN
? ? ? ?
?? = only
C.
MN
uu
??
= and
MN
? ? ? ?
?? = only
D.
MN
rr
uu = and
MN
rr rr
?? = only
Ans: option (D)
Sol:



19



Internal pressure causes the stress in radial as well as circumferential direction.

At r=b i.e. interference of the cylinder can be frictionless if Stress in radial direction must be equal.
Velocity in radial direction must be equal. (This condition will make the normal force Zero)
As radius of the cylinder increases due to inside pressure, there will be relative velocity between
the contact surfaces in the circumferential direction.

34. The binary phase diagram of metals P and Q is shown in the figure. An alloy X containing 60% P
and 40% Q (by weight) is cooled from liquid to solid state. The fractions of solid and liquid (in
weight percent) at 1250
o
C, respectively, will be

A. 22.2% and 77.8%
B. 68.0% and 32.0%
C. 77.8% and 22.2%
D. 32.0% and 68.0%
Ans: option (A)
Sol: Mass fraction of liquid =
?? ?? ??? 0
?? ?? ??? ??
?? ?? =
68?40
68?32
= 0.778=77.8%
?? ?? =1??? ?? =0.222=22.2%

35. The annual demand of valves per year in a company is 10,000 units. The current order quantity
is 400 valves per order. The holding cost is Rs. 24 per valve per year and the ordering cost is Rs.
400 per order. If the current order quantity is changed to Economic Order Quantity, then the
saving in the total cost of inventory per year will be Rs. __________ (round off to two decimal
places).
Ans: 943.59
Sol:
Annual Demand (D) = 10000 nos



20

Order Quantities (Q) = 400 / order
Holding cost (?? ?
)= 24 /valve/year
Ordering Cost (?? 0
) = RS 400 /order
?????? =
?? ?? ?? 0
+
?? 2
?? ?


?????? =
10000
400
400+
10000
2
24=14800

?????? ?=?2?? ?? 0
?? ?


?????? ?=13856.41

???????????? =14800?13856.41=???? .?????? .????

36. A slender uniform rigid bar of mass m is hinged at O and supported by two springs, with
stiffnesses 3k and k, and a damper with damping coefficient c, as shown in the figure. For the
system to be critically damped, the ratio c/?km should be

A. 4 B. 2
C. 4?7 D. 2?7
Ans: option (C)
Sol:
?? ?????
=?;?? ????? ???????????? ???? ???????????????????? ????????????

Suppose that we apply a external force downward at horizontal road at spring constant 3K and
leave it freely for to and fro motion.
Therefore, moment about point ?O?; ? ?? 0
=0
?? 0
??
? +?? (
3?? 4
?? )(
3?? 4
)+ 3?? (
?? 4
?? )(
?? 4
)+?? (
?? 4
?? ? )(
?? 4
)=0
?? 0
??
? +?? (
9?? 2
16
?? )+3?? (
?? 2
16
?? )+?? (
?? 2

16
?? ? )=0
Now, moment of inertia of rod about the center of the rod is ?? ?? =
?? ?? 2
12

And moment of inertia about the hinged point is ?? 0
=?? ?? +?? ?? 2
=
?? ?? 2
12
+?? (
?? 4
)
2
=
7
48
?? ?? 2

7
48
?? ?? 2
??
? +
1
16
?? ?? 2
?? ?+
12
16
?? ?? 2
?? =0

As we know that for critical dumping, the root of the quadratic equation should be real and equal.
FirstRanker.com - FirstRanker's Choice



2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6




3

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of ?? =
8+6
2
=7

6. X is an online media provider. By offering unlimited and exclusive online content at attractive
prices for a loyalty membership, X is almost forcing its customers towards its loyalty
membership. If its loyalty membership continues to grow at its current rate, within the next
eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
A. Most households that subscribe to X?s loyalty membership discontinue watching cable
television
B. Non-members prefer to watch cable television
C. The X is cancelling accounts of non-members
D. Cable television operators don?t subscribe to X?s loyalty membership
Ans: option (A)
Sol: option A is the most appropriate solution

7. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased
by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.
A. 35.70 B. 10.00
C. 37.50 D. 25.00
Ans: option (C)
Sol: Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04??? =0.04??
And the fiscal deficit in 2016 = 0.05?1.1?? =0.055??
Increase in fiscal deficit = 0.055x ? 0.04x = 0.015x
So, the percentage increase in fiscal deficit =
0.015?? 0.04?? ?100=37.5%

8. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can
empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is
opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is
_________.
A. 16.50 B. 14.50
C. 15.50 D. 13.50
Ans: option (B)
Sol: 1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(
1
6
? ?
1
12
? )=
1
3
?
Tank filled by when Q and R works for another 6 hours = 6(
1
9
? ?
1
12
? )=
1
6
?
Total tank filled in these 10 hours =
1
3
? +
1
6
? =0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in
9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours




4

9. While teaching a creative writing class in India, I was surprised at receiving stories from the
students that were all set in distant places: in the American West with cowboys and in
Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave
the writers in the once-colonised countries the confidence to see the shabby lives around them
as worthy of being ?told?.
The writer of this passage is surprised by the creative writing assignments of his students,
because __________.
A. Some of the students had written about ice cubes and cowboys
B. None of the students had written about ice cubes and cowboys
C. Some of the students had written stories set in foreign places
D. None of the students had written stories set in India
Ans: option (C)
Sol: option C is the most appropriate solution

10. Mola is a digital platform for taxis in a city. It offers three types of rides ? Pool, Mini and Prime.
The Table below presents the number of rides for the past four months. The platform earns one
US dollar per ride. What is the percentage share of revenue contributed by Prime to the total
revenues of Mola, for the entire duration?
Type
Month
January February March April
Pool 170 320 215 190
Mini 110 220 180 70
Prime 75 180 120 90

A. 38.74 B. 23.97
C. 25.86 D. 16.24

Ans: option (B)
Sol: Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580
Revenue contributed by Prime = 75 + 180 + 120 +90 = 465
Total revenue of Mola = 895 + 580 + 465 = 1940
So, the percentage share =
465
1940
?100=23.97%

MECHANICAL ENGINEERING
1. A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by
application of pure bending moments at its ends. The Young?s modulus of the material of the
wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.
Ans: 50
Sol: Tensile stress
?? =
?? ?? ?? =
100?10
3
1
(
1
1000?2
)=50 ??????





5

2. In an electrical discharge machining process, the breakdown voltage across inter electrode gap
(IEG) is 200 V and the capacitance of the RC circuit is 50 ?F. The energy (in J) released per
spark across the IEG is __________
Ans: 1
Sol:
?? =
1
2
??????????????????????? ????????????? ?? 2

?? =0.5?50?10
?6
?200
2
=1 ??


3. If x is the mean of data 3, x, 2 and 4, then the mode is _________
Ans: 3
Sol: ?? =
3+?? +2+4
4

4??? =3+?? +2+4
4??? ??? =3+2+4=9
?? =3
Mode is 3. (Maximum repeated value)

4. The cold forming process in which a hardened tool is pressed against a workpiece (when there is
relative motion between the tool and the workpiece) to produce a roughened surface with a
regular pattern is
A. Strip rolling B. Knurling
C. Roll forming D. Chamfering
Ans: option (B)
Sol: We provide special pattern to prevent the relative motion between contact surface. This special
pattern is known as Knurling.


5. Endurance limit of a beam subjected to pure bending decreases with
A. increase in the surface roughness and increase in the size of the beam
B. decrease in the surface roughness and decrease in the size of the beam
C. decrease in the surface roughness and increase in the size of the beam
D. increase in the surface roughness and decrease in the size of the beam
Ans: option (A)
Sol: Formula for endurance limit
?? ?? =?? ?? ??? ?? ??? ?? ??? ?? ??? ?? ?

?? ???????
?? ?? ????????? ????????????
?? ?? ??????????????? ????????????
?? ?? ????????? ????????????
?? ?? ??????????????????????? ????????????
?? ?? ?
??????????????????? ?????????????? ?
Form above formula it is clear that the Endurance limit increases with increase in size,
surface, load, temp and endurance strength.







6

6. In matrix equation [A] {X} = {R}.
? ?
4 8 4 2
8 16 4 , 1
4 4 15 4
AX
? ? ? ?
?? ??
= ? = ??
??
????
??
??
?
? ? ? ?
and ? ?
32
16 .
64
R
??
??
=
??
??
??

One of the eigenvalues of matrix [A] is
A. 4 B. 15
C. 8 D. 16
Ans: option (D)
Sol: [A] {X} = {R}.

We know ???? = ???? ;?? ??????? ?? ??????????? ??????????

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}={
32
16
64
}

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}=16{
2
1
4
}

Hence, ?? =????

7. Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number
ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit.
The Reynolds number at the exit of the pipe is___________.
Ans: 500
Sol: Reynold?s Number
???? =
?? ?? ????
?? ??
Where: -
?? ??????????? ??????????????
?? ????
??????????????? ????????????????
?? ??????????????? ???? ????????
?? ? Dynamic viscosity of Fluid
?? ?? =(
?? ?? ????
?? ?? )=
(

?? (
?? ???????? ?? ???????? ) ?? ?? )


From above expiration, Reynold?s Number is independent of flow profile. Hence, Reynold?s
Number for parabolic flow profile is 500.

8. For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure
and temperature, respectively. As per Maxwell?s relations,
p
v
s
? ??
??
?
??
is equal to
A.
T
p
v
? ??
??
?
??
B.
p
s
T
? ??
??
?
??
C.
s
T
p
?? ?
??
?
??
D.
p
T
v
? ??
?
??
?
??

Ans: option (C)
Sol: From mathematical relation expiration



7

???? = ?????? +??????
? (
????
????
)
?? = (
????
????
)
??
???????? ?????????????? ????????????????
?? ?= ?????? +??????
? (
????
????
)
?? = (
????
????
)
??

9. Hardenability of steel is a measure of
A. the ability to harden when it is cold worked
B. the maximum hardness that can be obtained when it is austenitized and then quenched
C. the ability to retain its hardness when it is heated to elevated temperatures
D. the depth to which required hardening is obtained when it is austenitized and then quenched
Ans: option (D)
Sol: The depth to which required hardening is obtained when it is austenitized and then quenched.

10. The directional derivative of the function f(x, y) = x
2
+ y
2
along a line directed from (0, 0) to (1,
1), evaluated at the point x = 1, y = 1 is
A. 2 B. ?2
C. 4?2 D. 2?2
Ans: option (D)
Sol: Directional derivative of function along the line is the scalar value of derivative along the line. i.e.
we have to calculate value of derivative of function in the direction of given line vector
? ?? = ??? (
????
????
)+ ??? (
????
????
)
? ?? = 2???+ 2???
Now, calculating the value of ? ?? in 1???+ 1???
D.D of given function is (2???+ 2??? ) ?
(??? + ?? ?)
|??? + ?? ?|
= 2 ?2

11. A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is
A.
2 D
T
?
B.
T
D

C.
D
T
?
D.
D
T

Ans: option (C)
Sol: circular pitch =
????
??

12. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the
instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of
points P and R are VP and VR, in the x and y directions, respectively. The magnitude of the
angular velocity of the body is




8

A. /3
R
V B. /3
P
V
C. 2VR D. 2VP
Ans: option (C)
Sol: The given body is a rigid body; Hence the given body will not have any deformation, and the
possible motion is translation and angular motion. we know that the angular motion of the object is
always defined as the motion about the point. Hence, first we have to find a point parallel to both
velocity ?? ?? and ?? ?? .


? Angular velocity, ?? =
???????????????? ?????????????????????????? ????????????????
?? =
?? ?? ????
=
?? ?? ????

???? =
?3
2
????????? ???? ???????????????? =
?3
2
?1=
?3
2

???? =
1
2
????????? ???? ???????????????? =
1
2
?1=
1
2


?? =
2?? ?? ?3
=
2?? ?? 1


13. Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4
m. The view factor F12 is
A. 0.25 B. 0.0625
C. 1.0 D. 0.5
Ans: option (C)
Sol: ?? 12
=1

14. The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
A.
10
01
??
??
?
??
B.
01
10
? ??
??
?
??

C.
01
10
??
??
??
D.
10
01
???
??
??

Ans: option (C)
Sol: The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
01
10
??
??
??




S



9

15. The state of stress at a point in a component is represented by a Mohr?s circle of radius 100 MPa
centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the
normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same
point is ___________ MPa.
Ans: 80
Sol:


?? =?100
2
?60
2
=80 ??????

16. One-dimensional steady state heat conduction takes place through a solid whose cross-sectional
area varies linearly in the direction of heat transfer. Assume there is no heat generation in the
solid and the thermal conductivity of the material is constant and independent of temperature.
The temperature distribution in the solid is
A. Quadratic B. Exponential
C. Logarithmic D. Linear
Ans: option (C)
Sol: Let the given body cross-sectional area varies linearly, and heat is flowing from left to right.





If there is no heat generation,
?? ????
(?????
????
????
)=0

?
?? ????
(?????
????
????
)=?0

(?????
????
????
)=??

??? (?? 0
+?? ?? ?? )
????
????
=??
???? =
? ?? ????
?? (?? 0
+?? ?? ?? )


? ????
2
1
=?
? ?? ????
?? (?? 0
+?? ?? ?? )
2
1


?? 2
??? 1
= ?
?? ?? ln(
?? ?? ?? 2
+?? 0
?? ?? ?? 1
+?? 0
)



10

17. An analytic function f(z) of complex variable z = x + I y may be written as f(z) = u(x, y) + iv (x,
y). Then, u(x, y) and v(x, y) must satisfy
A.
uv
xy
??
=?
??
and
uv
yx
??
=
??

B.
uv
xy
??
=?
??
and
uv
yx
??
=?
??

C.
uv
xy
??
=
??
and
uv
yx
??
=?
??

D.
uv
xy
??
=
??
and
uv
yx
??
=
??

Ans: option (C)
Sol: If f(z) = u(x, y) + iv(x, y) is analytic function then it must satisfy the following relations.

????
????
=
????
????


????
????
=?
????
????


18. A thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is
losing heat to the surroundings by natural convection. The temperatures of the plate and the
surroundings, and the properties of the surrounding fluid, are constant. The relationship between
the average Nusselt and Rayleigh numbers is given as Nu = K Ra ?, where K is a constant. The
length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the
plate is increased to 16L keeping all other factors constant.

If the average heat transfer coefficient for the first plate is h1 and that for the second plate is h2,
the value of the ratio h1/h2 is____________.
Ans: 2
Sol: ?? ?? =?? (?? ?? )
1
4
We know that ?? ?? =?? ?? ?? ??
?? ?? =?? (?? ?? ?? ?? )
1
4
??? ?? ?(?? ?? )
1
4 ?(
???? ??? ?? 3
?? 2
)
1
4

??? ??? 3
4
???? ?
1
4
?
2
?
1
?(
?? 1
?? 2
)
1
4
=>
?
1
?
2
?(
?? 2
?? 1
)
1
4
=(16)
1
4=2



11


19. Which one of the following modifications of the simple ideal Rankine cycle increases the thermal
efficiency and reduces the moisture content of the steam at the turbine outlet?
A. Decreasing the condenser pressure.
B. Increasing the boiler pressure.
C. Decreasing the boiler pressure.
D. Increasing the turbine inlet temperature.
Ans: option (D)
Sol: Due to increase of the turbine inlet temperature, quality of the stream at outlet of the turbine
improves. Which increases the thermal efficiency and reduces the moisture content of the steam at the
turbine outlet.

20. Consider a linear rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of
100 MPa along the length direction. Assume plane stress conditions in the plane normal to the
thickness. The Young?s modulus E = 200 MPa and Poisson?s ratio v = 0.3 are given. The principal
strains in the plane of the sheet are
A. (0.5, 0.0) B. (0.35, -0.15)
C. (0.5, -0.5) D. (0.5, -0.15)
Ans: option (D)
Sol: ?
1
=
?? 1
?? ???
?? 2
?? =
100
200
?0.3?
0
200
=0.5

?
2
=
?? 2
?? ???
?? 1
?? =
0
200
?0.3?
100
200
=?0.15


21. The figure shows an idealized plane truss. If a horizontal force of 300 N is applied at point A,
then the magnitude of the force produced in member CD is ________N.

Ans: 0

Sol:



12



The momentum about the point A must be zero, because there is no deformation of any truss.
Hence, ?? ????
=0 [?? ????
is not passing through the point A]

22. The fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase
in
A. freezing range
B. surface tension
C. degree of superheat
D. viscosity
Ans: option (C)
Sol: Fluidity of molten metal of cast alloys increases with increase in degree of superheat.

23. The most common limit gage used for inspecting the hole diameter is
A. Ring gage B. Snap gage
C. Plug gage D. Master gage
Ans: option (C)
Sol: The most common limit gage used for inspecting the hole diameter is Plug gage.

24. The differential equation 45
dy
y
dx
+= is valid in the domain 0 ? x ? 1 with y(0) = 2.25. The
solution of the differential equation is
A. y = e
-4x
+ 1.25
B. y = e
4x
+ 5
C. y = e
4x
+ 1.25
D. y = e
-4x
+ 5
Ans: option (A)
Sol: The given equation is.



13

???? ???? +4?? =5
If Integration factor = ?? ?4????
=?? 4??
? ?? ????? =?5????? ???? +??
? ?? ??? 4?? =5?
?? 4?? 4
+??
? ?? ??? 4?? =5?
?? 4?? 4
+?? ?.( 1)
Now for at x=0,
? 2.25 =
5
4
+ ??
? ?? =1
? Using the value of C in equ (1)
? ?? ?
?? 4?? ?? 4?? =
5
?? 4?? ?
?? 4?? 4
+
?? ?? 4??
? ?? =1.25+ ?? ?4??

25. A two-dimensional incompressible frictionless flow field is given by
??
. u xi yj =? If ? is the density
of the fluid, the expression for pressure gradient vector at any point in the flow field is given as
A.
( )
22
??
x i y j ??+ B.
( )
??
xi yj ??+
C.
( )
??
xi yj ? + D.
( )
??
xi yj ? ?
Ans: option (B)
Sol: Euler?s Equation of motion in 2D.

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

As there is no extra force acting on the fluid.
?? ?? ?????? ?? ?? =0
Now form the given expiration, u=x & v=y
?
????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????


?0+ ?? ?1+0+0=0?
1
?? ????
????

0+ 0+?? ?1+0=0?
1
?? ????
????

??????????? ???????? ?????? =
????
????
???+
????
????
???= ??? (?? ???+?? ??? )




14

26. A short shoe external drum brake is shown in the figure. The diameter of the brake drum is 500
mm. The dimensions a = 1000 mm, b = 500 mm and c = 200 mm. The coefficient of friction
between the drum and the shoe is 0.35. The force applied on the lever F = 100 N as shown in
the figure. The drum is rotating anti-clockwise. The braking torque on the drum is _______N.m
(round off to two decimal places).

Ans: 20.34
Sol:

Applying momentum about point O.

??? ?? =0

?? ??? +?? ?? ?? ??? ??? ?? ??? =0
?? ?? =232.55
Breaking Torque = ?? ?? ?? ?? ?? = 20.34

27. A uniform disc with radius r and a mass of m kg is mounted centrally on a horizontal axle of
negligible mass and length of 1.5r. The disc spins counter-clockwise about the axle with angular
speed ?, when viewed from the right-hand side bearing, Q. The axle precesses about a vertical
axis at
?p = ?/10 in the clockwise direction when viewed from above. Let RP and RQ (positive upwards)
be the resultant reaction forces due to the mass and the gyroscopic effect, at bearings P and Q,
respectively. Assuming ?
2
r = 300 m/s
2
and g = 10 m/s
2
, the ratio of the larger to the smaller
bearing reaction force (considering appropriate signs) is __________.



15


Ans: -3
Sol: ?????????????????? ???????????? (???? )=???? ?? ??

Using: ?? ?? =
?? 10
and ?? 2
?? =300

???? =
?? ?? 2
2
?? 2
10
=15????

Reaction at P and Q due to gravity

?? ?? 1
+?? ?? 1
=???? =10??
?? ?? 1
=5??
??? ?? 1
= 5 ??

Reaction at P and Q due to GC

Taking momentum about point p.
?? ?? 2
?1.5?? ?15???? =0
?? ?? 2
=
15????
1.5?? =10 ??
??? ?? 2
= ?10 ??
?????? ,
?? ?? ?? ?? =
?? ?? 1
+?? ?? 2

?? ?? 1
+?? ?? 2
=
5+10
5?10
= ?3

28. The figure shows a pouring arrangement for casting of a metal block. Frictional losses are
negligible. The acceleration due to gravity is 9.81 m/s
2
. The time (in s, round off to two decimal
places) to fill up the mold cavity (of size 40 cm ? 30 cm ? 15 cm) is ____________



16


Ans: 29.84
Sol: ???????? ?????????????? ???????? =
?? ?? ?? ?? .?2?? ?

???????? =
0.40?0.30?0.15
?? 0.02
2
4
.?2?9.81?0.20
28.94 ??????

29. The activities of a project, their duration and the precedence relationships are given in the table.
For example, in a precedence relationship ?X < Y, Z? means that X is predecessor of activities Y
and Z. The time to complete the activities along the critical path is ____________ weeks.
Activity Duration
(Weeks)
Precedence
Relationship
A 5 A < B, C, D
B 7 B < E, F, G
C 10 C < I
D 6 D < G
E 3 E < H
F 9 F < I
G 7 G < I
H 4 H < I
I 2 ---
A. 21 B. 25
C. 23 D. 17
Ans: option (C)
Sol:



17


30. The crank of a slider-crank mechanism rotates counter-clockwise (CCW) with a constant angular
velocity ?, as shown. Assume the length of the crank to be r.

Using exact analysis, the acceleration of the slider in the y-direction, at the instant shown, where
the crank is parallel to x-axis, is given by
A. -?
2
r B. 2?
2
r
C. ?
2
r D. -2?
2
r
Ans: option (C)
Sol:


Velocity of point A, ?? ?? = ?? ???
The radial acceleration of point A, ?? ????
=?? ?? 2

Since, the inclination of line AB is 45 degree, the acceleration of the point B will be equal to the
acceleration of point A. i.e. ?? ?? 2


31. A gas tungsten arc welding operation is performed using a current of 250 A and an arc voltage of
20 V at a welding speed of 5 mm/s. Assuming that the arc efficiency is 70%, the net heat input
per unit length of the weld will be ________ kJ/mm (round off to one decimal place).
Ans: 0.7
Sol: ???????? ?????????? =??Power
elec

???????? ?????????? =0.7?250?20=3500 ????????

???????? ?????????? per unit length=
3500
5
=700
?? ????

=0.7 KJ/mm

32. Water flows through two different pipes A and B of the same circular cross-section but at
different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both
the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes
is same, the ratio of volume flow rates QB/QA is ______ (round off to two decimal places).
A
O
B



18

Ans: 0.5
Sol: Frictional losses of pipe

??? ? ????
?? ?? ?? ? ????
(
?? ?? )
?? ?? ?????
?? ?? ?? ??

?
????
?????
=
?? ?? ?? ?? ?? ?? 2
?? ?? ?? ?? ?? ?? 2
;?? ??????? ?? =
64
????



?? ?? 2
?? ?? 2
=
?
????
?? ?? ?? ?? ??? ?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? ?? ??

?? ?? ?? ?? =
?? ?? ?? ?? =0.5

33. Consider two concentric circular cylinders of different materials M and N in contact with each
other at r = b, as shown below. The interface at r = b is frictionless. The composite cylinder
system is subjected to internal pressure P. Let
( )
,
MM
r
uu
?
and
( )
,
MM
rr ??
?? denote the radial and
tangential displacement and stress components, respectively, in material M Similarly,
( )
,
NN
r
uu
?

and
( )
,
NN
rr ??
?? denote the radial and tangential displacement and stress components, respectively,
in material N. The boundary conditions that need to be satisfied at the frictionless interface
between the two cylinders are :

A.
MN
rr
uu = and
MN
rr rr
?? = and
MN
uu
??
= and
MN
? ? ? ?
?? =
B.
MN
rr rr
?? = and
MN
? ? ? ?
?? = only
C.
MN
uu
??
= and
MN
? ? ? ?
?? = only
D.
MN
rr
uu = and
MN
rr rr
?? = only
Ans: option (D)
Sol:



19



Internal pressure causes the stress in radial as well as circumferential direction.

At r=b i.e. interference of the cylinder can be frictionless if Stress in radial direction must be equal.
Velocity in radial direction must be equal. (This condition will make the normal force Zero)
As radius of the cylinder increases due to inside pressure, there will be relative velocity between
the contact surfaces in the circumferential direction.

34. The binary phase diagram of metals P and Q is shown in the figure. An alloy X containing 60% P
and 40% Q (by weight) is cooled from liquid to solid state. The fractions of solid and liquid (in
weight percent) at 1250
o
C, respectively, will be

A. 22.2% and 77.8%
B. 68.0% and 32.0%
C. 77.8% and 22.2%
D. 32.0% and 68.0%
Ans: option (A)
Sol: Mass fraction of liquid =
?? ?? ??? 0
?? ?? ??? ??
?? ?? =
68?40
68?32
= 0.778=77.8%
?? ?? =1??? ?? =0.222=22.2%

35. The annual demand of valves per year in a company is 10,000 units. The current order quantity
is 400 valves per order. The holding cost is Rs. 24 per valve per year and the ordering cost is Rs.
400 per order. If the current order quantity is changed to Economic Order Quantity, then the
saving in the total cost of inventory per year will be Rs. __________ (round off to two decimal
places).
Ans: 943.59
Sol:
Annual Demand (D) = 10000 nos



20

Order Quantities (Q) = 400 / order
Holding cost (?? ?
)= 24 /valve/year
Ordering Cost (?? 0
) = RS 400 /order
?????? =
?? ?? ?? 0
+
?? 2
?? ?


?????? =
10000
400
400+
10000
2
24=14800

?????? ?=?2?? ?? 0
?? ?


?????? ?=13856.41

???????????? =14800?13856.41=???? .?????? .????

36. A slender uniform rigid bar of mass m is hinged at O and supported by two springs, with
stiffnesses 3k and k, and a damper with damping coefficient c, as shown in the figure. For the
system to be critically damped, the ratio c/?km should be

A. 4 B. 2
C. 4?7 D. 2?7
Ans: option (C)
Sol:
?? ?????
=?;?? ????? ???????????? ???? ???????????????????? ????????????

Suppose that we apply a external force downward at horizontal road at spring constant 3K and
leave it freely for to and fro motion.
Therefore, moment about point ?O?; ? ?? 0
=0
?? 0
??
? +?? (
3?? 4
?? )(
3?? 4
)+ 3?? (
?? 4
?? )(
?? 4
)+?? (
?? 4
?? ? )(
?? 4
)=0
?? 0
??
? +?? (
9?? 2
16
?? )+3?? (
?? 2
16
?? )+?? (
?? 2

16
?? ? )=0
Now, moment of inertia of rod about the center of the rod is ?? ?? =
?? ?? 2
12

And moment of inertia about the hinged point is ?? 0
=?? ?? +?? ?? 2
=
?? ?? 2
12
+?? (
?? 4
)
2
=
7
48
?? ?? 2

7
48
?? ?? 2
??
? +
1
16
?? ?? 2
?? ?+
12
16
?? ?? 2
?? =0

As we know that for critical dumping, the root of the quadratic equation should be real and equal.



21

? ?? 2
?4???? =0
(
1
16
?? ?? 2
)
2
?4 (
7
48
?? ?? 2
)(
12
16
?? ?? 2
)=0

?? =?4 (
7
1
?? )(
4
1
?? )=4?7????
?
?? ?????
= 4?7

37. The probability that a part manufactured by a company will be defective is 0.05. If 15 such parts
are selected randomly and inspected, then the probability that at least two parts will be
defective is __________ (round off to two decimal places).
Ans: 0.17
Sol: Total no. of parts = 15
P[defective(p)] = 0.05
P[non-defective(q)] = 1 ? 0.05 = 0.95
P[at least 2 defective] = 1 ? [P(no defective)+P(1 defective)]
Using the binomial distribution,
P[at least 2 defective] = 1 ? [
15
C0p
0
q
15
+
15
C1p
1
q
14
]= 1 ? [0.05
0
0.95
15
+ 15?0.05?0.95
14
] = 1 ?
[0.4639 + 0.3657] = 1 ? 0.8296 = 0.1704


38. A four bar mechanism is shown in the figure. The link numbers are mentioned near the links.
Input link 2 is rotating anti-clockwise with a constant angular speed ?2. Length of different links
are :

2 4 2
4
,
2.
OO O A L
AB O B L
==
==

The magnitude of the angular speed of the output link 4 is ?4 at the instant when link 2 makes
an angle of 90
o
with O2O4 as shown. The ratio
4
2
?
?
is __________ (round off to two decimal
places).

Ans: 0.79
Sol: Using Instantaneous center method
FirstRanker.com - FirstRanker's Choice



2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6




3

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of ?? =
8+6
2
=7

6. X is an online media provider. By offering unlimited and exclusive online content at attractive
prices for a loyalty membership, X is almost forcing its customers towards its loyalty
membership. If its loyalty membership continues to grow at its current rate, within the next
eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
A. Most households that subscribe to X?s loyalty membership discontinue watching cable
television
B. Non-members prefer to watch cable television
C. The X is cancelling accounts of non-members
D. Cable television operators don?t subscribe to X?s loyalty membership
Ans: option (A)
Sol: option A is the most appropriate solution

7. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased
by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.
A. 35.70 B. 10.00
C. 37.50 D. 25.00
Ans: option (C)
Sol: Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04??? =0.04??
And the fiscal deficit in 2016 = 0.05?1.1?? =0.055??
Increase in fiscal deficit = 0.055x ? 0.04x = 0.015x
So, the percentage increase in fiscal deficit =
0.015?? 0.04?? ?100=37.5%

8. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can
empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is
opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is
_________.
A. 16.50 B. 14.50
C. 15.50 D. 13.50
Ans: option (B)
Sol: 1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(
1
6
? ?
1
12
? )=
1
3
?
Tank filled by when Q and R works for another 6 hours = 6(
1
9
? ?
1
12
? )=
1
6
?
Total tank filled in these 10 hours =
1
3
? +
1
6
? =0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in
9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours




4

9. While teaching a creative writing class in India, I was surprised at receiving stories from the
students that were all set in distant places: in the American West with cowboys and in
Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave
the writers in the once-colonised countries the confidence to see the shabby lives around them
as worthy of being ?told?.
The writer of this passage is surprised by the creative writing assignments of his students,
because __________.
A. Some of the students had written about ice cubes and cowboys
B. None of the students had written about ice cubes and cowboys
C. Some of the students had written stories set in foreign places
D. None of the students had written stories set in India
Ans: option (C)
Sol: option C is the most appropriate solution

10. Mola is a digital platform for taxis in a city. It offers three types of rides ? Pool, Mini and Prime.
The Table below presents the number of rides for the past four months. The platform earns one
US dollar per ride. What is the percentage share of revenue contributed by Prime to the total
revenues of Mola, for the entire duration?
Type
Month
January February March April
Pool 170 320 215 190
Mini 110 220 180 70
Prime 75 180 120 90

A. 38.74 B. 23.97
C. 25.86 D. 16.24

Ans: option (B)
Sol: Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580
Revenue contributed by Prime = 75 + 180 + 120 +90 = 465
Total revenue of Mola = 895 + 580 + 465 = 1940
So, the percentage share =
465
1940
?100=23.97%

MECHANICAL ENGINEERING
1. A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by
application of pure bending moments at its ends. The Young?s modulus of the material of the
wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.
Ans: 50
Sol: Tensile stress
?? =
?? ?? ?? =
100?10
3
1
(
1
1000?2
)=50 ??????





5

2. In an electrical discharge machining process, the breakdown voltage across inter electrode gap
(IEG) is 200 V and the capacitance of the RC circuit is 50 ?F. The energy (in J) released per
spark across the IEG is __________
Ans: 1
Sol:
?? =
1
2
??????????????????????? ????????????? ?? 2

?? =0.5?50?10
?6
?200
2
=1 ??


3. If x is the mean of data 3, x, 2 and 4, then the mode is _________
Ans: 3
Sol: ?? =
3+?? +2+4
4

4??? =3+?? +2+4
4??? ??? =3+2+4=9
?? =3
Mode is 3. (Maximum repeated value)

4. The cold forming process in which a hardened tool is pressed against a workpiece (when there is
relative motion between the tool and the workpiece) to produce a roughened surface with a
regular pattern is
A. Strip rolling B. Knurling
C. Roll forming D. Chamfering
Ans: option (B)
Sol: We provide special pattern to prevent the relative motion between contact surface. This special
pattern is known as Knurling.


5. Endurance limit of a beam subjected to pure bending decreases with
A. increase in the surface roughness and increase in the size of the beam
B. decrease in the surface roughness and decrease in the size of the beam
C. decrease in the surface roughness and increase in the size of the beam
D. increase in the surface roughness and decrease in the size of the beam
Ans: option (A)
Sol: Formula for endurance limit
?? ?? =?? ?? ??? ?? ??? ?? ??? ?? ??? ?? ?

?? ???????
?? ?? ????????? ????????????
?? ?? ??????????????? ????????????
?? ?? ????????? ????????????
?? ?? ??????????????????????? ????????????
?? ?? ?
??????????????????? ?????????????? ?
Form above formula it is clear that the Endurance limit increases with increase in size,
surface, load, temp and endurance strength.







6

6. In matrix equation [A] {X} = {R}.
? ?
4 8 4 2
8 16 4 , 1
4 4 15 4
AX
? ? ? ?
?? ??
= ? = ??
??
????
??
??
?
? ? ? ?
and ? ?
32
16 .
64
R
??
??
=
??
??
??

One of the eigenvalues of matrix [A] is
A. 4 B. 15
C. 8 D. 16
Ans: option (D)
Sol: [A] {X} = {R}.

We know ???? = ???? ;?? ??????? ?? ??????????? ??????????

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}={
32
16
64
}

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}=16{
2
1
4
}

Hence, ?? =????

7. Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number
ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit.
The Reynolds number at the exit of the pipe is___________.
Ans: 500
Sol: Reynold?s Number
???? =
?? ?? ????
?? ??
Where: -
?? ??????????? ??????????????
?? ????
??????????????? ????????????????
?? ??????????????? ???? ????????
?? ? Dynamic viscosity of Fluid
?? ?? =(
?? ?? ????
?? ?? )=
(

?? (
?? ???????? ?? ???????? ) ?? ?? )


From above expiration, Reynold?s Number is independent of flow profile. Hence, Reynold?s
Number for parabolic flow profile is 500.

8. For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure
and temperature, respectively. As per Maxwell?s relations,
p
v
s
? ??
??
?
??
is equal to
A.
T
p
v
? ??
??
?
??
B.
p
s
T
? ??
??
?
??
C.
s
T
p
?? ?
??
?
??
D.
p
T
v
? ??
?
??
?
??

Ans: option (C)
Sol: From mathematical relation expiration



7

???? = ?????? +??????
? (
????
????
)
?? = (
????
????
)
??
???????? ?????????????? ????????????????
?? ?= ?????? +??????
? (
????
????
)
?? = (
????
????
)
??

9. Hardenability of steel is a measure of
A. the ability to harden when it is cold worked
B. the maximum hardness that can be obtained when it is austenitized and then quenched
C. the ability to retain its hardness when it is heated to elevated temperatures
D. the depth to which required hardening is obtained when it is austenitized and then quenched
Ans: option (D)
Sol: The depth to which required hardening is obtained when it is austenitized and then quenched.

10. The directional derivative of the function f(x, y) = x
2
+ y
2
along a line directed from (0, 0) to (1,
1), evaluated at the point x = 1, y = 1 is
A. 2 B. ?2
C. 4?2 D. 2?2
Ans: option (D)
Sol: Directional derivative of function along the line is the scalar value of derivative along the line. i.e.
we have to calculate value of derivative of function in the direction of given line vector
? ?? = ??? (
????
????
)+ ??? (
????
????
)
? ?? = 2???+ 2???
Now, calculating the value of ? ?? in 1???+ 1???
D.D of given function is (2???+ 2??? ) ?
(??? + ?? ?)
|??? + ?? ?|
= 2 ?2

11. A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is
A.
2 D
T
?
B.
T
D

C.
D
T
?
D.
D
T

Ans: option (C)
Sol: circular pitch =
????
??

12. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the
instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of
points P and R are VP and VR, in the x and y directions, respectively. The magnitude of the
angular velocity of the body is




8

A. /3
R
V B. /3
P
V
C. 2VR D. 2VP
Ans: option (C)
Sol: The given body is a rigid body; Hence the given body will not have any deformation, and the
possible motion is translation and angular motion. we know that the angular motion of the object is
always defined as the motion about the point. Hence, first we have to find a point parallel to both
velocity ?? ?? and ?? ?? .


? Angular velocity, ?? =
???????????????? ?????????????????????????? ????????????????
?? =
?? ?? ????
=
?? ?? ????

???? =
?3
2
????????? ???? ???????????????? =
?3
2
?1=
?3
2

???? =
1
2
????????? ???? ???????????????? =
1
2
?1=
1
2


?? =
2?? ?? ?3
=
2?? ?? 1


13. Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4
m. The view factor F12 is
A. 0.25 B. 0.0625
C. 1.0 D. 0.5
Ans: option (C)
Sol: ?? 12
=1

14. The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
A.
10
01
??
??
?
??
B.
01
10
? ??
??
?
??

C.
01
10
??
??
??
D.
10
01
???
??
??

Ans: option (C)
Sol: The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
01
10
??
??
??




S



9

15. The state of stress at a point in a component is represented by a Mohr?s circle of radius 100 MPa
centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the
normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same
point is ___________ MPa.
Ans: 80
Sol:


?? =?100
2
?60
2
=80 ??????

16. One-dimensional steady state heat conduction takes place through a solid whose cross-sectional
area varies linearly in the direction of heat transfer. Assume there is no heat generation in the
solid and the thermal conductivity of the material is constant and independent of temperature.
The temperature distribution in the solid is
A. Quadratic B. Exponential
C. Logarithmic D. Linear
Ans: option (C)
Sol: Let the given body cross-sectional area varies linearly, and heat is flowing from left to right.





If there is no heat generation,
?? ????
(?????
????
????
)=0

?
?? ????
(?????
????
????
)=?0

(?????
????
????
)=??

??? (?? 0
+?? ?? ?? )
????
????
=??
???? =
? ?? ????
?? (?? 0
+?? ?? ?? )


? ????
2
1
=?
? ?? ????
?? (?? 0
+?? ?? ?? )
2
1


?? 2
??? 1
= ?
?? ?? ln(
?? ?? ?? 2
+?? 0
?? ?? ?? 1
+?? 0
)



10

17. An analytic function f(z) of complex variable z = x + I y may be written as f(z) = u(x, y) + iv (x,
y). Then, u(x, y) and v(x, y) must satisfy
A.
uv
xy
??
=?
??
and
uv
yx
??
=
??

B.
uv
xy
??
=?
??
and
uv
yx
??
=?
??

C.
uv
xy
??
=
??
and
uv
yx
??
=?
??

D.
uv
xy
??
=
??
and
uv
yx
??
=
??

Ans: option (C)
Sol: If f(z) = u(x, y) + iv(x, y) is analytic function then it must satisfy the following relations.

????
????
=
????
????


????
????
=?
????
????


18. A thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is
losing heat to the surroundings by natural convection. The temperatures of the plate and the
surroundings, and the properties of the surrounding fluid, are constant. The relationship between
the average Nusselt and Rayleigh numbers is given as Nu = K Ra ?, where K is a constant. The
length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the
plate is increased to 16L keeping all other factors constant.

If the average heat transfer coefficient for the first plate is h1 and that for the second plate is h2,
the value of the ratio h1/h2 is____________.
Ans: 2
Sol: ?? ?? =?? (?? ?? )
1
4
We know that ?? ?? =?? ?? ?? ??
?? ?? =?? (?? ?? ?? ?? )
1
4
??? ?? ?(?? ?? )
1
4 ?(
???? ??? ?? 3
?? 2
)
1
4

??? ??? 3
4
???? ?
1
4
?
2
?
1
?(
?? 1
?? 2
)
1
4
=>
?
1
?
2
?(
?? 2
?? 1
)
1
4
=(16)
1
4=2



11


19. Which one of the following modifications of the simple ideal Rankine cycle increases the thermal
efficiency and reduces the moisture content of the steam at the turbine outlet?
A. Decreasing the condenser pressure.
B. Increasing the boiler pressure.
C. Decreasing the boiler pressure.
D. Increasing the turbine inlet temperature.
Ans: option (D)
Sol: Due to increase of the turbine inlet temperature, quality of the stream at outlet of the turbine
improves. Which increases the thermal efficiency and reduces the moisture content of the steam at the
turbine outlet.

20. Consider a linear rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of
100 MPa along the length direction. Assume plane stress conditions in the plane normal to the
thickness. The Young?s modulus E = 200 MPa and Poisson?s ratio v = 0.3 are given. The principal
strains in the plane of the sheet are
A. (0.5, 0.0) B. (0.35, -0.15)
C. (0.5, -0.5) D. (0.5, -0.15)
Ans: option (D)
Sol: ?
1
=
?? 1
?? ???
?? 2
?? =
100
200
?0.3?
0
200
=0.5

?
2
=
?? 2
?? ???
?? 1
?? =
0
200
?0.3?
100
200
=?0.15


21. The figure shows an idealized plane truss. If a horizontal force of 300 N is applied at point A,
then the magnitude of the force produced in member CD is ________N.

Ans: 0

Sol:



12



The momentum about the point A must be zero, because there is no deformation of any truss.
Hence, ?? ????
=0 [?? ????
is not passing through the point A]

22. The fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase
in
A. freezing range
B. surface tension
C. degree of superheat
D. viscosity
Ans: option (C)
Sol: Fluidity of molten metal of cast alloys increases with increase in degree of superheat.

23. The most common limit gage used for inspecting the hole diameter is
A. Ring gage B. Snap gage
C. Plug gage D. Master gage
Ans: option (C)
Sol: The most common limit gage used for inspecting the hole diameter is Plug gage.

24. The differential equation 45
dy
y
dx
+= is valid in the domain 0 ? x ? 1 with y(0) = 2.25. The
solution of the differential equation is
A. y = e
-4x
+ 1.25
B. y = e
4x
+ 5
C. y = e
4x
+ 1.25
D. y = e
-4x
+ 5
Ans: option (A)
Sol: The given equation is.



13

???? ???? +4?? =5
If Integration factor = ?? ?4????
=?? 4??
? ?? ????? =?5????? ???? +??
? ?? ??? 4?? =5?
?? 4?? 4
+??
? ?? ??? 4?? =5?
?? 4?? 4
+?? ?.( 1)
Now for at x=0,
? 2.25 =
5
4
+ ??
? ?? =1
? Using the value of C in equ (1)
? ?? ?
?? 4?? ?? 4?? =
5
?? 4?? ?
?? 4?? 4
+
?? ?? 4??
? ?? =1.25+ ?? ?4??

25. A two-dimensional incompressible frictionless flow field is given by
??
. u xi yj =? If ? is the density
of the fluid, the expression for pressure gradient vector at any point in the flow field is given as
A.
( )
22
??
x i y j ??+ B.
( )
??
xi yj ??+
C.
( )
??
xi yj ? + D.
( )
??
xi yj ? ?
Ans: option (B)
Sol: Euler?s Equation of motion in 2D.

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

As there is no extra force acting on the fluid.
?? ?? ?????? ?? ?? =0
Now form the given expiration, u=x & v=y
?
????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????


?0+ ?? ?1+0+0=0?
1
?? ????
????

0+ 0+?? ?1+0=0?
1
?? ????
????

??????????? ???????? ?????? =
????
????
???+
????
????
???= ??? (?? ???+?? ??? )




14

26. A short shoe external drum brake is shown in the figure. The diameter of the brake drum is 500
mm. The dimensions a = 1000 mm, b = 500 mm and c = 200 mm. The coefficient of friction
between the drum and the shoe is 0.35. The force applied on the lever F = 100 N as shown in
the figure. The drum is rotating anti-clockwise. The braking torque on the drum is _______N.m
(round off to two decimal places).

Ans: 20.34
Sol:

Applying momentum about point O.

??? ?? =0

?? ??? +?? ?? ?? ??? ??? ?? ??? =0
?? ?? =232.55
Breaking Torque = ?? ?? ?? ?? ?? = 20.34

27. A uniform disc with radius r and a mass of m kg is mounted centrally on a horizontal axle of
negligible mass and length of 1.5r. The disc spins counter-clockwise about the axle with angular
speed ?, when viewed from the right-hand side bearing, Q. The axle precesses about a vertical
axis at
?p = ?/10 in the clockwise direction when viewed from above. Let RP and RQ (positive upwards)
be the resultant reaction forces due to the mass and the gyroscopic effect, at bearings P and Q,
respectively. Assuming ?
2
r = 300 m/s
2
and g = 10 m/s
2
, the ratio of the larger to the smaller
bearing reaction force (considering appropriate signs) is __________.



15


Ans: -3
Sol: ?????????????????? ???????????? (???? )=???? ?? ??

Using: ?? ?? =
?? 10
and ?? 2
?? =300

???? =
?? ?? 2
2
?? 2
10
=15????

Reaction at P and Q due to gravity

?? ?? 1
+?? ?? 1
=???? =10??
?? ?? 1
=5??
??? ?? 1
= 5 ??

Reaction at P and Q due to GC

Taking momentum about point p.
?? ?? 2
?1.5?? ?15???? =0
?? ?? 2
=
15????
1.5?? =10 ??
??? ?? 2
= ?10 ??
?????? ,
?? ?? ?? ?? =
?? ?? 1
+?? ?? 2

?? ?? 1
+?? ?? 2
=
5+10
5?10
= ?3

28. The figure shows a pouring arrangement for casting of a metal block. Frictional losses are
negligible. The acceleration due to gravity is 9.81 m/s
2
. The time (in s, round off to two decimal
places) to fill up the mold cavity (of size 40 cm ? 30 cm ? 15 cm) is ____________



16


Ans: 29.84
Sol: ???????? ?????????????? ???????? =
?? ?? ?? ?? .?2?? ?

???????? =
0.40?0.30?0.15
?? 0.02
2
4
.?2?9.81?0.20
28.94 ??????

29. The activities of a project, their duration and the precedence relationships are given in the table.
For example, in a precedence relationship ?X < Y, Z? means that X is predecessor of activities Y
and Z. The time to complete the activities along the critical path is ____________ weeks.
Activity Duration
(Weeks)
Precedence
Relationship
A 5 A < B, C, D
B 7 B < E, F, G
C 10 C < I
D 6 D < G
E 3 E < H
F 9 F < I
G 7 G < I
H 4 H < I
I 2 ---
A. 21 B. 25
C. 23 D. 17
Ans: option (C)
Sol:



17


30. The crank of a slider-crank mechanism rotates counter-clockwise (CCW) with a constant angular
velocity ?, as shown. Assume the length of the crank to be r.

Using exact analysis, the acceleration of the slider in the y-direction, at the instant shown, where
the crank is parallel to x-axis, is given by
A. -?
2
r B. 2?
2
r
C. ?
2
r D. -2?
2
r
Ans: option (C)
Sol:


Velocity of point A, ?? ?? = ?? ???
The radial acceleration of point A, ?? ????
=?? ?? 2

Since, the inclination of line AB is 45 degree, the acceleration of the point B will be equal to the
acceleration of point A. i.e. ?? ?? 2


31. A gas tungsten arc welding operation is performed using a current of 250 A and an arc voltage of
20 V at a welding speed of 5 mm/s. Assuming that the arc efficiency is 70%, the net heat input
per unit length of the weld will be ________ kJ/mm (round off to one decimal place).
Ans: 0.7
Sol: ???????? ?????????? =??Power
elec

???????? ?????????? =0.7?250?20=3500 ????????

???????? ?????????? per unit length=
3500
5
=700
?? ????

=0.7 KJ/mm

32. Water flows through two different pipes A and B of the same circular cross-section but at
different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both
the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes
is same, the ratio of volume flow rates QB/QA is ______ (round off to two decimal places).
A
O
B



18

Ans: 0.5
Sol: Frictional losses of pipe

??? ? ????
?? ?? ?? ? ????
(
?? ?? )
?? ?? ?????
?? ?? ?? ??

?
????
?????
=
?? ?? ?? ?? ?? ?? 2
?? ?? ?? ?? ?? ?? 2
;?? ??????? ?? =
64
????



?? ?? 2
?? ?? 2
=
?
????
?? ?? ?? ?? ??? ?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? ?? ??

?? ?? ?? ?? =
?? ?? ?? ?? =0.5

33. Consider two concentric circular cylinders of different materials M and N in contact with each
other at r = b, as shown below. The interface at r = b is frictionless. The composite cylinder
system is subjected to internal pressure P. Let
( )
,
MM
r
uu
?
and
( )
,
MM
rr ??
?? denote the radial and
tangential displacement and stress components, respectively, in material M Similarly,
( )
,
NN
r
uu
?

and
( )
,
NN
rr ??
?? denote the radial and tangential displacement and stress components, respectively,
in material N. The boundary conditions that need to be satisfied at the frictionless interface
between the two cylinders are :

A.
MN
rr
uu = and
MN
rr rr
?? = and
MN
uu
??
= and
MN
? ? ? ?
?? =
B.
MN
rr rr
?? = and
MN
? ? ? ?
?? = only
C.
MN
uu
??
= and
MN
? ? ? ?
?? = only
D.
MN
rr
uu = and
MN
rr rr
?? = only
Ans: option (D)
Sol:



19



Internal pressure causes the stress in radial as well as circumferential direction.

At r=b i.e. interference of the cylinder can be frictionless if Stress in radial direction must be equal.
Velocity in radial direction must be equal. (This condition will make the normal force Zero)
As radius of the cylinder increases due to inside pressure, there will be relative velocity between
the contact surfaces in the circumferential direction.

34. The binary phase diagram of metals P and Q is shown in the figure. An alloy X containing 60% P
and 40% Q (by weight) is cooled from liquid to solid state. The fractions of solid and liquid (in
weight percent) at 1250
o
C, respectively, will be

A. 22.2% and 77.8%
B. 68.0% and 32.0%
C. 77.8% and 22.2%
D. 32.0% and 68.0%
Ans: option (A)
Sol: Mass fraction of liquid =
?? ?? ??? 0
?? ?? ??? ??
?? ?? =
68?40
68?32
= 0.778=77.8%
?? ?? =1??? ?? =0.222=22.2%

35. The annual demand of valves per year in a company is 10,000 units. The current order quantity
is 400 valves per order. The holding cost is Rs. 24 per valve per year and the ordering cost is Rs.
400 per order. If the current order quantity is changed to Economic Order Quantity, then the
saving in the total cost of inventory per year will be Rs. __________ (round off to two decimal
places).
Ans: 943.59
Sol:
Annual Demand (D) = 10000 nos



20

Order Quantities (Q) = 400 / order
Holding cost (?? ?
)= 24 /valve/year
Ordering Cost (?? 0
) = RS 400 /order
?????? =
?? ?? ?? 0
+
?? 2
?? ?


?????? =
10000
400
400+
10000
2
24=14800

?????? ?=?2?? ?? 0
?? ?


?????? ?=13856.41

???????????? =14800?13856.41=???? .?????? .????

36. A slender uniform rigid bar of mass m is hinged at O and supported by two springs, with
stiffnesses 3k and k, and a damper with damping coefficient c, as shown in the figure. For the
system to be critically damped, the ratio c/?km should be

A. 4 B. 2
C. 4?7 D. 2?7
Ans: option (C)
Sol:
?? ?????
=?;?? ????? ???????????? ???? ???????????????????? ????????????

Suppose that we apply a external force downward at horizontal road at spring constant 3K and
leave it freely for to and fro motion.
Therefore, moment about point ?O?; ? ?? 0
=0
?? 0
??
? +?? (
3?? 4
?? )(
3?? 4
)+ 3?? (
?? 4
?? )(
?? 4
)+?? (
?? 4
?? ? )(
?? 4
)=0
?? 0
??
? +?? (
9?? 2
16
?? )+3?? (
?? 2
16
?? )+?? (
?? 2

16
?? ? )=0
Now, moment of inertia of rod about the center of the rod is ?? ?? =
?? ?? 2
12

And moment of inertia about the hinged point is ?? 0
=?? ?? +?? ?? 2
=
?? ?? 2
12
+?? (
?? 4
)
2
=
7
48
?? ?? 2

7
48
?? ?? 2
??
? +
1
16
?? ?? 2
?? ?+
12
16
?? ?? 2
?? =0

As we know that for critical dumping, the root of the quadratic equation should be real and equal.



21

? ?? 2
?4???? =0
(
1
16
?? ?? 2
)
2
?4 (
7
48
?? ?? 2
)(
12
16
?? ?? 2
)=0

?? =?4 (
7
1
?? )(
4
1
?? )=4?7????
?
?? ?????
= 4?7

37. The probability that a part manufactured by a company will be defective is 0.05. If 15 such parts
are selected randomly and inspected, then the probability that at least two parts will be
defective is __________ (round off to two decimal places).
Ans: 0.17
Sol: Total no. of parts = 15
P[defective(p)] = 0.05
P[non-defective(q)] = 1 ? 0.05 = 0.95
P[at least 2 defective] = 1 ? [P(no defective)+P(1 defective)]
Using the binomial distribution,
P[at least 2 defective] = 1 ? [
15
C0p
0
q
15
+
15
C1p
1
q
14
]= 1 ? [0.05
0
0.95
15
+ 15?0.05?0.95
14
] = 1 ?
[0.4639 + 0.3657] = 1 ? 0.8296 = 0.1704


38. A four bar mechanism is shown in the figure. The link numbers are mentioned near the links.
Input link 2 is rotating anti-clockwise with a constant angular speed ?2. Length of different links
are :

2 4 2
4
,
2.
OO O A L
AB O B L
==
==

The magnitude of the angular speed of the output link 4 is ?4 at the instant when link 2 makes
an angle of 90
o
with O2O4 as shown. The ratio
4
2
?
?
is __________ (round off to two decimal
places).

Ans: 0.79
Sol: Using Instantaneous center method



22


?? 24
?? 12
?? 2
= ?? 24
?? 41
?? 4

?? 24
?? 12
=?? tan75
?? (???????? ? ?? 12
?? 23
?? 24
)
?? 24
?? 41
=?? +?? tan75
??
?
?? 4
?? 2
=
?? 24
?? 12
?? 24
?? 41
=
?? tan75
?? ?? +?? tan75
??
=0.788

39. Two masses A and B having mass ma and mb, respectively, lying in the plane of the figure
shown, are rigidly attached to a shaft which revolves about an axis through O perpendicular to
the figure. The radii of rotation of the masses ma and mb are ra and rb, respectively. The angle
between lines OA and OB is 90
o
. If ma = 10 kg, mb = 20 kg, ra = 200 mm and rb = 400 mm,
then the balance mass to be placed at a radius of 200 mm is _________ kg (round off to two
decimal places).

Ans: 41.23
Sol:
Let the balance mass be m
? ?? ?? =?? ?? ?? ?? ?????? 0?+?? ?? ?? ?? ?????? 90?+???????????? =0 -----(1)
? ?? ?? =?? ?? ?? ?? ?????? 0?+?? ?? ?? ?? ?????? 90?+???????????? =0------ (2)
From (1), ???????????? =?[?? ?? ?? ?? ?????? 0?+?? ?? ?? ?? ?????? 90?]
Or, ???????????? =?[10?200]=?2000
From (2), ???????????? =?[?? ?? ?? ?? ?????? 0+?? ?? ?? ?? ?????? 90?]
Or, ???????????? =?[20?400]=?8000
Using ?(???????????? )
2
+(???????????? )
2
=???? =?2000
2
+8000
2
=8246.21
Now, since the radius of the balance mass is 200mm, therefore ?? =
8246.21
200
? =41.23????

40. A prismatic, straight elastic, cantilever beam is subjected to a linearly distributed transverse load
as shown below. If the beam length is L, Young?s modulus E, and area moment of inertia I, the
magnitude of the maximum deflection is
FirstRanker.com - FirstRanker's Choice



2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6




3

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of ?? =
8+6
2
=7

6. X is an online media provider. By offering unlimited and exclusive online content at attractive
prices for a loyalty membership, X is almost forcing its customers towards its loyalty
membership. If its loyalty membership continues to grow at its current rate, within the next
eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
A. Most households that subscribe to X?s loyalty membership discontinue watching cable
television
B. Non-members prefer to watch cable television
C. The X is cancelling accounts of non-members
D. Cable television operators don?t subscribe to X?s loyalty membership
Ans: option (A)
Sol: option A is the most appropriate solution

7. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased
by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.
A. 35.70 B. 10.00
C. 37.50 D. 25.00
Ans: option (C)
Sol: Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04??? =0.04??
And the fiscal deficit in 2016 = 0.05?1.1?? =0.055??
Increase in fiscal deficit = 0.055x ? 0.04x = 0.015x
So, the percentage increase in fiscal deficit =
0.015?? 0.04?? ?100=37.5%

8. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can
empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is
opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is
_________.
A. 16.50 B. 14.50
C. 15.50 D. 13.50
Ans: option (B)
Sol: 1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(
1
6
? ?
1
12
? )=
1
3
?
Tank filled by when Q and R works for another 6 hours = 6(
1
9
? ?
1
12
? )=
1
6
?
Total tank filled in these 10 hours =
1
3
? +
1
6
? =0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in
9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours




4

9. While teaching a creative writing class in India, I was surprised at receiving stories from the
students that were all set in distant places: in the American West with cowboys and in
Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave
the writers in the once-colonised countries the confidence to see the shabby lives around them
as worthy of being ?told?.
The writer of this passage is surprised by the creative writing assignments of his students,
because __________.
A. Some of the students had written about ice cubes and cowboys
B. None of the students had written about ice cubes and cowboys
C. Some of the students had written stories set in foreign places
D. None of the students had written stories set in India
Ans: option (C)
Sol: option C is the most appropriate solution

10. Mola is a digital platform for taxis in a city. It offers three types of rides ? Pool, Mini and Prime.
The Table below presents the number of rides for the past four months. The platform earns one
US dollar per ride. What is the percentage share of revenue contributed by Prime to the total
revenues of Mola, for the entire duration?
Type
Month
January February March April
Pool 170 320 215 190
Mini 110 220 180 70
Prime 75 180 120 90

A. 38.74 B. 23.97
C. 25.86 D. 16.24

Ans: option (B)
Sol: Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580
Revenue contributed by Prime = 75 + 180 + 120 +90 = 465
Total revenue of Mola = 895 + 580 + 465 = 1940
So, the percentage share =
465
1940
?100=23.97%

MECHANICAL ENGINEERING
1. A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by
application of pure bending moments at its ends. The Young?s modulus of the material of the
wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.
Ans: 50
Sol: Tensile stress
?? =
?? ?? ?? =
100?10
3
1
(
1
1000?2
)=50 ??????





5

2. In an electrical discharge machining process, the breakdown voltage across inter electrode gap
(IEG) is 200 V and the capacitance of the RC circuit is 50 ?F. The energy (in J) released per
spark across the IEG is __________
Ans: 1
Sol:
?? =
1
2
??????????????????????? ????????????? ?? 2

?? =0.5?50?10
?6
?200
2
=1 ??


3. If x is the mean of data 3, x, 2 and 4, then the mode is _________
Ans: 3
Sol: ?? =
3+?? +2+4
4

4??? =3+?? +2+4
4??? ??? =3+2+4=9
?? =3
Mode is 3. (Maximum repeated value)

4. The cold forming process in which a hardened tool is pressed against a workpiece (when there is
relative motion between the tool and the workpiece) to produce a roughened surface with a
regular pattern is
A. Strip rolling B. Knurling
C. Roll forming D. Chamfering
Ans: option (B)
Sol: We provide special pattern to prevent the relative motion between contact surface. This special
pattern is known as Knurling.


5. Endurance limit of a beam subjected to pure bending decreases with
A. increase in the surface roughness and increase in the size of the beam
B. decrease in the surface roughness and decrease in the size of the beam
C. decrease in the surface roughness and increase in the size of the beam
D. increase in the surface roughness and decrease in the size of the beam
Ans: option (A)
Sol: Formula for endurance limit
?? ?? =?? ?? ??? ?? ??? ?? ??? ?? ??? ?? ?

?? ???????
?? ?? ????????? ????????????
?? ?? ??????????????? ????????????
?? ?? ????????? ????????????
?? ?? ??????????????????????? ????????????
?? ?? ?
??????????????????? ?????????????? ?
Form above formula it is clear that the Endurance limit increases with increase in size,
surface, load, temp and endurance strength.







6

6. In matrix equation [A] {X} = {R}.
? ?
4 8 4 2
8 16 4 , 1
4 4 15 4
AX
? ? ? ?
?? ??
= ? = ??
??
????
??
??
?
? ? ? ?
and ? ?
32
16 .
64
R
??
??
=
??
??
??

One of the eigenvalues of matrix [A] is
A. 4 B. 15
C. 8 D. 16
Ans: option (D)
Sol: [A] {X} = {R}.

We know ???? = ???? ;?? ??????? ?? ??????????? ??????????

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}={
32
16
64
}

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}=16{
2
1
4
}

Hence, ?? =????

7. Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number
ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit.
The Reynolds number at the exit of the pipe is___________.
Ans: 500
Sol: Reynold?s Number
???? =
?? ?? ????
?? ??
Where: -
?? ??????????? ??????????????
?? ????
??????????????? ????????????????
?? ??????????????? ???? ????????
?? ? Dynamic viscosity of Fluid
?? ?? =(
?? ?? ????
?? ?? )=
(

?? (
?? ???????? ?? ???????? ) ?? ?? )


From above expiration, Reynold?s Number is independent of flow profile. Hence, Reynold?s
Number for parabolic flow profile is 500.

8. For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure
and temperature, respectively. As per Maxwell?s relations,
p
v
s
? ??
??
?
??
is equal to
A.
T
p
v
? ??
??
?
??
B.
p
s
T
? ??
??
?
??
C.
s
T
p
?? ?
??
?
??
D.
p
T
v
? ??
?
??
?
??

Ans: option (C)
Sol: From mathematical relation expiration



7

???? = ?????? +??????
? (
????
????
)
?? = (
????
????
)
??
???????? ?????????????? ????????????????
?? ?= ?????? +??????
? (
????
????
)
?? = (
????
????
)
??

9. Hardenability of steel is a measure of
A. the ability to harden when it is cold worked
B. the maximum hardness that can be obtained when it is austenitized and then quenched
C. the ability to retain its hardness when it is heated to elevated temperatures
D. the depth to which required hardening is obtained when it is austenitized and then quenched
Ans: option (D)
Sol: The depth to which required hardening is obtained when it is austenitized and then quenched.

10. The directional derivative of the function f(x, y) = x
2
+ y
2
along a line directed from (0, 0) to (1,
1), evaluated at the point x = 1, y = 1 is
A. 2 B. ?2
C. 4?2 D. 2?2
Ans: option (D)
Sol: Directional derivative of function along the line is the scalar value of derivative along the line. i.e.
we have to calculate value of derivative of function in the direction of given line vector
? ?? = ??? (
????
????
)+ ??? (
????
????
)
? ?? = 2???+ 2???
Now, calculating the value of ? ?? in 1???+ 1???
D.D of given function is (2???+ 2??? ) ?
(??? + ?? ?)
|??? + ?? ?|
= 2 ?2

11. A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is
A.
2 D
T
?
B.
T
D

C.
D
T
?
D.
D
T

Ans: option (C)
Sol: circular pitch =
????
??

12. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the
instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of
points P and R are VP and VR, in the x and y directions, respectively. The magnitude of the
angular velocity of the body is




8

A. /3
R
V B. /3
P
V
C. 2VR D. 2VP
Ans: option (C)
Sol: The given body is a rigid body; Hence the given body will not have any deformation, and the
possible motion is translation and angular motion. we know that the angular motion of the object is
always defined as the motion about the point. Hence, first we have to find a point parallel to both
velocity ?? ?? and ?? ?? .


? Angular velocity, ?? =
???????????????? ?????????????????????????? ????????????????
?? =
?? ?? ????
=
?? ?? ????

???? =
?3
2
????????? ???? ???????????????? =
?3
2
?1=
?3
2

???? =
1
2
????????? ???? ???????????????? =
1
2
?1=
1
2


?? =
2?? ?? ?3
=
2?? ?? 1


13. Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4
m. The view factor F12 is
A. 0.25 B. 0.0625
C. 1.0 D. 0.5
Ans: option (C)
Sol: ?? 12
=1

14. The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
A.
10
01
??
??
?
??
B.
01
10
? ??
??
?
??

C.
01
10
??
??
??
D.
10
01
???
??
??

Ans: option (C)
Sol: The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
01
10
??
??
??




S



9

15. The state of stress at a point in a component is represented by a Mohr?s circle of radius 100 MPa
centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the
normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same
point is ___________ MPa.
Ans: 80
Sol:


?? =?100
2
?60
2
=80 ??????

16. One-dimensional steady state heat conduction takes place through a solid whose cross-sectional
area varies linearly in the direction of heat transfer. Assume there is no heat generation in the
solid and the thermal conductivity of the material is constant and independent of temperature.
The temperature distribution in the solid is
A. Quadratic B. Exponential
C. Logarithmic D. Linear
Ans: option (C)
Sol: Let the given body cross-sectional area varies linearly, and heat is flowing from left to right.





If there is no heat generation,
?? ????
(?????
????
????
)=0

?
?? ????
(?????
????
????
)=?0

(?????
????
????
)=??

??? (?? 0
+?? ?? ?? )
????
????
=??
???? =
? ?? ????
?? (?? 0
+?? ?? ?? )


? ????
2
1
=?
? ?? ????
?? (?? 0
+?? ?? ?? )
2
1


?? 2
??? 1
= ?
?? ?? ln(
?? ?? ?? 2
+?? 0
?? ?? ?? 1
+?? 0
)



10

17. An analytic function f(z) of complex variable z = x + I y may be written as f(z) = u(x, y) + iv (x,
y). Then, u(x, y) and v(x, y) must satisfy
A.
uv
xy
??
=?
??
and
uv
yx
??
=
??

B.
uv
xy
??
=?
??
and
uv
yx
??
=?
??

C.
uv
xy
??
=
??
and
uv
yx
??
=?
??

D.
uv
xy
??
=
??
and
uv
yx
??
=
??

Ans: option (C)
Sol: If f(z) = u(x, y) + iv(x, y) is analytic function then it must satisfy the following relations.

????
????
=
????
????


????
????
=?
????
????


18. A thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is
losing heat to the surroundings by natural convection. The temperatures of the plate and the
surroundings, and the properties of the surrounding fluid, are constant. The relationship between
the average Nusselt and Rayleigh numbers is given as Nu = K Ra ?, where K is a constant. The
length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the
plate is increased to 16L keeping all other factors constant.

If the average heat transfer coefficient for the first plate is h1 and that for the second plate is h2,
the value of the ratio h1/h2 is____________.
Ans: 2
Sol: ?? ?? =?? (?? ?? )
1
4
We know that ?? ?? =?? ?? ?? ??
?? ?? =?? (?? ?? ?? ?? )
1
4
??? ?? ?(?? ?? )
1
4 ?(
???? ??? ?? 3
?? 2
)
1
4

??? ??? 3
4
???? ?
1
4
?
2
?
1
?(
?? 1
?? 2
)
1
4
=>
?
1
?
2
?(
?? 2
?? 1
)
1
4
=(16)
1
4=2



11


19. Which one of the following modifications of the simple ideal Rankine cycle increases the thermal
efficiency and reduces the moisture content of the steam at the turbine outlet?
A. Decreasing the condenser pressure.
B. Increasing the boiler pressure.
C. Decreasing the boiler pressure.
D. Increasing the turbine inlet temperature.
Ans: option (D)
Sol: Due to increase of the turbine inlet temperature, quality of the stream at outlet of the turbine
improves. Which increases the thermal efficiency and reduces the moisture content of the steam at the
turbine outlet.

20. Consider a linear rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of
100 MPa along the length direction. Assume plane stress conditions in the plane normal to the
thickness. The Young?s modulus E = 200 MPa and Poisson?s ratio v = 0.3 are given. The principal
strains in the plane of the sheet are
A. (0.5, 0.0) B. (0.35, -0.15)
C. (0.5, -0.5) D. (0.5, -0.15)
Ans: option (D)
Sol: ?
1
=
?? 1
?? ???
?? 2
?? =
100
200
?0.3?
0
200
=0.5

?
2
=
?? 2
?? ???
?? 1
?? =
0
200
?0.3?
100
200
=?0.15


21. The figure shows an idealized plane truss. If a horizontal force of 300 N is applied at point A,
then the magnitude of the force produced in member CD is ________N.

Ans: 0

Sol:



12



The momentum about the point A must be zero, because there is no deformation of any truss.
Hence, ?? ????
=0 [?? ????
is not passing through the point A]

22. The fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase
in
A. freezing range
B. surface tension
C. degree of superheat
D. viscosity
Ans: option (C)
Sol: Fluidity of molten metal of cast alloys increases with increase in degree of superheat.

23. The most common limit gage used for inspecting the hole diameter is
A. Ring gage B. Snap gage
C. Plug gage D. Master gage
Ans: option (C)
Sol: The most common limit gage used for inspecting the hole diameter is Plug gage.

24. The differential equation 45
dy
y
dx
+= is valid in the domain 0 ? x ? 1 with y(0) = 2.25. The
solution of the differential equation is
A. y = e
-4x
+ 1.25
B. y = e
4x
+ 5
C. y = e
4x
+ 1.25
D. y = e
-4x
+ 5
Ans: option (A)
Sol: The given equation is.



13

???? ???? +4?? =5
If Integration factor = ?? ?4????
=?? 4??
? ?? ????? =?5????? ???? +??
? ?? ??? 4?? =5?
?? 4?? 4
+??
? ?? ??? 4?? =5?
?? 4?? 4
+?? ?.( 1)
Now for at x=0,
? 2.25 =
5
4
+ ??
? ?? =1
? Using the value of C in equ (1)
? ?? ?
?? 4?? ?? 4?? =
5
?? 4?? ?
?? 4?? 4
+
?? ?? 4??
? ?? =1.25+ ?? ?4??

25. A two-dimensional incompressible frictionless flow field is given by
??
. u xi yj =? If ? is the density
of the fluid, the expression for pressure gradient vector at any point in the flow field is given as
A.
( )
22
??
x i y j ??+ B.
( )
??
xi yj ??+
C.
( )
??
xi yj ? + D.
( )
??
xi yj ? ?
Ans: option (B)
Sol: Euler?s Equation of motion in 2D.

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

As there is no extra force acting on the fluid.
?? ?? ?????? ?? ?? =0
Now form the given expiration, u=x & v=y
?
????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????


?0+ ?? ?1+0+0=0?
1
?? ????
????

0+ 0+?? ?1+0=0?
1
?? ????
????

??????????? ???????? ?????? =
????
????
???+
????
????
???= ??? (?? ???+?? ??? )




14

26. A short shoe external drum brake is shown in the figure. The diameter of the brake drum is 500
mm. The dimensions a = 1000 mm, b = 500 mm and c = 200 mm. The coefficient of friction
between the drum and the shoe is 0.35. The force applied on the lever F = 100 N as shown in
the figure. The drum is rotating anti-clockwise. The braking torque on the drum is _______N.m
(round off to two decimal places).

Ans: 20.34
Sol:

Applying momentum about point O.

??? ?? =0

?? ??? +?? ?? ?? ??? ??? ?? ??? =0
?? ?? =232.55
Breaking Torque = ?? ?? ?? ?? ?? = 20.34

27. A uniform disc with radius r and a mass of m kg is mounted centrally on a horizontal axle of
negligible mass and length of 1.5r. The disc spins counter-clockwise about the axle with angular
speed ?, when viewed from the right-hand side bearing, Q. The axle precesses about a vertical
axis at
?p = ?/10 in the clockwise direction when viewed from above. Let RP and RQ (positive upwards)
be the resultant reaction forces due to the mass and the gyroscopic effect, at bearings P and Q,
respectively. Assuming ?
2
r = 300 m/s
2
and g = 10 m/s
2
, the ratio of the larger to the smaller
bearing reaction force (considering appropriate signs) is __________.



15


Ans: -3
Sol: ?????????????????? ???????????? (???? )=???? ?? ??

Using: ?? ?? =
?? 10
and ?? 2
?? =300

???? =
?? ?? 2
2
?? 2
10
=15????

Reaction at P and Q due to gravity

?? ?? 1
+?? ?? 1
=???? =10??
?? ?? 1
=5??
??? ?? 1
= 5 ??

Reaction at P and Q due to GC

Taking momentum about point p.
?? ?? 2
?1.5?? ?15???? =0
?? ?? 2
=
15????
1.5?? =10 ??
??? ?? 2
= ?10 ??
?????? ,
?? ?? ?? ?? =
?? ?? 1
+?? ?? 2

?? ?? 1
+?? ?? 2
=
5+10
5?10
= ?3

28. The figure shows a pouring arrangement for casting of a metal block. Frictional losses are
negligible. The acceleration due to gravity is 9.81 m/s
2
. The time (in s, round off to two decimal
places) to fill up the mold cavity (of size 40 cm ? 30 cm ? 15 cm) is ____________



16


Ans: 29.84
Sol: ???????? ?????????????? ???????? =
?? ?? ?? ?? .?2?? ?

???????? =
0.40?0.30?0.15
?? 0.02
2
4
.?2?9.81?0.20
28.94 ??????

29. The activities of a project, their duration and the precedence relationships are given in the table.
For example, in a precedence relationship ?X < Y, Z? means that X is predecessor of activities Y
and Z. The time to complete the activities along the critical path is ____________ weeks.
Activity Duration
(Weeks)
Precedence
Relationship
A 5 A < B, C, D
B 7 B < E, F, G
C 10 C < I
D 6 D < G
E 3 E < H
F 9 F < I
G 7 G < I
H 4 H < I
I 2 ---
A. 21 B. 25
C. 23 D. 17
Ans: option (C)
Sol:



17


30. The crank of a slider-crank mechanism rotates counter-clockwise (CCW) with a constant angular
velocity ?, as shown. Assume the length of the crank to be r.

Using exact analysis, the acceleration of the slider in the y-direction, at the instant shown, where
the crank is parallel to x-axis, is given by
A. -?
2
r B. 2?
2
r
C. ?
2
r D. -2?
2
r
Ans: option (C)
Sol:


Velocity of point A, ?? ?? = ?? ???
The radial acceleration of point A, ?? ????
=?? ?? 2

Since, the inclination of line AB is 45 degree, the acceleration of the point B will be equal to the
acceleration of point A. i.e. ?? ?? 2


31. A gas tungsten arc welding operation is performed using a current of 250 A and an arc voltage of
20 V at a welding speed of 5 mm/s. Assuming that the arc efficiency is 70%, the net heat input
per unit length of the weld will be ________ kJ/mm (round off to one decimal place).
Ans: 0.7
Sol: ???????? ?????????? =??Power
elec

???????? ?????????? =0.7?250?20=3500 ????????

???????? ?????????? per unit length=
3500
5
=700
?? ????

=0.7 KJ/mm

32. Water flows through two different pipes A and B of the same circular cross-section but at
different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both
the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes
is same, the ratio of volume flow rates QB/QA is ______ (round off to two decimal places).
A
O
B



18

Ans: 0.5
Sol: Frictional losses of pipe

??? ? ????
?? ?? ?? ? ????
(
?? ?? )
?? ?? ?????
?? ?? ?? ??

?
????
?????
=
?? ?? ?? ?? ?? ?? 2
?? ?? ?? ?? ?? ?? 2
;?? ??????? ?? =
64
????



?? ?? 2
?? ?? 2
=
?
????
?? ?? ?? ?? ??? ?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? ?? ??

?? ?? ?? ?? =
?? ?? ?? ?? =0.5

33. Consider two concentric circular cylinders of different materials M and N in contact with each
other at r = b, as shown below. The interface at r = b is frictionless. The composite cylinder
system is subjected to internal pressure P. Let
( )
,
MM
r
uu
?
and
( )
,
MM
rr ??
?? denote the radial and
tangential displacement and stress components, respectively, in material M Similarly,
( )
,
NN
r
uu
?

and
( )
,
NN
rr ??
?? denote the radial and tangential displacement and stress components, respectively,
in material N. The boundary conditions that need to be satisfied at the frictionless interface
between the two cylinders are :

A.
MN
rr
uu = and
MN
rr rr
?? = and
MN
uu
??
= and
MN
? ? ? ?
?? =
B.
MN
rr rr
?? = and
MN
? ? ? ?
?? = only
C.
MN
uu
??
= and
MN
? ? ? ?
?? = only
D.
MN
rr
uu = and
MN
rr rr
?? = only
Ans: option (D)
Sol:



19



Internal pressure causes the stress in radial as well as circumferential direction.

At r=b i.e. interference of the cylinder can be frictionless if Stress in radial direction must be equal.
Velocity in radial direction must be equal. (This condition will make the normal force Zero)
As radius of the cylinder increases due to inside pressure, there will be relative velocity between
the contact surfaces in the circumferential direction.

34. The binary phase diagram of metals P and Q is shown in the figure. An alloy X containing 60% P
and 40% Q (by weight) is cooled from liquid to solid state. The fractions of solid and liquid (in
weight percent) at 1250
o
C, respectively, will be

A. 22.2% and 77.8%
B. 68.0% and 32.0%
C. 77.8% and 22.2%
D. 32.0% and 68.0%
Ans: option (A)
Sol: Mass fraction of liquid =
?? ?? ??? 0
?? ?? ??? ??
?? ?? =
68?40
68?32
= 0.778=77.8%
?? ?? =1??? ?? =0.222=22.2%

35. The annual demand of valves per year in a company is 10,000 units. The current order quantity
is 400 valves per order. The holding cost is Rs. 24 per valve per year and the ordering cost is Rs.
400 per order. If the current order quantity is changed to Economic Order Quantity, then the
saving in the total cost of inventory per year will be Rs. __________ (round off to two decimal
places).
Ans: 943.59
Sol:
Annual Demand (D) = 10000 nos



20

Order Quantities (Q) = 400 / order
Holding cost (?? ?
)= 24 /valve/year
Ordering Cost (?? 0
) = RS 400 /order
?????? =
?? ?? ?? 0
+
?? 2
?? ?


?????? =
10000
400
400+
10000
2
24=14800

?????? ?=?2?? ?? 0
?? ?


?????? ?=13856.41

???????????? =14800?13856.41=???? .?????? .????

36. A slender uniform rigid bar of mass m is hinged at O and supported by two springs, with
stiffnesses 3k and k, and a damper with damping coefficient c, as shown in the figure. For the
system to be critically damped, the ratio c/?km should be

A. 4 B. 2
C. 4?7 D. 2?7
Ans: option (C)
Sol:
?? ?????
=?;?? ????? ???????????? ???? ???????????????????? ????????????

Suppose that we apply a external force downward at horizontal road at spring constant 3K and
leave it freely for to and fro motion.
Therefore, moment about point ?O?; ? ?? 0
=0
?? 0
??
? +?? (
3?? 4
?? )(
3?? 4
)+ 3?? (
?? 4
?? )(
?? 4
)+?? (
?? 4
?? ? )(
?? 4
)=0
?? 0
??
? +?? (
9?? 2
16
?? )+3?? (
?? 2
16
?? )+?? (
?? 2

16
?? ? )=0
Now, moment of inertia of rod about the center of the rod is ?? ?? =
?? ?? 2
12

And moment of inertia about the hinged point is ?? 0
=?? ?? +?? ?? 2
=
?? ?? 2
12
+?? (
?? 4
)
2
=
7
48
?? ?? 2

7
48
?? ?? 2
??
? +
1
16
?? ?? 2
?? ?+
12
16
?? ?? 2
?? =0

As we know that for critical dumping, the root of the quadratic equation should be real and equal.



21

? ?? 2
?4???? =0
(
1
16
?? ?? 2
)
2
?4 (
7
48
?? ?? 2
)(
12
16
?? ?? 2
)=0

?? =?4 (
7
1
?? )(
4
1
?? )=4?7????
?
?? ?????
= 4?7

37. The probability that a part manufactured by a company will be defective is 0.05. If 15 such parts
are selected randomly and inspected, then the probability that at least two parts will be
defective is __________ (round off to two decimal places).
Ans: 0.17
Sol: Total no. of parts = 15
P[defective(p)] = 0.05
P[non-defective(q)] = 1 ? 0.05 = 0.95
P[at least 2 defective] = 1 ? [P(no defective)+P(1 defective)]
Using the binomial distribution,
P[at least 2 defective] = 1 ? [
15
C0p
0
q
15
+
15
C1p
1
q
14
]= 1 ? [0.05
0
0.95
15
+ 15?0.05?0.95
14
] = 1 ?
[0.4639 + 0.3657] = 1 ? 0.8296 = 0.1704


38. A four bar mechanism is shown in the figure. The link numbers are mentioned near the links.
Input link 2 is rotating anti-clockwise with a constant angular speed ?2. Length of different links
are :

2 4 2
4
,
2.
OO O A L
AB O B L
==
==

The magnitude of the angular speed of the output link 4 is ?4 at the instant when link 2 makes
an angle of 90
o
with O2O4 as shown. The ratio
4
2
?
?
is __________ (round off to two decimal
places).

Ans: 0.79
Sol: Using Instantaneous center method



22


?? 24
?? 12
?? 2
= ?? 24
?? 41
?? 4

?? 24
?? 12
=?? tan75
?? (???????? ? ?? 12
?? 23
?? 24
)
?? 24
?? 41
=?? +?? tan75
??
?
?? 4
?? 2
=
?? 24
?? 12
?? 24
?? 41
=
?? tan75
?? ?? +?? tan75
??
=0.788

39. Two masses A and B having mass ma and mb, respectively, lying in the plane of the figure
shown, are rigidly attached to a shaft which revolves about an axis through O perpendicular to
the figure. The radii of rotation of the masses ma and mb are ra and rb, respectively. The angle
between lines OA and OB is 90
o
. If ma = 10 kg, mb = 20 kg, ra = 200 mm and rb = 400 mm,
then the balance mass to be placed at a radius of 200 mm is _________ kg (round off to two
decimal places).

Ans: 41.23
Sol:
Let the balance mass be m
? ?? ?? =?? ?? ?? ?? ?????? 0?+?? ?? ?? ?? ?????? 90?+???????????? =0 -----(1)
? ?? ?? =?? ?? ?? ?? ?????? 0?+?? ?? ?? ?? ?????? 90?+???????????? =0------ (2)
From (1), ???????????? =?[?? ?? ?? ?? ?????? 0?+?? ?? ?? ?? ?????? 90?]
Or, ???????????? =?[10?200]=?2000
From (2), ???????????? =?[?? ?? ?? ?? ?????? 0+?? ?? ?? ?? ?????? 90?]
Or, ???????????? =?[20?400]=?8000
Using ?(???????????? )
2
+(???????????? )
2
=???? =?2000
2
+8000
2
=8246.21
Now, since the radius of the balance mass is 200mm, therefore ?? =
8246.21
200
? =41.23????

40. A prismatic, straight elastic, cantilever beam is subjected to a linearly distributed transverse load
as shown below. If the beam length is L, Young?s modulus E, and area moment of inertia I, the
magnitude of the maximum deflection is



23


A.
4
60
qL
EI
B.
4
30
qL
EI

C.
4
10
qL
EI
D.
4
15
qL
EI

Ans: option (B)
Sol: The maximum deflection of the cantilever beam subjected to uniformly varying load (UVL) is given
by
4
30
qL
EI


41. Given a vector
( )
3 3 3
1
? ??
3
u y i x j z k = ? + + and ? n as the unit normal vector to the surface of the
hemisphere (x
2
+ y
2
+ z
2
= 1;z ?0), the value of integral
( )
? u n dS ? ? ?
?
evaluated on the
curved surface of the hemisphere S is
A. ? B.
3
?

C.
2
?
D.
2
?
?
Ans: option (C)
Sol: Hemisphere (x
2
+ y
2
+ z
2
= 1;z ?0)



To find the integration of the given expiration, it is easy if we are using the stoke?s theorem.
Surface integral will become line integral.
?(?? ???? )???????? = ???? ?????

Now, putting the value of ?? in the above equation.
?(?? ???? )???????? =?
1
3
(??? 3
???? +?? 3
???? +?? 3
???? )
??

=?
1
3
(??? 3
???? +?? 3
???? )
?? ??? =0 ???? ???????? ????????????
FirstRanker.com - FirstRanker's Choice



2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6




3

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of ?? =
8+6
2
=7

6. X is an online media provider. By offering unlimited and exclusive online content at attractive
prices for a loyalty membership, X is almost forcing its customers towards its loyalty
membership. If its loyalty membership continues to grow at its current rate, within the next
eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
A. Most households that subscribe to X?s loyalty membership discontinue watching cable
television
B. Non-members prefer to watch cable television
C. The X is cancelling accounts of non-members
D. Cable television operators don?t subscribe to X?s loyalty membership
Ans: option (A)
Sol: option A is the most appropriate solution

7. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased
by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.
A. 35.70 B. 10.00
C. 37.50 D. 25.00
Ans: option (C)
Sol: Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04??? =0.04??
And the fiscal deficit in 2016 = 0.05?1.1?? =0.055??
Increase in fiscal deficit = 0.055x ? 0.04x = 0.015x
So, the percentage increase in fiscal deficit =
0.015?? 0.04?? ?100=37.5%

8. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can
empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is
opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is
_________.
A. 16.50 B. 14.50
C. 15.50 D. 13.50
Ans: option (B)
Sol: 1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(
1
6
? ?
1
12
? )=
1
3
?
Tank filled by when Q and R works for another 6 hours = 6(
1
9
? ?
1
12
? )=
1
6
?
Total tank filled in these 10 hours =
1
3
? +
1
6
? =0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in
9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours




4

9. While teaching a creative writing class in India, I was surprised at receiving stories from the
students that were all set in distant places: in the American West with cowboys and in
Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave
the writers in the once-colonised countries the confidence to see the shabby lives around them
as worthy of being ?told?.
The writer of this passage is surprised by the creative writing assignments of his students,
because __________.
A. Some of the students had written about ice cubes and cowboys
B. None of the students had written about ice cubes and cowboys
C. Some of the students had written stories set in foreign places
D. None of the students had written stories set in India
Ans: option (C)
Sol: option C is the most appropriate solution

10. Mola is a digital platform for taxis in a city. It offers three types of rides ? Pool, Mini and Prime.
The Table below presents the number of rides for the past four months. The platform earns one
US dollar per ride. What is the percentage share of revenue contributed by Prime to the total
revenues of Mola, for the entire duration?
Type
Month
January February March April
Pool 170 320 215 190
Mini 110 220 180 70
Prime 75 180 120 90

A. 38.74 B. 23.97
C. 25.86 D. 16.24

Ans: option (B)
Sol: Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580
Revenue contributed by Prime = 75 + 180 + 120 +90 = 465
Total revenue of Mola = 895 + 580 + 465 = 1940
So, the percentage share =
465
1940
?100=23.97%

MECHANICAL ENGINEERING
1. A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by
application of pure bending moments at its ends. The Young?s modulus of the material of the
wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.
Ans: 50
Sol: Tensile stress
?? =
?? ?? ?? =
100?10
3
1
(
1
1000?2
)=50 ??????





5

2. In an electrical discharge machining process, the breakdown voltage across inter electrode gap
(IEG) is 200 V and the capacitance of the RC circuit is 50 ?F. The energy (in J) released per
spark across the IEG is __________
Ans: 1
Sol:
?? =
1
2
??????????????????????? ????????????? ?? 2

?? =0.5?50?10
?6
?200
2
=1 ??


3. If x is the mean of data 3, x, 2 and 4, then the mode is _________
Ans: 3
Sol: ?? =
3+?? +2+4
4

4??? =3+?? +2+4
4??? ??? =3+2+4=9
?? =3
Mode is 3. (Maximum repeated value)

4. The cold forming process in which a hardened tool is pressed against a workpiece (when there is
relative motion between the tool and the workpiece) to produce a roughened surface with a
regular pattern is
A. Strip rolling B. Knurling
C. Roll forming D. Chamfering
Ans: option (B)
Sol: We provide special pattern to prevent the relative motion between contact surface. This special
pattern is known as Knurling.


5. Endurance limit of a beam subjected to pure bending decreases with
A. increase in the surface roughness and increase in the size of the beam
B. decrease in the surface roughness and decrease in the size of the beam
C. decrease in the surface roughness and increase in the size of the beam
D. increase in the surface roughness and decrease in the size of the beam
Ans: option (A)
Sol: Formula for endurance limit
?? ?? =?? ?? ??? ?? ??? ?? ??? ?? ??? ?? ?

?? ???????
?? ?? ????????? ????????????
?? ?? ??????????????? ????????????
?? ?? ????????? ????????????
?? ?? ??????????????????????? ????????????
?? ?? ?
??????????????????? ?????????????? ?
Form above formula it is clear that the Endurance limit increases with increase in size,
surface, load, temp and endurance strength.







6

6. In matrix equation [A] {X} = {R}.
? ?
4 8 4 2
8 16 4 , 1
4 4 15 4
AX
? ? ? ?
?? ??
= ? = ??
??
????
??
??
?
? ? ? ?
and ? ?
32
16 .
64
R
??
??
=
??
??
??

One of the eigenvalues of matrix [A] is
A. 4 B. 15
C. 8 D. 16
Ans: option (D)
Sol: [A] {X} = {R}.

We know ???? = ???? ;?? ??????? ?? ??????????? ??????????

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}={
32
16
64
}

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}=16{
2
1
4
}

Hence, ?? =????

7. Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number
ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit.
The Reynolds number at the exit of the pipe is___________.
Ans: 500
Sol: Reynold?s Number
???? =
?? ?? ????
?? ??
Where: -
?? ??????????? ??????????????
?? ????
??????????????? ????????????????
?? ??????????????? ???? ????????
?? ? Dynamic viscosity of Fluid
?? ?? =(
?? ?? ????
?? ?? )=
(

?? (
?? ???????? ?? ???????? ) ?? ?? )


From above expiration, Reynold?s Number is independent of flow profile. Hence, Reynold?s
Number for parabolic flow profile is 500.

8. For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure
and temperature, respectively. As per Maxwell?s relations,
p
v
s
? ??
??
?
??
is equal to
A.
T
p
v
? ??
??
?
??
B.
p
s
T
? ??
??
?
??
C.
s
T
p
?? ?
??
?
??
D.
p
T
v
? ??
?
??
?
??

Ans: option (C)
Sol: From mathematical relation expiration



7

???? = ?????? +??????
? (
????
????
)
?? = (
????
????
)
??
???????? ?????????????? ????????????????
?? ?= ?????? +??????
? (
????
????
)
?? = (
????
????
)
??

9. Hardenability of steel is a measure of
A. the ability to harden when it is cold worked
B. the maximum hardness that can be obtained when it is austenitized and then quenched
C. the ability to retain its hardness when it is heated to elevated temperatures
D. the depth to which required hardening is obtained when it is austenitized and then quenched
Ans: option (D)
Sol: The depth to which required hardening is obtained when it is austenitized and then quenched.

10. The directional derivative of the function f(x, y) = x
2
+ y
2
along a line directed from (0, 0) to (1,
1), evaluated at the point x = 1, y = 1 is
A. 2 B. ?2
C. 4?2 D. 2?2
Ans: option (D)
Sol: Directional derivative of function along the line is the scalar value of derivative along the line. i.e.
we have to calculate value of derivative of function in the direction of given line vector
? ?? = ??? (
????
????
)+ ??? (
????
????
)
? ?? = 2???+ 2???
Now, calculating the value of ? ?? in 1???+ 1???
D.D of given function is (2???+ 2??? ) ?
(??? + ?? ?)
|??? + ?? ?|
= 2 ?2

11. A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is
A.
2 D
T
?
B.
T
D

C.
D
T
?
D.
D
T

Ans: option (C)
Sol: circular pitch =
????
??

12. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the
instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of
points P and R are VP and VR, in the x and y directions, respectively. The magnitude of the
angular velocity of the body is




8

A. /3
R
V B. /3
P
V
C. 2VR D. 2VP
Ans: option (C)
Sol: The given body is a rigid body; Hence the given body will not have any deformation, and the
possible motion is translation and angular motion. we know that the angular motion of the object is
always defined as the motion about the point. Hence, first we have to find a point parallel to both
velocity ?? ?? and ?? ?? .


? Angular velocity, ?? =
???????????????? ?????????????????????????? ????????????????
?? =
?? ?? ????
=
?? ?? ????

???? =
?3
2
????????? ???? ???????????????? =
?3
2
?1=
?3
2

???? =
1
2
????????? ???? ???????????????? =
1
2
?1=
1
2


?? =
2?? ?? ?3
=
2?? ?? 1


13. Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4
m. The view factor F12 is
A. 0.25 B. 0.0625
C. 1.0 D. 0.5
Ans: option (C)
Sol: ?? 12
=1

14. The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
A.
10
01
??
??
?
??
B.
01
10
? ??
??
?
??

C.
01
10
??
??
??
D.
10
01
???
??
??

Ans: option (C)
Sol: The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
01
10
??
??
??




S



9

15. The state of stress at a point in a component is represented by a Mohr?s circle of radius 100 MPa
centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the
normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same
point is ___________ MPa.
Ans: 80
Sol:


?? =?100
2
?60
2
=80 ??????

16. One-dimensional steady state heat conduction takes place through a solid whose cross-sectional
area varies linearly in the direction of heat transfer. Assume there is no heat generation in the
solid and the thermal conductivity of the material is constant and independent of temperature.
The temperature distribution in the solid is
A. Quadratic B. Exponential
C. Logarithmic D. Linear
Ans: option (C)
Sol: Let the given body cross-sectional area varies linearly, and heat is flowing from left to right.





If there is no heat generation,
?? ????
(?????
????
????
)=0

?
?? ????
(?????
????
????
)=?0

(?????
????
????
)=??

??? (?? 0
+?? ?? ?? )
????
????
=??
???? =
? ?? ????
?? (?? 0
+?? ?? ?? )


? ????
2
1
=?
? ?? ????
?? (?? 0
+?? ?? ?? )
2
1


?? 2
??? 1
= ?
?? ?? ln(
?? ?? ?? 2
+?? 0
?? ?? ?? 1
+?? 0
)



10

17. An analytic function f(z) of complex variable z = x + I y may be written as f(z) = u(x, y) + iv (x,
y). Then, u(x, y) and v(x, y) must satisfy
A.
uv
xy
??
=?
??
and
uv
yx
??
=
??

B.
uv
xy
??
=?
??
and
uv
yx
??
=?
??

C.
uv
xy
??
=
??
and
uv
yx
??
=?
??

D.
uv
xy
??
=
??
and
uv
yx
??
=
??

Ans: option (C)
Sol: If f(z) = u(x, y) + iv(x, y) is analytic function then it must satisfy the following relations.

????
????
=
????
????


????
????
=?
????
????


18. A thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is
losing heat to the surroundings by natural convection. The temperatures of the plate and the
surroundings, and the properties of the surrounding fluid, are constant. The relationship between
the average Nusselt and Rayleigh numbers is given as Nu = K Ra ?, where K is a constant. The
length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the
plate is increased to 16L keeping all other factors constant.

If the average heat transfer coefficient for the first plate is h1 and that for the second plate is h2,
the value of the ratio h1/h2 is____________.
Ans: 2
Sol: ?? ?? =?? (?? ?? )
1
4
We know that ?? ?? =?? ?? ?? ??
?? ?? =?? (?? ?? ?? ?? )
1
4
??? ?? ?(?? ?? )
1
4 ?(
???? ??? ?? 3
?? 2
)
1
4

??? ??? 3
4
???? ?
1
4
?
2
?
1
?(
?? 1
?? 2
)
1
4
=>
?
1
?
2
?(
?? 2
?? 1
)
1
4
=(16)
1
4=2



11


19. Which one of the following modifications of the simple ideal Rankine cycle increases the thermal
efficiency and reduces the moisture content of the steam at the turbine outlet?
A. Decreasing the condenser pressure.
B. Increasing the boiler pressure.
C. Decreasing the boiler pressure.
D. Increasing the turbine inlet temperature.
Ans: option (D)
Sol: Due to increase of the turbine inlet temperature, quality of the stream at outlet of the turbine
improves. Which increases the thermal efficiency and reduces the moisture content of the steam at the
turbine outlet.

20. Consider a linear rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of
100 MPa along the length direction. Assume plane stress conditions in the plane normal to the
thickness. The Young?s modulus E = 200 MPa and Poisson?s ratio v = 0.3 are given. The principal
strains in the plane of the sheet are
A. (0.5, 0.0) B. (0.35, -0.15)
C. (0.5, -0.5) D. (0.5, -0.15)
Ans: option (D)
Sol: ?
1
=
?? 1
?? ???
?? 2
?? =
100
200
?0.3?
0
200
=0.5

?
2
=
?? 2
?? ???
?? 1
?? =
0
200
?0.3?
100
200
=?0.15


21. The figure shows an idealized plane truss. If a horizontal force of 300 N is applied at point A,
then the magnitude of the force produced in member CD is ________N.

Ans: 0

Sol:



12



The momentum about the point A must be zero, because there is no deformation of any truss.
Hence, ?? ????
=0 [?? ????
is not passing through the point A]

22. The fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase
in
A. freezing range
B. surface tension
C. degree of superheat
D. viscosity
Ans: option (C)
Sol: Fluidity of molten metal of cast alloys increases with increase in degree of superheat.

23. The most common limit gage used for inspecting the hole diameter is
A. Ring gage B. Snap gage
C. Plug gage D. Master gage
Ans: option (C)
Sol: The most common limit gage used for inspecting the hole diameter is Plug gage.

24. The differential equation 45
dy
y
dx
+= is valid in the domain 0 ? x ? 1 with y(0) = 2.25. The
solution of the differential equation is
A. y = e
-4x
+ 1.25
B. y = e
4x
+ 5
C. y = e
4x
+ 1.25
D. y = e
-4x
+ 5
Ans: option (A)
Sol: The given equation is.



13

???? ???? +4?? =5
If Integration factor = ?? ?4????
=?? 4??
? ?? ????? =?5????? ???? +??
? ?? ??? 4?? =5?
?? 4?? 4
+??
? ?? ??? 4?? =5?
?? 4?? 4
+?? ?.( 1)
Now for at x=0,
? 2.25 =
5
4
+ ??
? ?? =1
? Using the value of C in equ (1)
? ?? ?
?? 4?? ?? 4?? =
5
?? 4?? ?
?? 4?? 4
+
?? ?? 4??
? ?? =1.25+ ?? ?4??

25. A two-dimensional incompressible frictionless flow field is given by
??
. u xi yj =? If ? is the density
of the fluid, the expression for pressure gradient vector at any point in the flow field is given as
A.
( )
22
??
x i y j ??+ B.
( )
??
xi yj ??+
C.
( )
??
xi yj ? + D.
( )
??
xi yj ? ?
Ans: option (B)
Sol: Euler?s Equation of motion in 2D.

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

As there is no extra force acting on the fluid.
?? ?? ?????? ?? ?? =0
Now form the given expiration, u=x & v=y
?
????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????


?0+ ?? ?1+0+0=0?
1
?? ????
????

0+ 0+?? ?1+0=0?
1
?? ????
????

??????????? ???????? ?????? =
????
????
???+
????
????
???= ??? (?? ???+?? ??? )




14

26. A short shoe external drum brake is shown in the figure. The diameter of the brake drum is 500
mm. The dimensions a = 1000 mm, b = 500 mm and c = 200 mm. The coefficient of friction
between the drum and the shoe is 0.35. The force applied on the lever F = 100 N as shown in
the figure. The drum is rotating anti-clockwise. The braking torque on the drum is _______N.m
(round off to two decimal places).

Ans: 20.34
Sol:

Applying momentum about point O.

??? ?? =0

?? ??? +?? ?? ?? ??? ??? ?? ??? =0
?? ?? =232.55
Breaking Torque = ?? ?? ?? ?? ?? = 20.34

27. A uniform disc with radius r and a mass of m kg is mounted centrally on a horizontal axle of
negligible mass and length of 1.5r. The disc spins counter-clockwise about the axle with angular
speed ?, when viewed from the right-hand side bearing, Q. The axle precesses about a vertical
axis at
?p = ?/10 in the clockwise direction when viewed from above. Let RP and RQ (positive upwards)
be the resultant reaction forces due to the mass and the gyroscopic effect, at bearings P and Q,
respectively. Assuming ?
2
r = 300 m/s
2
and g = 10 m/s
2
, the ratio of the larger to the smaller
bearing reaction force (considering appropriate signs) is __________.



15


Ans: -3
Sol: ?????????????????? ???????????? (???? )=???? ?? ??

Using: ?? ?? =
?? 10
and ?? 2
?? =300

???? =
?? ?? 2
2
?? 2
10
=15????

Reaction at P and Q due to gravity

?? ?? 1
+?? ?? 1
=???? =10??
?? ?? 1
=5??
??? ?? 1
= 5 ??

Reaction at P and Q due to GC

Taking momentum about point p.
?? ?? 2
?1.5?? ?15???? =0
?? ?? 2
=
15????
1.5?? =10 ??
??? ?? 2
= ?10 ??
?????? ,
?? ?? ?? ?? =
?? ?? 1
+?? ?? 2

?? ?? 1
+?? ?? 2
=
5+10
5?10
= ?3

28. The figure shows a pouring arrangement for casting of a metal block. Frictional losses are
negligible. The acceleration due to gravity is 9.81 m/s
2
. The time (in s, round off to two decimal
places) to fill up the mold cavity (of size 40 cm ? 30 cm ? 15 cm) is ____________



16


Ans: 29.84
Sol: ???????? ?????????????? ???????? =
?? ?? ?? ?? .?2?? ?

???????? =
0.40?0.30?0.15
?? 0.02
2
4
.?2?9.81?0.20
28.94 ??????

29. The activities of a project, their duration and the precedence relationships are given in the table.
For example, in a precedence relationship ?X < Y, Z? means that X is predecessor of activities Y
and Z. The time to complete the activities along the critical path is ____________ weeks.
Activity Duration
(Weeks)
Precedence
Relationship
A 5 A < B, C, D
B 7 B < E, F, G
C 10 C < I
D 6 D < G
E 3 E < H
F 9 F < I
G 7 G < I
H 4 H < I
I 2 ---
A. 21 B. 25
C. 23 D. 17
Ans: option (C)
Sol:



17


30. The crank of a slider-crank mechanism rotates counter-clockwise (CCW) with a constant angular
velocity ?, as shown. Assume the length of the crank to be r.

Using exact analysis, the acceleration of the slider in the y-direction, at the instant shown, where
the crank is parallel to x-axis, is given by
A. -?
2
r B. 2?
2
r
C. ?
2
r D. -2?
2
r
Ans: option (C)
Sol:


Velocity of point A, ?? ?? = ?? ???
The radial acceleration of point A, ?? ????
=?? ?? 2

Since, the inclination of line AB is 45 degree, the acceleration of the point B will be equal to the
acceleration of point A. i.e. ?? ?? 2


31. A gas tungsten arc welding operation is performed using a current of 250 A and an arc voltage of
20 V at a welding speed of 5 mm/s. Assuming that the arc efficiency is 70%, the net heat input
per unit length of the weld will be ________ kJ/mm (round off to one decimal place).
Ans: 0.7
Sol: ???????? ?????????? =??Power
elec

???????? ?????????? =0.7?250?20=3500 ????????

???????? ?????????? per unit length=
3500
5
=700
?? ????

=0.7 KJ/mm

32. Water flows through two different pipes A and B of the same circular cross-section but at
different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both
the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes
is same, the ratio of volume flow rates QB/QA is ______ (round off to two decimal places).
A
O
B



18

Ans: 0.5
Sol: Frictional losses of pipe

??? ? ????
?? ?? ?? ? ????
(
?? ?? )
?? ?? ?????
?? ?? ?? ??

?
????
?????
=
?? ?? ?? ?? ?? ?? 2
?? ?? ?? ?? ?? ?? 2
;?? ??????? ?? =
64
????



?? ?? 2
?? ?? 2
=
?
????
?? ?? ?? ?? ??? ?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? ?? ??

?? ?? ?? ?? =
?? ?? ?? ?? =0.5

33. Consider two concentric circular cylinders of different materials M and N in contact with each
other at r = b, as shown below. The interface at r = b is frictionless. The composite cylinder
system is subjected to internal pressure P. Let
( )
,
MM
r
uu
?
and
( )
,
MM
rr ??
?? denote the radial and
tangential displacement and stress components, respectively, in material M Similarly,
( )
,
NN
r
uu
?

and
( )
,
NN
rr ??
?? denote the radial and tangential displacement and stress components, respectively,
in material N. The boundary conditions that need to be satisfied at the frictionless interface
between the two cylinders are :

A.
MN
rr
uu = and
MN
rr rr
?? = and
MN
uu
??
= and
MN
? ? ? ?
?? =
B.
MN
rr rr
?? = and
MN
? ? ? ?
?? = only
C.
MN
uu
??
= and
MN
? ? ? ?
?? = only
D.
MN
rr
uu = and
MN
rr rr
?? = only
Ans: option (D)
Sol:



19



Internal pressure causes the stress in radial as well as circumferential direction.

At r=b i.e. interference of the cylinder can be frictionless if Stress in radial direction must be equal.
Velocity in radial direction must be equal. (This condition will make the normal force Zero)
As radius of the cylinder increases due to inside pressure, there will be relative velocity between
the contact surfaces in the circumferential direction.

34. The binary phase diagram of metals P and Q is shown in the figure. An alloy X containing 60% P
and 40% Q (by weight) is cooled from liquid to solid state. The fractions of solid and liquid (in
weight percent) at 1250
o
C, respectively, will be

A. 22.2% and 77.8%
B. 68.0% and 32.0%
C. 77.8% and 22.2%
D. 32.0% and 68.0%
Ans: option (A)
Sol: Mass fraction of liquid =
?? ?? ??? 0
?? ?? ??? ??
?? ?? =
68?40
68?32
= 0.778=77.8%
?? ?? =1??? ?? =0.222=22.2%

35. The annual demand of valves per year in a company is 10,000 units. The current order quantity
is 400 valves per order. The holding cost is Rs. 24 per valve per year and the ordering cost is Rs.
400 per order. If the current order quantity is changed to Economic Order Quantity, then the
saving in the total cost of inventory per year will be Rs. __________ (round off to two decimal
places).
Ans: 943.59
Sol:
Annual Demand (D) = 10000 nos



20

Order Quantities (Q) = 400 / order
Holding cost (?? ?
)= 24 /valve/year
Ordering Cost (?? 0
) = RS 400 /order
?????? =
?? ?? ?? 0
+
?? 2
?? ?


?????? =
10000
400
400+
10000
2
24=14800

?????? ?=?2?? ?? 0
?? ?


?????? ?=13856.41

???????????? =14800?13856.41=???? .?????? .????

36. A slender uniform rigid bar of mass m is hinged at O and supported by two springs, with
stiffnesses 3k and k, and a damper with damping coefficient c, as shown in the figure. For the
system to be critically damped, the ratio c/?km should be

A. 4 B. 2
C. 4?7 D. 2?7
Ans: option (C)
Sol:
?? ?????
=?;?? ????? ???????????? ???? ???????????????????? ????????????

Suppose that we apply a external force downward at horizontal road at spring constant 3K and
leave it freely for to and fro motion.
Therefore, moment about point ?O?; ? ?? 0
=0
?? 0
??
? +?? (
3?? 4
?? )(
3?? 4
)+ 3?? (
?? 4
?? )(
?? 4
)+?? (
?? 4
?? ? )(
?? 4
)=0
?? 0
??
? +?? (
9?? 2
16
?? )+3?? (
?? 2
16
?? )+?? (
?? 2

16
?? ? )=0
Now, moment of inertia of rod about the center of the rod is ?? ?? =
?? ?? 2
12

And moment of inertia about the hinged point is ?? 0
=?? ?? +?? ?? 2
=
?? ?? 2
12
+?? (
?? 4
)
2
=
7
48
?? ?? 2

7
48
?? ?? 2
??
? +
1
16
?? ?? 2
?? ?+
12
16
?? ?? 2
?? =0

As we know that for critical dumping, the root of the quadratic equation should be real and equal.



21

? ?? 2
?4???? =0
(
1
16
?? ?? 2
)
2
?4 (
7
48
?? ?? 2
)(
12
16
?? ?? 2
)=0

?? =?4 (
7
1
?? )(
4
1
?? )=4?7????
?
?? ?????
= 4?7

37. The probability that a part manufactured by a company will be defective is 0.05. If 15 such parts
are selected randomly and inspected, then the probability that at least two parts will be
defective is __________ (round off to two decimal places).
Ans: 0.17
Sol: Total no. of parts = 15
P[defective(p)] = 0.05
P[non-defective(q)] = 1 ? 0.05 = 0.95
P[at least 2 defective] = 1 ? [P(no defective)+P(1 defective)]
Using the binomial distribution,
P[at least 2 defective] = 1 ? [
15
C0p
0
q
15
+
15
C1p
1
q
14
]= 1 ? [0.05
0
0.95
15
+ 15?0.05?0.95
14
] = 1 ?
[0.4639 + 0.3657] = 1 ? 0.8296 = 0.1704


38. A four bar mechanism is shown in the figure. The link numbers are mentioned near the links.
Input link 2 is rotating anti-clockwise with a constant angular speed ?2. Length of different links
are :

2 4 2
4
,
2.
OO O A L
AB O B L
==
==

The magnitude of the angular speed of the output link 4 is ?4 at the instant when link 2 makes
an angle of 90
o
with O2O4 as shown. The ratio
4
2
?
?
is __________ (round off to two decimal
places).

Ans: 0.79
Sol: Using Instantaneous center method



22


?? 24
?? 12
?? 2
= ?? 24
?? 41
?? 4

?? 24
?? 12
=?? tan75
?? (???????? ? ?? 12
?? 23
?? 24
)
?? 24
?? 41
=?? +?? tan75
??
?
?? 4
?? 2
=
?? 24
?? 12
?? 24
?? 41
=
?? tan75
?? ?? +?? tan75
??
=0.788

39. Two masses A and B having mass ma and mb, respectively, lying in the plane of the figure
shown, are rigidly attached to a shaft which revolves about an axis through O perpendicular to
the figure. The radii of rotation of the masses ma and mb are ra and rb, respectively. The angle
between lines OA and OB is 90
o
. If ma = 10 kg, mb = 20 kg, ra = 200 mm and rb = 400 mm,
then the balance mass to be placed at a radius of 200 mm is _________ kg (round off to two
decimal places).

Ans: 41.23
Sol:
Let the balance mass be m
? ?? ?? =?? ?? ?? ?? ?????? 0?+?? ?? ?? ?? ?????? 90?+???????????? =0 -----(1)
? ?? ?? =?? ?? ?? ?? ?????? 0?+?? ?? ?? ?? ?????? 90?+???????????? =0------ (2)
From (1), ???????????? =?[?? ?? ?? ?? ?????? 0?+?? ?? ?? ?? ?????? 90?]
Or, ???????????? =?[10?200]=?2000
From (2), ???????????? =?[?? ?? ?? ?? ?????? 0+?? ?? ?? ?? ?????? 90?]
Or, ???????????? =?[20?400]=?8000
Using ?(???????????? )
2
+(???????????? )
2
=???? =?2000
2
+8000
2
=8246.21
Now, since the radius of the balance mass is 200mm, therefore ?? =
8246.21
200
? =41.23????

40. A prismatic, straight elastic, cantilever beam is subjected to a linearly distributed transverse load
as shown below. If the beam length is L, Young?s modulus E, and area moment of inertia I, the
magnitude of the maximum deflection is



23


A.
4
60
qL
EI
B.
4
30
qL
EI

C.
4
10
qL
EI
D.
4
15
qL
EI

Ans: option (B)
Sol: The maximum deflection of the cantilever beam subjected to uniformly varying load (UVL) is given
by
4
30
qL
EI


41. Given a vector
( )
3 3 3
1
? ??
3
u y i x j z k = ? + + and ? n as the unit normal vector to the surface of the
hemisphere (x
2
+ y
2
+ z
2
= 1;z ?0), the value of integral
( )
? u n dS ? ? ?
?
evaluated on the
curved surface of the hemisphere S is
A. ? B.
3
?

C.
2
?
D.
2
?
?
Ans: option (C)
Sol: Hemisphere (x
2
+ y
2
+ z
2
= 1;z ?0)



To find the integration of the given expiration, it is easy if we are using the stoke?s theorem.
Surface integral will become line integral.
?(?? ???? )???????? = ???? ?????

Now, putting the value of ?? in the above equation.
?(?? ???? )???????? =?
1
3
(??? 3
???? +?? 3
???? +?? 3
???? )
??

=?
1
3
(??? 3
???? +?? 3
???? )
?? ??? =0 ???? ???????? ????????????



24

=? (?? 2
???????? +?? 2
???????? )
?? [using green theorem]
=?(?? 2
+?? 2
)????????
Now converting the above equation into polar coordinate
?? 2
+?? 2
=?? 2


? ? ?? 2
?? ???? ????
1
?? =0
=
2?? ?? =0
? (? ?? 3
????
1
?? =0
)????
2?? ?? =0
=
?? 2



42. The thickness of a sheet is reduced by rolling (without any change in width) using 600 mm
diameter rolls. Neglect elastic deflection of the rolls and assume that the coefficient of friction at
the roll-workpiece interface is 0.05. The sheet enters the rotating rolls unaided. If the initial
sheet thickness is 2 mm, the minimum possible final thickness that can be produced by this
process in a single pass is ________ mm (round off to two decimal places).
Ans: 1.25
Sol: Draft = (??? )
?????? =?? 2
?? =0.05
2
?300=0.75????
Hence, final thickness of the sheet = 2 ? 0.75 = 1.25mm

43. A ball of mass 3 kg moving with a velocity of 4 m/s undergoes a perfectly-elastic direct-central
impact with a stationary ball of mass m. After the impact is over, the kinetic energy of the 3 kg
ball is 6 J. The possible value (s) of m is/are
A. 6 kg only B. 1 kg, 9 kg
C. 1 kg only D. 1 kg, 6 kg
Ans: option (D)
Sol: Conservation of momentum gives m1u1 + m2u2 = m1v1 + m2v2
?? 1
=3???? , ?? 1
=4?? /?? , ?? 2
=?? ???? , ?? 2
=0
Substituting in the above equation,
3?4+?? ?0=3??? 1
+?? ??? 2

Or, 12=3?? 1
+?? ?? 2
-------(1)
For perfectly-elastic impact,
?? =
?? 2
??? 1
?? 1
??? 2
=1
Or, ?? 2
??? 1
=?? 1
??? 2
=4?? /?? ------- (2)
Conservation of kinetic energy gives
1
2
?? 1
?? 1
2
+
1
2
?? 2
?? 2
2
=
1
2
?? 1
?? 1
2
+
1
2
?? 2
?? 2
2

Or,
1
2
3(4)
2
+0=6+
1
2
?? 2
?? 2
2

Or, ?? ?? 2
2
=36 ---------(3)
From equation (2), ?? 1
=?? 2
?4
Substituting in equation (1),
12=3(?? 2
?4)+?? ?? 2

Or 12=3?? 2
?12+ ?? ?? 2

Or ?? 2
(3+?? )=24
Or ?? 2
=
24
3+??
Substituting in equation (3)
FirstRanker.com - FirstRanker's Choice



2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6




3

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of ?? =
8+6
2
=7

6. X is an online media provider. By offering unlimited and exclusive online content at attractive
prices for a loyalty membership, X is almost forcing its customers towards its loyalty
membership. If its loyalty membership continues to grow at its current rate, within the next
eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
A. Most households that subscribe to X?s loyalty membership discontinue watching cable
television
B. Non-members prefer to watch cable television
C. The X is cancelling accounts of non-members
D. Cable television operators don?t subscribe to X?s loyalty membership
Ans: option (A)
Sol: option A is the most appropriate solution

7. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased
by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.
A. 35.70 B. 10.00
C. 37.50 D. 25.00
Ans: option (C)
Sol: Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04??? =0.04??
And the fiscal deficit in 2016 = 0.05?1.1?? =0.055??
Increase in fiscal deficit = 0.055x ? 0.04x = 0.015x
So, the percentage increase in fiscal deficit =
0.015?? 0.04?? ?100=37.5%

8. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can
empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is
opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is
_________.
A. 16.50 B. 14.50
C. 15.50 D. 13.50
Ans: option (B)
Sol: 1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(
1
6
? ?
1
12
? )=
1
3
?
Tank filled by when Q and R works for another 6 hours = 6(
1
9
? ?
1
12
? )=
1
6
?
Total tank filled in these 10 hours =
1
3
? +
1
6
? =0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in
9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours




4

9. While teaching a creative writing class in India, I was surprised at receiving stories from the
students that were all set in distant places: in the American West with cowboys and in
Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave
the writers in the once-colonised countries the confidence to see the shabby lives around them
as worthy of being ?told?.
The writer of this passage is surprised by the creative writing assignments of his students,
because __________.
A. Some of the students had written about ice cubes and cowboys
B. None of the students had written about ice cubes and cowboys
C. Some of the students had written stories set in foreign places
D. None of the students had written stories set in India
Ans: option (C)
Sol: option C is the most appropriate solution

10. Mola is a digital platform for taxis in a city. It offers three types of rides ? Pool, Mini and Prime.
The Table below presents the number of rides for the past four months. The platform earns one
US dollar per ride. What is the percentage share of revenue contributed by Prime to the total
revenues of Mola, for the entire duration?
Type
Month
January February March April
Pool 170 320 215 190
Mini 110 220 180 70
Prime 75 180 120 90

A. 38.74 B. 23.97
C. 25.86 D. 16.24

Ans: option (B)
Sol: Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580
Revenue contributed by Prime = 75 + 180 + 120 +90 = 465
Total revenue of Mola = 895 + 580 + 465 = 1940
So, the percentage share =
465
1940
?100=23.97%

MECHANICAL ENGINEERING
1. A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by
application of pure bending moments at its ends. The Young?s modulus of the material of the
wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.
Ans: 50
Sol: Tensile stress
?? =
?? ?? ?? =
100?10
3
1
(
1
1000?2
)=50 ??????





5

2. In an electrical discharge machining process, the breakdown voltage across inter electrode gap
(IEG) is 200 V and the capacitance of the RC circuit is 50 ?F. The energy (in J) released per
spark across the IEG is __________
Ans: 1
Sol:
?? =
1
2
??????????????????????? ????????????? ?? 2

?? =0.5?50?10
?6
?200
2
=1 ??


3. If x is the mean of data 3, x, 2 and 4, then the mode is _________
Ans: 3
Sol: ?? =
3+?? +2+4
4

4??? =3+?? +2+4
4??? ??? =3+2+4=9
?? =3
Mode is 3. (Maximum repeated value)

4. The cold forming process in which a hardened tool is pressed against a workpiece (when there is
relative motion between the tool and the workpiece) to produce a roughened surface with a
regular pattern is
A. Strip rolling B. Knurling
C. Roll forming D. Chamfering
Ans: option (B)
Sol: We provide special pattern to prevent the relative motion between contact surface. This special
pattern is known as Knurling.


5. Endurance limit of a beam subjected to pure bending decreases with
A. increase in the surface roughness and increase in the size of the beam
B. decrease in the surface roughness and decrease in the size of the beam
C. decrease in the surface roughness and increase in the size of the beam
D. increase in the surface roughness and decrease in the size of the beam
Ans: option (A)
Sol: Formula for endurance limit
?? ?? =?? ?? ??? ?? ??? ?? ??? ?? ??? ?? ?

?? ???????
?? ?? ????????? ????????????
?? ?? ??????????????? ????????????
?? ?? ????????? ????????????
?? ?? ??????????????????????? ????????????
?? ?? ?
??????????????????? ?????????????? ?
Form above formula it is clear that the Endurance limit increases with increase in size,
surface, load, temp and endurance strength.







6

6. In matrix equation [A] {X} = {R}.
? ?
4 8 4 2
8 16 4 , 1
4 4 15 4
AX
? ? ? ?
?? ??
= ? = ??
??
????
??
??
?
? ? ? ?
and ? ?
32
16 .
64
R
??
??
=
??
??
??

One of the eigenvalues of matrix [A] is
A. 4 B. 15
C. 8 D. 16
Ans: option (D)
Sol: [A] {X} = {R}.

We know ???? = ???? ;?? ??????? ?? ??????????? ??????????

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}={
32
16
64
}

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}=16{
2
1
4
}

Hence, ?? =????

7. Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number
ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit.
The Reynolds number at the exit of the pipe is___________.
Ans: 500
Sol: Reynold?s Number
???? =
?? ?? ????
?? ??
Where: -
?? ??????????? ??????????????
?? ????
??????????????? ????????????????
?? ??????????????? ???? ????????
?? ? Dynamic viscosity of Fluid
?? ?? =(
?? ?? ????
?? ?? )=
(

?? (
?? ???????? ?? ???????? ) ?? ?? )


From above expiration, Reynold?s Number is independent of flow profile. Hence, Reynold?s
Number for parabolic flow profile is 500.

8. For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure
and temperature, respectively. As per Maxwell?s relations,
p
v
s
? ??
??
?
??
is equal to
A.
T
p
v
? ??
??
?
??
B.
p
s
T
? ??
??
?
??
C.
s
T
p
?? ?
??
?
??
D.
p
T
v
? ??
?
??
?
??

Ans: option (C)
Sol: From mathematical relation expiration



7

???? = ?????? +??????
? (
????
????
)
?? = (
????
????
)
??
???????? ?????????????? ????????????????
?? ?= ?????? +??????
? (
????
????
)
?? = (
????
????
)
??

9. Hardenability of steel is a measure of
A. the ability to harden when it is cold worked
B. the maximum hardness that can be obtained when it is austenitized and then quenched
C. the ability to retain its hardness when it is heated to elevated temperatures
D. the depth to which required hardening is obtained when it is austenitized and then quenched
Ans: option (D)
Sol: The depth to which required hardening is obtained when it is austenitized and then quenched.

10. The directional derivative of the function f(x, y) = x
2
+ y
2
along a line directed from (0, 0) to (1,
1), evaluated at the point x = 1, y = 1 is
A. 2 B. ?2
C. 4?2 D. 2?2
Ans: option (D)
Sol: Directional derivative of function along the line is the scalar value of derivative along the line. i.e.
we have to calculate value of derivative of function in the direction of given line vector
? ?? = ??? (
????
????
)+ ??? (
????
????
)
? ?? = 2???+ 2???
Now, calculating the value of ? ?? in 1???+ 1???
D.D of given function is (2???+ 2??? ) ?
(??? + ?? ?)
|??? + ?? ?|
= 2 ?2

11. A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is
A.
2 D
T
?
B.
T
D

C.
D
T
?
D.
D
T

Ans: option (C)
Sol: circular pitch =
????
??

12. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the
instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of
points P and R are VP and VR, in the x and y directions, respectively. The magnitude of the
angular velocity of the body is




8

A. /3
R
V B. /3
P
V
C. 2VR D. 2VP
Ans: option (C)
Sol: The given body is a rigid body; Hence the given body will not have any deformation, and the
possible motion is translation and angular motion. we know that the angular motion of the object is
always defined as the motion about the point. Hence, first we have to find a point parallel to both
velocity ?? ?? and ?? ?? .


? Angular velocity, ?? =
???????????????? ?????????????????????????? ????????????????
?? =
?? ?? ????
=
?? ?? ????

???? =
?3
2
????????? ???? ???????????????? =
?3
2
?1=
?3
2

???? =
1
2
????????? ???? ???????????????? =
1
2
?1=
1
2


?? =
2?? ?? ?3
=
2?? ?? 1


13. Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4
m. The view factor F12 is
A. 0.25 B. 0.0625
C. 1.0 D. 0.5
Ans: option (C)
Sol: ?? 12
=1

14. The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
A.
10
01
??
??
?
??
B.
01
10
? ??
??
?
??

C.
01
10
??
??
??
D.
10
01
???
??
??

Ans: option (C)
Sol: The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
01
10
??
??
??




S



9

15. The state of stress at a point in a component is represented by a Mohr?s circle of radius 100 MPa
centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the
normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same
point is ___________ MPa.
Ans: 80
Sol:


?? =?100
2
?60
2
=80 ??????

16. One-dimensional steady state heat conduction takes place through a solid whose cross-sectional
area varies linearly in the direction of heat transfer. Assume there is no heat generation in the
solid and the thermal conductivity of the material is constant and independent of temperature.
The temperature distribution in the solid is
A. Quadratic B. Exponential
C. Logarithmic D. Linear
Ans: option (C)
Sol: Let the given body cross-sectional area varies linearly, and heat is flowing from left to right.





If there is no heat generation,
?? ????
(?????
????
????
)=0

?
?? ????
(?????
????
????
)=?0

(?????
????
????
)=??

??? (?? 0
+?? ?? ?? )
????
????
=??
???? =
? ?? ????
?? (?? 0
+?? ?? ?? )


? ????
2
1
=?
? ?? ????
?? (?? 0
+?? ?? ?? )
2
1


?? 2
??? 1
= ?
?? ?? ln(
?? ?? ?? 2
+?? 0
?? ?? ?? 1
+?? 0
)



10

17. An analytic function f(z) of complex variable z = x + I y may be written as f(z) = u(x, y) + iv (x,
y). Then, u(x, y) and v(x, y) must satisfy
A.
uv
xy
??
=?
??
and
uv
yx
??
=
??

B.
uv
xy
??
=?
??
and
uv
yx
??
=?
??

C.
uv
xy
??
=
??
and
uv
yx
??
=?
??

D.
uv
xy
??
=
??
and
uv
yx
??
=
??

Ans: option (C)
Sol: If f(z) = u(x, y) + iv(x, y) is analytic function then it must satisfy the following relations.

????
????
=
????
????


????
????
=?
????
????


18. A thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is
losing heat to the surroundings by natural convection. The temperatures of the plate and the
surroundings, and the properties of the surrounding fluid, are constant. The relationship between
the average Nusselt and Rayleigh numbers is given as Nu = K Ra ?, where K is a constant. The
length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the
plate is increased to 16L keeping all other factors constant.

If the average heat transfer coefficient for the first plate is h1 and that for the second plate is h2,
the value of the ratio h1/h2 is____________.
Ans: 2
Sol: ?? ?? =?? (?? ?? )
1
4
We know that ?? ?? =?? ?? ?? ??
?? ?? =?? (?? ?? ?? ?? )
1
4
??? ?? ?(?? ?? )
1
4 ?(
???? ??? ?? 3
?? 2
)
1
4

??? ??? 3
4
???? ?
1
4
?
2
?
1
?(
?? 1
?? 2
)
1
4
=>
?
1
?
2
?(
?? 2
?? 1
)
1
4
=(16)
1
4=2



11


19. Which one of the following modifications of the simple ideal Rankine cycle increases the thermal
efficiency and reduces the moisture content of the steam at the turbine outlet?
A. Decreasing the condenser pressure.
B. Increasing the boiler pressure.
C. Decreasing the boiler pressure.
D. Increasing the turbine inlet temperature.
Ans: option (D)
Sol: Due to increase of the turbine inlet temperature, quality of the stream at outlet of the turbine
improves. Which increases the thermal efficiency and reduces the moisture content of the steam at the
turbine outlet.

20. Consider a linear rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of
100 MPa along the length direction. Assume plane stress conditions in the plane normal to the
thickness. The Young?s modulus E = 200 MPa and Poisson?s ratio v = 0.3 are given. The principal
strains in the plane of the sheet are
A. (0.5, 0.0) B. (0.35, -0.15)
C. (0.5, -0.5) D. (0.5, -0.15)
Ans: option (D)
Sol: ?
1
=
?? 1
?? ???
?? 2
?? =
100
200
?0.3?
0
200
=0.5

?
2
=
?? 2
?? ???
?? 1
?? =
0
200
?0.3?
100
200
=?0.15


21. The figure shows an idealized plane truss. If a horizontal force of 300 N is applied at point A,
then the magnitude of the force produced in member CD is ________N.

Ans: 0

Sol:



12



The momentum about the point A must be zero, because there is no deformation of any truss.
Hence, ?? ????
=0 [?? ????
is not passing through the point A]

22. The fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase
in
A. freezing range
B. surface tension
C. degree of superheat
D. viscosity
Ans: option (C)
Sol: Fluidity of molten metal of cast alloys increases with increase in degree of superheat.

23. The most common limit gage used for inspecting the hole diameter is
A. Ring gage B. Snap gage
C. Plug gage D. Master gage
Ans: option (C)
Sol: The most common limit gage used for inspecting the hole diameter is Plug gage.

24. The differential equation 45
dy
y
dx
+= is valid in the domain 0 ? x ? 1 with y(0) = 2.25. The
solution of the differential equation is
A. y = e
-4x
+ 1.25
B. y = e
4x
+ 5
C. y = e
4x
+ 1.25
D. y = e
-4x
+ 5
Ans: option (A)
Sol: The given equation is.



13

???? ???? +4?? =5
If Integration factor = ?? ?4????
=?? 4??
? ?? ????? =?5????? ???? +??
? ?? ??? 4?? =5?
?? 4?? 4
+??
? ?? ??? 4?? =5?
?? 4?? 4
+?? ?.( 1)
Now for at x=0,
? 2.25 =
5
4
+ ??
? ?? =1
? Using the value of C in equ (1)
? ?? ?
?? 4?? ?? 4?? =
5
?? 4?? ?
?? 4?? 4
+
?? ?? 4??
? ?? =1.25+ ?? ?4??

25. A two-dimensional incompressible frictionless flow field is given by
??
. u xi yj =? If ? is the density
of the fluid, the expression for pressure gradient vector at any point in the flow field is given as
A.
( )
22
??
x i y j ??+ B.
( )
??
xi yj ??+
C.
( )
??
xi yj ? + D.
( )
??
xi yj ? ?
Ans: option (B)
Sol: Euler?s Equation of motion in 2D.

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

As there is no extra force acting on the fluid.
?? ?? ?????? ?? ?? =0
Now form the given expiration, u=x & v=y
?
????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????


?0+ ?? ?1+0+0=0?
1
?? ????
????

0+ 0+?? ?1+0=0?
1
?? ????
????

??????????? ???????? ?????? =
????
????
???+
????
????
???= ??? (?? ???+?? ??? )




14

26. A short shoe external drum brake is shown in the figure. The diameter of the brake drum is 500
mm. The dimensions a = 1000 mm, b = 500 mm and c = 200 mm. The coefficient of friction
between the drum and the shoe is 0.35. The force applied on the lever F = 100 N as shown in
the figure. The drum is rotating anti-clockwise. The braking torque on the drum is _______N.m
(round off to two decimal places).

Ans: 20.34
Sol:

Applying momentum about point O.

??? ?? =0

?? ??? +?? ?? ?? ??? ??? ?? ??? =0
?? ?? =232.55
Breaking Torque = ?? ?? ?? ?? ?? = 20.34

27. A uniform disc with radius r and a mass of m kg is mounted centrally on a horizontal axle of
negligible mass and length of 1.5r. The disc spins counter-clockwise about the axle with angular
speed ?, when viewed from the right-hand side bearing, Q. The axle precesses about a vertical
axis at
?p = ?/10 in the clockwise direction when viewed from above. Let RP and RQ (positive upwards)
be the resultant reaction forces due to the mass and the gyroscopic effect, at bearings P and Q,
respectively. Assuming ?
2
r = 300 m/s
2
and g = 10 m/s
2
, the ratio of the larger to the smaller
bearing reaction force (considering appropriate signs) is __________.



15


Ans: -3
Sol: ?????????????????? ???????????? (???? )=???? ?? ??

Using: ?? ?? =
?? 10
and ?? 2
?? =300

???? =
?? ?? 2
2
?? 2
10
=15????

Reaction at P and Q due to gravity

?? ?? 1
+?? ?? 1
=???? =10??
?? ?? 1
=5??
??? ?? 1
= 5 ??

Reaction at P and Q due to GC

Taking momentum about point p.
?? ?? 2
?1.5?? ?15???? =0
?? ?? 2
=
15????
1.5?? =10 ??
??? ?? 2
= ?10 ??
?????? ,
?? ?? ?? ?? =
?? ?? 1
+?? ?? 2

?? ?? 1
+?? ?? 2
=
5+10
5?10
= ?3

28. The figure shows a pouring arrangement for casting of a metal block. Frictional losses are
negligible. The acceleration due to gravity is 9.81 m/s
2
. The time (in s, round off to two decimal
places) to fill up the mold cavity (of size 40 cm ? 30 cm ? 15 cm) is ____________



16


Ans: 29.84
Sol: ???????? ?????????????? ???????? =
?? ?? ?? ?? .?2?? ?

???????? =
0.40?0.30?0.15
?? 0.02
2
4
.?2?9.81?0.20
28.94 ??????

29. The activities of a project, their duration and the precedence relationships are given in the table.
For example, in a precedence relationship ?X < Y, Z? means that X is predecessor of activities Y
and Z. The time to complete the activities along the critical path is ____________ weeks.
Activity Duration
(Weeks)
Precedence
Relationship
A 5 A < B, C, D
B 7 B < E, F, G
C 10 C < I
D 6 D < G
E 3 E < H
F 9 F < I
G 7 G < I
H 4 H < I
I 2 ---
A. 21 B. 25
C. 23 D. 17
Ans: option (C)
Sol:



17


30. The crank of a slider-crank mechanism rotates counter-clockwise (CCW) with a constant angular
velocity ?, as shown. Assume the length of the crank to be r.

Using exact analysis, the acceleration of the slider in the y-direction, at the instant shown, where
the crank is parallel to x-axis, is given by
A. -?
2
r B. 2?
2
r
C. ?
2
r D. -2?
2
r
Ans: option (C)
Sol:


Velocity of point A, ?? ?? = ?? ???
The radial acceleration of point A, ?? ????
=?? ?? 2

Since, the inclination of line AB is 45 degree, the acceleration of the point B will be equal to the
acceleration of point A. i.e. ?? ?? 2


31. A gas tungsten arc welding operation is performed using a current of 250 A and an arc voltage of
20 V at a welding speed of 5 mm/s. Assuming that the arc efficiency is 70%, the net heat input
per unit length of the weld will be ________ kJ/mm (round off to one decimal place).
Ans: 0.7
Sol: ???????? ?????????? =??Power
elec

???????? ?????????? =0.7?250?20=3500 ????????

???????? ?????????? per unit length=
3500
5
=700
?? ????

=0.7 KJ/mm

32. Water flows through two different pipes A and B of the same circular cross-section but at
different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both
the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes
is same, the ratio of volume flow rates QB/QA is ______ (round off to two decimal places).
A
O
B



18

Ans: 0.5
Sol: Frictional losses of pipe

??? ? ????
?? ?? ?? ? ????
(
?? ?? )
?? ?? ?????
?? ?? ?? ??

?
????
?????
=
?? ?? ?? ?? ?? ?? 2
?? ?? ?? ?? ?? ?? 2
;?? ??????? ?? =
64
????



?? ?? 2
?? ?? 2
=
?
????
?? ?? ?? ?? ??? ?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? ?? ??

?? ?? ?? ?? =
?? ?? ?? ?? =0.5

33. Consider two concentric circular cylinders of different materials M and N in contact with each
other at r = b, as shown below. The interface at r = b is frictionless. The composite cylinder
system is subjected to internal pressure P. Let
( )
,
MM
r
uu
?
and
( )
,
MM
rr ??
?? denote the radial and
tangential displacement and stress components, respectively, in material M Similarly,
( )
,
NN
r
uu
?

and
( )
,
NN
rr ??
?? denote the radial and tangential displacement and stress components, respectively,
in material N. The boundary conditions that need to be satisfied at the frictionless interface
between the two cylinders are :

A.
MN
rr
uu = and
MN
rr rr
?? = and
MN
uu
??
= and
MN
? ? ? ?
?? =
B.
MN
rr rr
?? = and
MN
? ? ? ?
?? = only
C.
MN
uu
??
= and
MN
? ? ? ?
?? = only
D.
MN
rr
uu = and
MN
rr rr
?? = only
Ans: option (D)
Sol:



19



Internal pressure causes the stress in radial as well as circumferential direction.

At r=b i.e. interference of the cylinder can be frictionless if Stress in radial direction must be equal.
Velocity in radial direction must be equal. (This condition will make the normal force Zero)
As radius of the cylinder increases due to inside pressure, there will be relative velocity between
the contact surfaces in the circumferential direction.

34. The binary phase diagram of metals P and Q is shown in the figure. An alloy X containing 60% P
and 40% Q (by weight) is cooled from liquid to solid state. The fractions of solid and liquid (in
weight percent) at 1250
o
C, respectively, will be

A. 22.2% and 77.8%
B. 68.0% and 32.0%
C. 77.8% and 22.2%
D. 32.0% and 68.0%
Ans: option (A)
Sol: Mass fraction of liquid =
?? ?? ??? 0
?? ?? ??? ??
?? ?? =
68?40
68?32
= 0.778=77.8%
?? ?? =1??? ?? =0.222=22.2%

35. The annual demand of valves per year in a company is 10,000 units. The current order quantity
is 400 valves per order. The holding cost is Rs. 24 per valve per year and the ordering cost is Rs.
400 per order. If the current order quantity is changed to Economic Order Quantity, then the
saving in the total cost of inventory per year will be Rs. __________ (round off to two decimal
places).
Ans: 943.59
Sol:
Annual Demand (D) = 10000 nos



20

Order Quantities (Q) = 400 / order
Holding cost (?? ?
)= 24 /valve/year
Ordering Cost (?? 0
) = RS 400 /order
?????? =
?? ?? ?? 0
+
?? 2
?? ?


?????? =
10000
400
400+
10000
2
24=14800

?????? ?=?2?? ?? 0
?? ?


?????? ?=13856.41

???????????? =14800?13856.41=???? .?????? .????

36. A slender uniform rigid bar of mass m is hinged at O and supported by two springs, with
stiffnesses 3k and k, and a damper with damping coefficient c, as shown in the figure. For the
system to be critically damped, the ratio c/?km should be

A. 4 B. 2
C. 4?7 D. 2?7
Ans: option (C)
Sol:
?? ?????
=?;?? ????? ???????????? ???? ???????????????????? ????????????

Suppose that we apply a external force downward at horizontal road at spring constant 3K and
leave it freely for to and fro motion.
Therefore, moment about point ?O?; ? ?? 0
=0
?? 0
??
? +?? (
3?? 4
?? )(
3?? 4
)+ 3?? (
?? 4
?? )(
?? 4
)+?? (
?? 4
?? ? )(
?? 4
)=0
?? 0
??
? +?? (
9?? 2
16
?? )+3?? (
?? 2
16
?? )+?? (
?? 2

16
?? ? )=0
Now, moment of inertia of rod about the center of the rod is ?? ?? =
?? ?? 2
12

And moment of inertia about the hinged point is ?? 0
=?? ?? +?? ?? 2
=
?? ?? 2
12
+?? (
?? 4
)
2
=
7
48
?? ?? 2

7
48
?? ?? 2
??
? +
1
16
?? ?? 2
?? ?+
12
16
?? ?? 2
?? =0

As we know that for critical dumping, the root of the quadratic equation should be real and equal.



21

? ?? 2
?4???? =0
(
1
16
?? ?? 2
)
2
?4 (
7
48
?? ?? 2
)(
12
16
?? ?? 2
)=0

?? =?4 (
7
1
?? )(
4
1
?? )=4?7????
?
?? ?????
= 4?7

37. The probability that a part manufactured by a company will be defective is 0.05. If 15 such parts
are selected randomly and inspected, then the probability that at least two parts will be
defective is __________ (round off to two decimal places).
Ans: 0.17
Sol: Total no. of parts = 15
P[defective(p)] = 0.05
P[non-defective(q)] = 1 ? 0.05 = 0.95
P[at least 2 defective] = 1 ? [P(no defective)+P(1 defective)]
Using the binomial distribution,
P[at least 2 defective] = 1 ? [
15
C0p
0
q
15
+
15
C1p
1
q
14
]= 1 ? [0.05
0
0.95
15
+ 15?0.05?0.95
14
] = 1 ?
[0.4639 + 0.3657] = 1 ? 0.8296 = 0.1704


38. A four bar mechanism is shown in the figure. The link numbers are mentioned near the links.
Input link 2 is rotating anti-clockwise with a constant angular speed ?2. Length of different links
are :

2 4 2
4
,
2.
OO O A L
AB O B L
==
==

The magnitude of the angular speed of the output link 4 is ?4 at the instant when link 2 makes
an angle of 90
o
with O2O4 as shown. The ratio
4
2
?
?
is __________ (round off to two decimal
places).

Ans: 0.79
Sol: Using Instantaneous center method



22


?? 24
?? 12
?? 2
= ?? 24
?? 41
?? 4

?? 24
?? 12
=?? tan75
?? (???????? ? ?? 12
?? 23
?? 24
)
?? 24
?? 41
=?? +?? tan75
??
?
?? 4
?? 2
=
?? 24
?? 12
?? 24
?? 41
=
?? tan75
?? ?? +?? tan75
??
=0.788

39. Two masses A and B having mass ma and mb, respectively, lying in the plane of the figure
shown, are rigidly attached to a shaft which revolves about an axis through O perpendicular to
the figure. The radii of rotation of the masses ma and mb are ra and rb, respectively. The angle
between lines OA and OB is 90
o
. If ma = 10 kg, mb = 20 kg, ra = 200 mm and rb = 400 mm,
then the balance mass to be placed at a radius of 200 mm is _________ kg (round off to two
decimal places).

Ans: 41.23
Sol:
Let the balance mass be m
? ?? ?? =?? ?? ?? ?? ?????? 0?+?? ?? ?? ?? ?????? 90?+???????????? =0 -----(1)
? ?? ?? =?? ?? ?? ?? ?????? 0?+?? ?? ?? ?? ?????? 90?+???????????? =0------ (2)
From (1), ???????????? =?[?? ?? ?? ?? ?????? 0?+?? ?? ?? ?? ?????? 90?]
Or, ???????????? =?[10?200]=?2000
From (2), ???????????? =?[?? ?? ?? ?? ?????? 0+?? ?? ?? ?? ?????? 90?]
Or, ???????????? =?[20?400]=?8000
Using ?(???????????? )
2
+(???????????? )
2
=???? =?2000
2
+8000
2
=8246.21
Now, since the radius of the balance mass is 200mm, therefore ?? =
8246.21
200
? =41.23????

40. A prismatic, straight elastic, cantilever beam is subjected to a linearly distributed transverse load
as shown below. If the beam length is L, Young?s modulus E, and area moment of inertia I, the
magnitude of the maximum deflection is



23


A.
4
60
qL
EI
B.
4
30
qL
EI

C.
4
10
qL
EI
D.
4
15
qL
EI

Ans: option (B)
Sol: The maximum deflection of the cantilever beam subjected to uniformly varying load (UVL) is given
by
4
30
qL
EI


41. Given a vector
( )
3 3 3
1
? ??
3
u y i x j z k = ? + + and ? n as the unit normal vector to the surface of the
hemisphere (x
2
+ y
2
+ z
2
= 1;z ?0), the value of integral
( )
? u n dS ? ? ?
?
evaluated on the
curved surface of the hemisphere S is
A. ? B.
3
?

C.
2
?
D.
2
?
?
Ans: option (C)
Sol: Hemisphere (x
2
+ y
2
+ z
2
= 1;z ?0)



To find the integration of the given expiration, it is easy if we are using the stoke?s theorem.
Surface integral will become line integral.
?(?? ???? )???????? = ???? ?????

Now, putting the value of ?? in the above equation.
?(?? ???? )???????? =?
1
3
(??? 3
???? +?? 3
???? +?? 3
???? )
??

=?
1
3
(??? 3
???? +?? 3
???? )
?? ??? =0 ???? ???????? ????????????



24

=? (?? 2
???????? +?? 2
???????? )
?? [using green theorem]
=?(?? 2
+?? 2
)????????
Now converting the above equation into polar coordinate
?? 2
+?? 2
=?? 2


? ? ?? 2
?? ???? ????
1
?? =0
=
2?? ?? =0
? (? ?? 3
????
1
?? =0
)????
2?? ?? =0
=
?? 2



42. The thickness of a sheet is reduced by rolling (without any change in width) using 600 mm
diameter rolls. Neglect elastic deflection of the rolls and assume that the coefficient of friction at
the roll-workpiece interface is 0.05. The sheet enters the rotating rolls unaided. If the initial
sheet thickness is 2 mm, the minimum possible final thickness that can be produced by this
process in a single pass is ________ mm (round off to two decimal places).
Ans: 1.25
Sol: Draft = (??? )
?????? =?? 2
?? =0.05
2
?300=0.75????
Hence, final thickness of the sheet = 2 ? 0.75 = 1.25mm

43. A ball of mass 3 kg moving with a velocity of 4 m/s undergoes a perfectly-elastic direct-central
impact with a stationary ball of mass m. After the impact is over, the kinetic energy of the 3 kg
ball is 6 J. The possible value (s) of m is/are
A. 6 kg only B. 1 kg, 9 kg
C. 1 kg only D. 1 kg, 6 kg
Ans: option (D)
Sol: Conservation of momentum gives m1u1 + m2u2 = m1v1 + m2v2
?? 1
=3???? , ?? 1
=4?? /?? , ?? 2
=?? ???? , ?? 2
=0
Substituting in the above equation,
3?4+?? ?0=3??? 1
+?? ??? 2

Or, 12=3?? 1
+?? ?? 2
-------(1)
For perfectly-elastic impact,
?? =
?? 2
??? 1
?? 1
??? 2
=1
Or, ?? 2
??? 1
=?? 1
??? 2
=4?? /?? ------- (2)
Conservation of kinetic energy gives
1
2
?? 1
?? 1
2
+
1
2
?? 2
?? 2
2
=
1
2
?? 1
?? 1
2
+
1
2
?? 2
?? 2
2

Or,
1
2
3(4)
2
+0=6+
1
2
?? 2
?? 2
2

Or, ?? ?? 2
2
=36 ---------(3)
From equation (2), ?? 1
=?? 2
?4
Substituting in equation (1),
12=3(?? 2
?4)+?? ?? 2

Or 12=3?? 2
?12+ ?? ?? 2

Or ?? 2
(3+?? )=24
Or ?? 2
=
24
3+??
Substituting in equation (3)



25

?? (
24
3+?? )
2
=36
576?? =36(3+?? )
2

?16?? =9+?? 2
+6??
?? 2
?10?? +9=0
On solving, we get
?? =1,9
Therefore, possible values of m are 1 kg and 9 kg.


44. The derivative of f(x) = cos(x) can be estimated using the approximation
( )
( ) ( )
'.
2
f x h f x h
fx
h
+ ? ?
= The percentage error is calculated as
Exact value-Approximate value
100.
Exact value
??
?
??
??
The percentage error in the derivative of f(x) at x = ?/6
radian, choosing h = 0.1 radian, is
A. > 1% and < 5%
B. < 0.1%
C. > 0.1% and < 1%
D. > 5%
Ans: option (C)
Sol: f(x) = cos(x)
? f?(x) = -sin(x) = ?sin(
?? 6
? )=?0.5 (exact value)
Approximate value = ( )
( ) ( )
'.
2
f x h f x h
fx
h
+ ? ?
=
?? ?
(?? )=
cos(?? +?)?cos?? ??
2?

cos(?? +?)=?????????????? ???????????????? ?
?????? (?? ??)=?????????????? ?+?????????????? ?
So,
?? ?
(?? )=
?????????????? ???????????????? ??[?????????????? ?+?????????????? ?]
2?

=
?2?????????????? ?
2?
=
??????????????? ?
?

Or, ?? ?
(?? )=
?sin(
?? 6
)?????? (0.1)
0.1
=
?0.5?0.0998
0.1
=?0.4992

So, percentage error =
?0.5?(?0.4992)
?0.5
?100=0.166


45. The aerodynamic drag on a sports car depends on its shape. The car has a drag coefficient of 0.1
with the windows and the roof closed. With the windows and the roof open, the drag coefficient
becomes 0.8. The car travels at 44 km/h with the windows and roof closed. For the same
amount of power needed to overcome the aerodynamic drag, the speed of the car with the
windows and roof open (round off to two decimal places), is ________km/h (the density of air
and frontal area may be assumed to be constant).
Ans: 22
FirstRanker.com - FirstRanker's Choice



2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6




3

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of ?? =
8+6
2
=7

6. X is an online media provider. By offering unlimited and exclusive online content at attractive
prices for a loyalty membership, X is almost forcing its customers towards its loyalty
membership. If its loyalty membership continues to grow at its current rate, within the next
eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
A. Most households that subscribe to X?s loyalty membership discontinue watching cable
television
B. Non-members prefer to watch cable television
C. The X is cancelling accounts of non-members
D. Cable television operators don?t subscribe to X?s loyalty membership
Ans: option (A)
Sol: option A is the most appropriate solution

7. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased
by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.
A. 35.70 B. 10.00
C. 37.50 D. 25.00
Ans: option (C)
Sol: Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04??? =0.04??
And the fiscal deficit in 2016 = 0.05?1.1?? =0.055??
Increase in fiscal deficit = 0.055x ? 0.04x = 0.015x
So, the percentage increase in fiscal deficit =
0.015?? 0.04?? ?100=37.5%

8. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can
empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is
opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is
_________.
A. 16.50 B. 14.50
C. 15.50 D. 13.50
Ans: option (B)
Sol: 1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(
1
6
? ?
1
12
? )=
1
3
?
Tank filled by when Q and R works for another 6 hours = 6(
1
9
? ?
1
12
? )=
1
6
?
Total tank filled in these 10 hours =
1
3
? +
1
6
? =0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in
9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours




4

9. While teaching a creative writing class in India, I was surprised at receiving stories from the
students that were all set in distant places: in the American West with cowboys and in
Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave
the writers in the once-colonised countries the confidence to see the shabby lives around them
as worthy of being ?told?.
The writer of this passage is surprised by the creative writing assignments of his students,
because __________.
A. Some of the students had written about ice cubes and cowboys
B. None of the students had written about ice cubes and cowboys
C. Some of the students had written stories set in foreign places
D. None of the students had written stories set in India
Ans: option (C)
Sol: option C is the most appropriate solution

10. Mola is a digital platform for taxis in a city. It offers three types of rides ? Pool, Mini and Prime.
The Table below presents the number of rides for the past four months. The platform earns one
US dollar per ride. What is the percentage share of revenue contributed by Prime to the total
revenues of Mola, for the entire duration?
Type
Month
January February March April
Pool 170 320 215 190
Mini 110 220 180 70
Prime 75 180 120 90

A. 38.74 B. 23.97
C. 25.86 D. 16.24

Ans: option (B)
Sol: Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580
Revenue contributed by Prime = 75 + 180 + 120 +90 = 465
Total revenue of Mola = 895 + 580 + 465 = 1940
So, the percentage share =
465
1940
?100=23.97%

MECHANICAL ENGINEERING
1. A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by
application of pure bending moments at its ends. The Young?s modulus of the material of the
wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.
Ans: 50
Sol: Tensile stress
?? =
?? ?? ?? =
100?10
3
1
(
1
1000?2
)=50 ??????





5

2. In an electrical discharge machining process, the breakdown voltage across inter electrode gap
(IEG) is 200 V and the capacitance of the RC circuit is 50 ?F. The energy (in J) released per
spark across the IEG is __________
Ans: 1
Sol:
?? =
1
2
??????????????????????? ????????????? ?? 2

?? =0.5?50?10
?6
?200
2
=1 ??


3. If x is the mean of data 3, x, 2 and 4, then the mode is _________
Ans: 3
Sol: ?? =
3+?? +2+4
4

4??? =3+?? +2+4
4??? ??? =3+2+4=9
?? =3
Mode is 3. (Maximum repeated value)

4. The cold forming process in which a hardened tool is pressed against a workpiece (when there is
relative motion between the tool and the workpiece) to produce a roughened surface with a
regular pattern is
A. Strip rolling B. Knurling
C. Roll forming D. Chamfering
Ans: option (B)
Sol: We provide special pattern to prevent the relative motion between contact surface. This special
pattern is known as Knurling.


5. Endurance limit of a beam subjected to pure bending decreases with
A. increase in the surface roughness and increase in the size of the beam
B. decrease in the surface roughness and decrease in the size of the beam
C. decrease in the surface roughness and increase in the size of the beam
D. increase in the surface roughness and decrease in the size of the beam
Ans: option (A)
Sol: Formula for endurance limit
?? ?? =?? ?? ??? ?? ??? ?? ??? ?? ??? ?? ?

?? ???????
?? ?? ????????? ????????????
?? ?? ??????????????? ????????????
?? ?? ????????? ????????????
?? ?? ??????????????????????? ????????????
?? ?? ?
??????????????????? ?????????????? ?
Form above formula it is clear that the Endurance limit increases with increase in size,
surface, load, temp and endurance strength.







6

6. In matrix equation [A] {X} = {R}.
? ?
4 8 4 2
8 16 4 , 1
4 4 15 4
AX
? ? ? ?
?? ??
= ? = ??
??
????
??
??
?
? ? ? ?
and ? ?
32
16 .
64
R
??
??
=
??
??
??

One of the eigenvalues of matrix [A] is
A. 4 B. 15
C. 8 D. 16
Ans: option (D)
Sol: [A] {X} = {R}.

We know ???? = ???? ;?? ??????? ?? ??????????? ??????????

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}={
32
16
64
}

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}=16{
2
1
4
}

Hence, ?? =????

7. Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number
ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit.
The Reynolds number at the exit of the pipe is___________.
Ans: 500
Sol: Reynold?s Number
???? =
?? ?? ????
?? ??
Where: -
?? ??????????? ??????????????
?? ????
??????????????? ????????????????
?? ??????????????? ???? ????????
?? ? Dynamic viscosity of Fluid
?? ?? =(
?? ?? ????
?? ?? )=
(

?? (
?? ???????? ?? ???????? ) ?? ?? )


From above expiration, Reynold?s Number is independent of flow profile. Hence, Reynold?s
Number for parabolic flow profile is 500.

8. For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure
and temperature, respectively. As per Maxwell?s relations,
p
v
s
? ??
??
?
??
is equal to
A.
T
p
v
? ??
??
?
??
B.
p
s
T
? ??
??
?
??
C.
s
T
p
?? ?
??
?
??
D.
p
T
v
? ??
?
??
?
??

Ans: option (C)
Sol: From mathematical relation expiration



7

???? = ?????? +??????
? (
????
????
)
?? = (
????
????
)
??
???????? ?????????????? ????????????????
?? ?= ?????? +??????
? (
????
????
)
?? = (
????
????
)
??

9. Hardenability of steel is a measure of
A. the ability to harden when it is cold worked
B. the maximum hardness that can be obtained when it is austenitized and then quenched
C. the ability to retain its hardness when it is heated to elevated temperatures
D. the depth to which required hardening is obtained when it is austenitized and then quenched
Ans: option (D)
Sol: The depth to which required hardening is obtained when it is austenitized and then quenched.

10. The directional derivative of the function f(x, y) = x
2
+ y
2
along a line directed from (0, 0) to (1,
1), evaluated at the point x = 1, y = 1 is
A. 2 B. ?2
C. 4?2 D. 2?2
Ans: option (D)
Sol: Directional derivative of function along the line is the scalar value of derivative along the line. i.e.
we have to calculate value of derivative of function in the direction of given line vector
? ?? = ??? (
????
????
)+ ??? (
????
????
)
? ?? = 2???+ 2???
Now, calculating the value of ? ?? in 1???+ 1???
D.D of given function is (2???+ 2??? ) ?
(??? + ?? ?)
|??? + ?? ?|
= 2 ?2

11. A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is
A.
2 D
T
?
B.
T
D

C.
D
T
?
D.
D
T

Ans: option (C)
Sol: circular pitch =
????
??

12. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the
instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of
points P and R are VP and VR, in the x and y directions, respectively. The magnitude of the
angular velocity of the body is




8

A. /3
R
V B. /3
P
V
C. 2VR D. 2VP
Ans: option (C)
Sol: The given body is a rigid body; Hence the given body will not have any deformation, and the
possible motion is translation and angular motion. we know that the angular motion of the object is
always defined as the motion about the point. Hence, first we have to find a point parallel to both
velocity ?? ?? and ?? ?? .


? Angular velocity, ?? =
???????????????? ?????????????????????????? ????????????????
?? =
?? ?? ????
=
?? ?? ????

???? =
?3
2
????????? ???? ???????????????? =
?3
2
?1=
?3
2

???? =
1
2
????????? ???? ???????????????? =
1
2
?1=
1
2


?? =
2?? ?? ?3
=
2?? ?? 1


13. Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4
m. The view factor F12 is
A. 0.25 B. 0.0625
C. 1.0 D. 0.5
Ans: option (C)
Sol: ?? 12
=1

14. The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
A.
10
01
??
??
?
??
B.
01
10
? ??
??
?
??

C.
01
10
??
??
??
D.
10
01
???
??
??

Ans: option (C)
Sol: The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
01
10
??
??
??




S



9

15. The state of stress at a point in a component is represented by a Mohr?s circle of radius 100 MPa
centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the
normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same
point is ___________ MPa.
Ans: 80
Sol:


?? =?100
2
?60
2
=80 ??????

16. One-dimensional steady state heat conduction takes place through a solid whose cross-sectional
area varies linearly in the direction of heat transfer. Assume there is no heat generation in the
solid and the thermal conductivity of the material is constant and independent of temperature.
The temperature distribution in the solid is
A. Quadratic B. Exponential
C. Logarithmic D. Linear
Ans: option (C)
Sol: Let the given body cross-sectional area varies linearly, and heat is flowing from left to right.





If there is no heat generation,
?? ????
(?????
????
????
)=0

?
?? ????
(?????
????
????
)=?0

(?????
????
????
)=??

??? (?? 0
+?? ?? ?? )
????
????
=??
???? =
? ?? ????
?? (?? 0
+?? ?? ?? )


? ????
2
1
=?
? ?? ????
?? (?? 0
+?? ?? ?? )
2
1


?? 2
??? 1
= ?
?? ?? ln(
?? ?? ?? 2
+?? 0
?? ?? ?? 1
+?? 0
)



10

17. An analytic function f(z) of complex variable z = x + I y may be written as f(z) = u(x, y) + iv (x,
y). Then, u(x, y) and v(x, y) must satisfy
A.
uv
xy
??
=?
??
and
uv
yx
??
=
??

B.
uv
xy
??
=?
??
and
uv
yx
??
=?
??

C.
uv
xy
??
=
??
and
uv
yx
??
=?
??

D.
uv
xy
??
=
??
and
uv
yx
??
=
??

Ans: option (C)
Sol: If f(z) = u(x, y) + iv(x, y) is analytic function then it must satisfy the following relations.

????
????
=
????
????


????
????
=?
????
????


18. A thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is
losing heat to the surroundings by natural convection. The temperatures of the plate and the
surroundings, and the properties of the surrounding fluid, are constant. The relationship between
the average Nusselt and Rayleigh numbers is given as Nu = K Ra ?, where K is a constant. The
length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the
plate is increased to 16L keeping all other factors constant.

If the average heat transfer coefficient for the first plate is h1 and that for the second plate is h2,
the value of the ratio h1/h2 is____________.
Ans: 2
Sol: ?? ?? =?? (?? ?? )
1
4
We know that ?? ?? =?? ?? ?? ??
?? ?? =?? (?? ?? ?? ?? )
1
4
??? ?? ?(?? ?? )
1
4 ?(
???? ??? ?? 3
?? 2
)
1
4

??? ??? 3
4
???? ?
1
4
?
2
?
1
?(
?? 1
?? 2
)
1
4
=>
?
1
?
2
?(
?? 2
?? 1
)
1
4
=(16)
1
4=2



11


19. Which one of the following modifications of the simple ideal Rankine cycle increases the thermal
efficiency and reduces the moisture content of the steam at the turbine outlet?
A. Decreasing the condenser pressure.
B. Increasing the boiler pressure.
C. Decreasing the boiler pressure.
D. Increasing the turbine inlet temperature.
Ans: option (D)
Sol: Due to increase of the turbine inlet temperature, quality of the stream at outlet of the turbine
improves. Which increases the thermal efficiency and reduces the moisture content of the steam at the
turbine outlet.

20. Consider a linear rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of
100 MPa along the length direction. Assume plane stress conditions in the plane normal to the
thickness. The Young?s modulus E = 200 MPa and Poisson?s ratio v = 0.3 are given. The principal
strains in the plane of the sheet are
A. (0.5, 0.0) B. (0.35, -0.15)
C. (0.5, -0.5) D. (0.5, -0.15)
Ans: option (D)
Sol: ?
1
=
?? 1
?? ???
?? 2
?? =
100
200
?0.3?
0
200
=0.5

?
2
=
?? 2
?? ???
?? 1
?? =
0
200
?0.3?
100
200
=?0.15


21. The figure shows an idealized plane truss. If a horizontal force of 300 N is applied at point A,
then the magnitude of the force produced in member CD is ________N.

Ans: 0

Sol:



12



The momentum about the point A must be zero, because there is no deformation of any truss.
Hence, ?? ????
=0 [?? ????
is not passing through the point A]

22. The fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase
in
A. freezing range
B. surface tension
C. degree of superheat
D. viscosity
Ans: option (C)
Sol: Fluidity of molten metal of cast alloys increases with increase in degree of superheat.

23. The most common limit gage used for inspecting the hole diameter is
A. Ring gage B. Snap gage
C. Plug gage D. Master gage
Ans: option (C)
Sol: The most common limit gage used for inspecting the hole diameter is Plug gage.

24. The differential equation 45
dy
y
dx
+= is valid in the domain 0 ? x ? 1 with y(0) = 2.25. The
solution of the differential equation is
A. y = e
-4x
+ 1.25
B. y = e
4x
+ 5
C. y = e
4x
+ 1.25
D. y = e
-4x
+ 5
Ans: option (A)
Sol: The given equation is.



13

???? ???? +4?? =5
If Integration factor = ?? ?4????
=?? 4??
? ?? ????? =?5????? ???? +??
? ?? ??? 4?? =5?
?? 4?? 4
+??
? ?? ??? 4?? =5?
?? 4?? 4
+?? ?.( 1)
Now for at x=0,
? 2.25 =
5
4
+ ??
? ?? =1
? Using the value of C in equ (1)
? ?? ?
?? 4?? ?? 4?? =
5
?? 4?? ?
?? 4?? 4
+
?? ?? 4??
? ?? =1.25+ ?? ?4??

25. A two-dimensional incompressible frictionless flow field is given by
??
. u xi yj =? If ? is the density
of the fluid, the expression for pressure gradient vector at any point in the flow field is given as
A.
( )
22
??
x i y j ??+ B.
( )
??
xi yj ??+
C.
( )
??
xi yj ? + D.
( )
??
xi yj ? ?
Ans: option (B)
Sol: Euler?s Equation of motion in 2D.

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

As there is no extra force acting on the fluid.
?? ?? ?????? ?? ?? =0
Now form the given expiration, u=x & v=y
?
????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????


?0+ ?? ?1+0+0=0?
1
?? ????
????

0+ 0+?? ?1+0=0?
1
?? ????
????

??????????? ???????? ?????? =
????
????
???+
????
????
???= ??? (?? ???+?? ??? )




14

26. A short shoe external drum brake is shown in the figure. The diameter of the brake drum is 500
mm. The dimensions a = 1000 mm, b = 500 mm and c = 200 mm. The coefficient of friction
between the drum and the shoe is 0.35. The force applied on the lever F = 100 N as shown in
the figure. The drum is rotating anti-clockwise. The braking torque on the drum is _______N.m
(round off to two decimal places).

Ans: 20.34
Sol:

Applying momentum about point O.

??? ?? =0

?? ??? +?? ?? ?? ??? ??? ?? ??? =0
?? ?? =232.55
Breaking Torque = ?? ?? ?? ?? ?? = 20.34

27. A uniform disc with radius r and a mass of m kg is mounted centrally on a horizontal axle of
negligible mass and length of 1.5r. The disc spins counter-clockwise about the axle with angular
speed ?, when viewed from the right-hand side bearing, Q. The axle precesses about a vertical
axis at
?p = ?/10 in the clockwise direction when viewed from above. Let RP and RQ (positive upwards)
be the resultant reaction forces due to the mass and the gyroscopic effect, at bearings P and Q,
respectively. Assuming ?
2
r = 300 m/s
2
and g = 10 m/s
2
, the ratio of the larger to the smaller
bearing reaction force (considering appropriate signs) is __________.



15


Ans: -3
Sol: ?????????????????? ???????????? (???? )=???? ?? ??

Using: ?? ?? =
?? 10
and ?? 2
?? =300

???? =
?? ?? 2
2
?? 2
10
=15????

Reaction at P and Q due to gravity

?? ?? 1
+?? ?? 1
=???? =10??
?? ?? 1
=5??
??? ?? 1
= 5 ??

Reaction at P and Q due to GC

Taking momentum about point p.
?? ?? 2
?1.5?? ?15???? =0
?? ?? 2
=
15????
1.5?? =10 ??
??? ?? 2
= ?10 ??
?????? ,
?? ?? ?? ?? =
?? ?? 1
+?? ?? 2

?? ?? 1
+?? ?? 2
=
5+10
5?10
= ?3

28. The figure shows a pouring arrangement for casting of a metal block. Frictional losses are
negligible. The acceleration due to gravity is 9.81 m/s
2
. The time (in s, round off to two decimal
places) to fill up the mold cavity (of size 40 cm ? 30 cm ? 15 cm) is ____________



16


Ans: 29.84
Sol: ???????? ?????????????? ???????? =
?? ?? ?? ?? .?2?? ?

???????? =
0.40?0.30?0.15
?? 0.02
2
4
.?2?9.81?0.20
28.94 ??????

29. The activities of a project, their duration and the precedence relationships are given in the table.
For example, in a precedence relationship ?X < Y, Z? means that X is predecessor of activities Y
and Z. The time to complete the activities along the critical path is ____________ weeks.
Activity Duration
(Weeks)
Precedence
Relationship
A 5 A < B, C, D
B 7 B < E, F, G
C 10 C < I
D 6 D < G
E 3 E < H
F 9 F < I
G 7 G < I
H 4 H < I
I 2 ---
A. 21 B. 25
C. 23 D. 17
Ans: option (C)
Sol:



17


30. The crank of a slider-crank mechanism rotates counter-clockwise (CCW) with a constant angular
velocity ?, as shown. Assume the length of the crank to be r.

Using exact analysis, the acceleration of the slider in the y-direction, at the instant shown, where
the crank is parallel to x-axis, is given by
A. -?
2
r B. 2?
2
r
C. ?
2
r D. -2?
2
r
Ans: option (C)
Sol:


Velocity of point A, ?? ?? = ?? ???
The radial acceleration of point A, ?? ????
=?? ?? 2

Since, the inclination of line AB is 45 degree, the acceleration of the point B will be equal to the
acceleration of point A. i.e. ?? ?? 2


31. A gas tungsten arc welding operation is performed using a current of 250 A and an arc voltage of
20 V at a welding speed of 5 mm/s. Assuming that the arc efficiency is 70%, the net heat input
per unit length of the weld will be ________ kJ/mm (round off to one decimal place).
Ans: 0.7
Sol: ???????? ?????????? =??Power
elec

???????? ?????????? =0.7?250?20=3500 ????????

???????? ?????????? per unit length=
3500
5
=700
?? ????

=0.7 KJ/mm

32. Water flows through two different pipes A and B of the same circular cross-section but at
different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both
the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes
is same, the ratio of volume flow rates QB/QA is ______ (round off to two decimal places).
A
O
B



18

Ans: 0.5
Sol: Frictional losses of pipe

??? ? ????
?? ?? ?? ? ????
(
?? ?? )
?? ?? ?????
?? ?? ?? ??

?
????
?????
=
?? ?? ?? ?? ?? ?? 2
?? ?? ?? ?? ?? ?? 2
;?? ??????? ?? =
64
????



?? ?? 2
?? ?? 2
=
?
????
?? ?? ?? ?? ??? ?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? ?? ??

?? ?? ?? ?? =
?? ?? ?? ?? =0.5

33. Consider two concentric circular cylinders of different materials M and N in contact with each
other at r = b, as shown below. The interface at r = b is frictionless. The composite cylinder
system is subjected to internal pressure P. Let
( )
,
MM
r
uu
?
and
( )
,
MM
rr ??
?? denote the radial and
tangential displacement and stress components, respectively, in material M Similarly,
( )
,
NN
r
uu
?

and
( )
,
NN
rr ??
?? denote the radial and tangential displacement and stress components, respectively,
in material N. The boundary conditions that need to be satisfied at the frictionless interface
between the two cylinders are :

A.
MN
rr
uu = and
MN
rr rr
?? = and
MN
uu
??
= and
MN
? ? ? ?
?? =
B.
MN
rr rr
?? = and
MN
? ? ? ?
?? = only
C.
MN
uu
??
= and
MN
? ? ? ?
?? = only
D.
MN
rr
uu = and
MN
rr rr
?? = only
Ans: option (D)
Sol:



19



Internal pressure causes the stress in radial as well as circumferential direction.

At r=b i.e. interference of the cylinder can be frictionless if Stress in radial direction must be equal.
Velocity in radial direction must be equal. (This condition will make the normal force Zero)
As radius of the cylinder increases due to inside pressure, there will be relative velocity between
the contact surfaces in the circumferential direction.

34. The binary phase diagram of metals P and Q is shown in the figure. An alloy X containing 60% P
and 40% Q (by weight) is cooled from liquid to solid state. The fractions of solid and liquid (in
weight percent) at 1250
o
C, respectively, will be

A. 22.2% and 77.8%
B. 68.0% and 32.0%
C. 77.8% and 22.2%
D. 32.0% and 68.0%
Ans: option (A)
Sol: Mass fraction of liquid =
?? ?? ??? 0
?? ?? ??? ??
?? ?? =
68?40
68?32
= 0.778=77.8%
?? ?? =1??? ?? =0.222=22.2%

35. The annual demand of valves per year in a company is 10,000 units. The current order quantity
is 400 valves per order. The holding cost is Rs. 24 per valve per year and the ordering cost is Rs.
400 per order. If the current order quantity is changed to Economic Order Quantity, then the
saving in the total cost of inventory per year will be Rs. __________ (round off to two decimal
places).
Ans: 943.59
Sol:
Annual Demand (D) = 10000 nos



20

Order Quantities (Q) = 400 / order
Holding cost (?? ?
)= 24 /valve/year
Ordering Cost (?? 0
) = RS 400 /order
?????? =
?? ?? ?? 0
+
?? 2
?? ?


?????? =
10000
400
400+
10000
2
24=14800

?????? ?=?2?? ?? 0
?? ?


?????? ?=13856.41

???????????? =14800?13856.41=???? .?????? .????

36. A slender uniform rigid bar of mass m is hinged at O and supported by two springs, with
stiffnesses 3k and k, and a damper with damping coefficient c, as shown in the figure. For the
system to be critically damped, the ratio c/?km should be

A. 4 B. 2
C. 4?7 D. 2?7
Ans: option (C)
Sol:
?? ?????
=?;?? ????? ???????????? ???? ???????????????????? ????????????

Suppose that we apply a external force downward at horizontal road at spring constant 3K and
leave it freely for to and fro motion.
Therefore, moment about point ?O?; ? ?? 0
=0
?? 0
??
? +?? (
3?? 4
?? )(
3?? 4
)+ 3?? (
?? 4
?? )(
?? 4
)+?? (
?? 4
?? ? )(
?? 4
)=0
?? 0
??
? +?? (
9?? 2
16
?? )+3?? (
?? 2
16
?? )+?? (
?? 2

16
?? ? )=0
Now, moment of inertia of rod about the center of the rod is ?? ?? =
?? ?? 2
12

And moment of inertia about the hinged point is ?? 0
=?? ?? +?? ?? 2
=
?? ?? 2
12
+?? (
?? 4
)
2
=
7
48
?? ?? 2

7
48
?? ?? 2
??
? +
1
16
?? ?? 2
?? ?+
12
16
?? ?? 2
?? =0

As we know that for critical dumping, the root of the quadratic equation should be real and equal.



21

? ?? 2
?4???? =0
(
1
16
?? ?? 2
)
2
?4 (
7
48
?? ?? 2
)(
12
16
?? ?? 2
)=0

?? =?4 (
7
1
?? )(
4
1
?? )=4?7????
?
?? ?????
= 4?7

37. The probability that a part manufactured by a company will be defective is 0.05. If 15 such parts
are selected randomly and inspected, then the probability that at least two parts will be
defective is __________ (round off to two decimal places).
Ans: 0.17
Sol: Total no. of parts = 15
P[defective(p)] = 0.05
P[non-defective(q)] = 1 ? 0.05 = 0.95
P[at least 2 defective] = 1 ? [P(no defective)+P(1 defective)]
Using the binomial distribution,
P[at least 2 defective] = 1 ? [
15
C0p
0
q
15
+
15
C1p
1
q
14
]= 1 ? [0.05
0
0.95
15
+ 15?0.05?0.95
14
] = 1 ?
[0.4639 + 0.3657] = 1 ? 0.8296 = 0.1704


38. A four bar mechanism is shown in the figure. The link numbers are mentioned near the links.
Input link 2 is rotating anti-clockwise with a constant angular speed ?2. Length of different links
are :

2 4 2
4
,
2.
OO O A L
AB O B L
==
==

The magnitude of the angular speed of the output link 4 is ?4 at the instant when link 2 makes
an angle of 90
o
with O2O4 as shown. The ratio
4
2
?
?
is __________ (round off to two decimal
places).

Ans: 0.79
Sol: Using Instantaneous center method



22


?? 24
?? 12
?? 2
= ?? 24
?? 41
?? 4

?? 24
?? 12
=?? tan75
?? (???????? ? ?? 12
?? 23
?? 24
)
?? 24
?? 41
=?? +?? tan75
??
?
?? 4
?? 2
=
?? 24
?? 12
?? 24
?? 41
=
?? tan75
?? ?? +?? tan75
??
=0.788

39. Two masses A and B having mass ma and mb, respectively, lying in the plane of the figure
shown, are rigidly attached to a shaft which revolves about an axis through O perpendicular to
the figure. The radii of rotation of the masses ma and mb are ra and rb, respectively. The angle
between lines OA and OB is 90
o
. If ma = 10 kg, mb = 20 kg, ra = 200 mm and rb = 400 mm,
then the balance mass to be placed at a radius of 200 mm is _________ kg (round off to two
decimal places).

Ans: 41.23
Sol:
Let the balance mass be m
? ?? ?? =?? ?? ?? ?? ?????? 0?+?? ?? ?? ?? ?????? 90?+???????????? =0 -----(1)
? ?? ?? =?? ?? ?? ?? ?????? 0?+?? ?? ?? ?? ?????? 90?+???????????? =0------ (2)
From (1), ???????????? =?[?? ?? ?? ?? ?????? 0?+?? ?? ?? ?? ?????? 90?]
Or, ???????????? =?[10?200]=?2000
From (2), ???????????? =?[?? ?? ?? ?? ?????? 0+?? ?? ?? ?? ?????? 90?]
Or, ???????????? =?[20?400]=?8000
Using ?(???????????? )
2
+(???????????? )
2
=???? =?2000
2
+8000
2
=8246.21
Now, since the radius of the balance mass is 200mm, therefore ?? =
8246.21
200
? =41.23????

40. A prismatic, straight elastic, cantilever beam is subjected to a linearly distributed transverse load
as shown below. If the beam length is L, Young?s modulus E, and area moment of inertia I, the
magnitude of the maximum deflection is



23


A.
4
60
qL
EI
B.
4
30
qL
EI

C.
4
10
qL
EI
D.
4
15
qL
EI

Ans: option (B)
Sol: The maximum deflection of the cantilever beam subjected to uniformly varying load (UVL) is given
by
4
30
qL
EI


41. Given a vector
( )
3 3 3
1
? ??
3
u y i x j z k = ? + + and ? n as the unit normal vector to the surface of the
hemisphere (x
2
+ y
2
+ z
2
= 1;z ?0), the value of integral
( )
? u n dS ? ? ?
?
evaluated on the
curved surface of the hemisphere S is
A. ? B.
3
?

C.
2
?
D.
2
?
?
Ans: option (C)
Sol: Hemisphere (x
2
+ y
2
+ z
2
= 1;z ?0)



To find the integration of the given expiration, it is easy if we are using the stoke?s theorem.
Surface integral will become line integral.
?(?? ???? )???????? = ???? ?????

Now, putting the value of ?? in the above equation.
?(?? ???? )???????? =?
1
3
(??? 3
???? +?? 3
???? +?? 3
???? )
??

=?
1
3
(??? 3
???? +?? 3
???? )
?? ??? =0 ???? ???????? ????????????



24

=? (?? 2
???????? +?? 2
???????? )
?? [using green theorem]
=?(?? 2
+?? 2
)????????
Now converting the above equation into polar coordinate
?? 2
+?? 2
=?? 2


? ? ?? 2
?? ???? ????
1
?? =0
=
2?? ?? =0
? (? ?? 3
????
1
?? =0
)????
2?? ?? =0
=
?? 2



42. The thickness of a sheet is reduced by rolling (without any change in width) using 600 mm
diameter rolls. Neglect elastic deflection of the rolls and assume that the coefficient of friction at
the roll-workpiece interface is 0.05. The sheet enters the rotating rolls unaided. If the initial
sheet thickness is 2 mm, the minimum possible final thickness that can be produced by this
process in a single pass is ________ mm (round off to two decimal places).
Ans: 1.25
Sol: Draft = (??? )
?????? =?? 2
?? =0.05
2
?300=0.75????
Hence, final thickness of the sheet = 2 ? 0.75 = 1.25mm

43. A ball of mass 3 kg moving with a velocity of 4 m/s undergoes a perfectly-elastic direct-central
impact with a stationary ball of mass m. After the impact is over, the kinetic energy of the 3 kg
ball is 6 J. The possible value (s) of m is/are
A. 6 kg only B. 1 kg, 9 kg
C. 1 kg only D. 1 kg, 6 kg
Ans: option (D)
Sol: Conservation of momentum gives m1u1 + m2u2 = m1v1 + m2v2
?? 1
=3???? , ?? 1
=4?? /?? , ?? 2
=?? ???? , ?? 2
=0
Substituting in the above equation,
3?4+?? ?0=3??? 1
+?? ??? 2

Or, 12=3?? 1
+?? ?? 2
-------(1)
For perfectly-elastic impact,
?? =
?? 2
??? 1
?? 1
??? 2
=1
Or, ?? 2
??? 1
=?? 1
??? 2
=4?? /?? ------- (2)
Conservation of kinetic energy gives
1
2
?? 1
?? 1
2
+
1
2
?? 2
?? 2
2
=
1
2
?? 1
?? 1
2
+
1
2
?? 2
?? 2
2

Or,
1
2
3(4)
2
+0=6+
1
2
?? 2
?? 2
2

Or, ?? ?? 2
2
=36 ---------(3)
From equation (2), ?? 1
=?? 2
?4
Substituting in equation (1),
12=3(?? 2
?4)+?? ?? 2

Or 12=3?? 2
?12+ ?? ?? 2

Or ?? 2
(3+?? )=24
Or ?? 2
=
24
3+??
Substituting in equation (3)



25

?? (
24
3+?? )
2
=36
576?? =36(3+?? )
2

?16?? =9+?? 2
+6??
?? 2
?10?? +9=0
On solving, we get
?? =1,9
Therefore, possible values of m are 1 kg and 9 kg.


44. The derivative of f(x) = cos(x) can be estimated using the approximation
( )
( ) ( )
'.
2
f x h f x h
fx
h
+ ? ?
= The percentage error is calculated as
Exact value-Approximate value
100.
Exact value
??
?
??
??
The percentage error in the derivative of f(x) at x = ?/6
radian, choosing h = 0.1 radian, is
A. > 1% and < 5%
B. < 0.1%
C. > 0.1% and < 1%
D. > 5%
Ans: option (C)
Sol: f(x) = cos(x)
? f?(x) = -sin(x) = ?sin(
?? 6
? )=?0.5 (exact value)
Approximate value = ( )
( ) ( )
'.
2
f x h f x h
fx
h
+ ? ?
=
?? ?
(?? )=
cos(?? +?)?cos?? ??
2?

cos(?? +?)=?????????????? ???????????????? ?
?????? (?? ??)=?????????????? ?+?????????????? ?
So,
?? ?
(?? )=
?????????????? ???????????????? ??[?????????????? ?+?????????????? ?]
2?

=
?2?????????????? ?
2?
=
??????????????? ?
?

Or, ?? ?
(?? )=
?sin(
?? 6
)?????? (0.1)
0.1
=
?0.5?0.0998
0.1
=?0.4992

So, percentage error =
?0.5?(?0.4992)
?0.5
?100=0.166


45. The aerodynamic drag on a sports car depends on its shape. The car has a drag coefficient of 0.1
with the windows and the roof closed. With the windows and the roof open, the drag coefficient
becomes 0.8. The car travels at 44 km/h with the windows and roof closed. For the same
amount of power needed to overcome the aerodynamic drag, the speed of the car with the
windows and roof open (round off to two decimal places), is ________km/h (the density of air
and frontal area may be assumed to be constant).
Ans: 22



26

Sol: The power needed to overcome the aerodynamic drag is given by ?? ?? ???
Where, ?? ?? is the drag force given by
?? ?? =
1
2
? ?? ?? ???? ?? 2

For the power to remain same in both the cases of windows closed and open, then
(?? ?? ??? )
?????????????? ???????????? =(?? ?? ??? )
?????????????? ????????
Or,
(
1
2
? ?? ?? ???? ?? 3
)
?????????????? ???????????? =(
1
2
? ?? ?? ???? ?? 3
)
?????????????? ????????
Or, 0.1?44
3
=0.8??? 3

Or V = 22 km/h


46. An idealized centrifugal pump (blade outer radius of 50 mm) consumes 2 kW power while
running at 3000 rpm. The entry of the liquid into the pump is axial and exit from the pump is
radial with respect to impeller. If the losses are neglected, then the mass flow rate of the liquid
through the pump is ________ kg/s (round off to two decimal places).
Ans: 8.106
Sol: Diameter = 2????????????? ???? ?????????? =2?50=100???? =0.1 ??
?? =
?????? 60
=
?? ?0.1?3000
60
=15.71 ?? /??????
Now, power = mass flow rate ? ?? 2

?2000=?? ? ?(15.71)
2

Or, ?? ? =8.106


47. The figure shows a heat engine (HE) working between two reservoirs. The amount of heat (Q2)
rejected by the heat engine is drawn by a heat pump (HP). The heat pump receives the entire
work output (W) of the heat engine. If temperatures.
T1 > T3 > T2, then the relation between the efficiency (?) of the heat engine and the coefficient
of performance (COP) of the heat pump is

A. COP = ? B. OCP = 1 + ?
C. COP = ?
-1
D. COP = ?
-1
-1
Ans: option (C)
Sol: For heat engine, ?? =
?? ?? 1

For Heat engine, ?????? =
?? 3
??
Energy balance for Heat engine gives ?? 2
=?? 1
???
And energy balance for Heat pump gives ?? 3
=?? 2
+?? =?? 1
??? +?? =?? 1

FirstRanker.com - FirstRanker's Choice



2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6




3

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of ?? =
8+6
2
=7

6. X is an online media provider. By offering unlimited and exclusive online content at attractive
prices for a loyalty membership, X is almost forcing its customers towards its loyalty
membership. If its loyalty membership continues to grow at its current rate, within the next
eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
A. Most households that subscribe to X?s loyalty membership discontinue watching cable
television
B. Non-members prefer to watch cable television
C. The X is cancelling accounts of non-members
D. Cable television operators don?t subscribe to X?s loyalty membership
Ans: option (A)
Sol: option A is the most appropriate solution

7. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased
by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.
A. 35.70 B. 10.00
C. 37.50 D. 25.00
Ans: option (C)
Sol: Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04??? =0.04??
And the fiscal deficit in 2016 = 0.05?1.1?? =0.055??
Increase in fiscal deficit = 0.055x ? 0.04x = 0.015x
So, the percentage increase in fiscal deficit =
0.015?? 0.04?? ?100=37.5%

8. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can
empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is
opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is
_________.
A. 16.50 B. 14.50
C. 15.50 D. 13.50
Ans: option (B)
Sol: 1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(
1
6
? ?
1
12
? )=
1
3
?
Tank filled by when Q and R works for another 6 hours = 6(
1
9
? ?
1
12
? )=
1
6
?
Total tank filled in these 10 hours =
1
3
? +
1
6
? =0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in
9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours




4

9. While teaching a creative writing class in India, I was surprised at receiving stories from the
students that were all set in distant places: in the American West with cowboys and in
Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave
the writers in the once-colonised countries the confidence to see the shabby lives around them
as worthy of being ?told?.
The writer of this passage is surprised by the creative writing assignments of his students,
because __________.
A. Some of the students had written about ice cubes and cowboys
B. None of the students had written about ice cubes and cowboys
C. Some of the students had written stories set in foreign places
D. None of the students had written stories set in India
Ans: option (C)
Sol: option C is the most appropriate solution

10. Mola is a digital platform for taxis in a city. It offers three types of rides ? Pool, Mini and Prime.
The Table below presents the number of rides for the past four months. The platform earns one
US dollar per ride. What is the percentage share of revenue contributed by Prime to the total
revenues of Mola, for the entire duration?
Type
Month
January February March April
Pool 170 320 215 190
Mini 110 220 180 70
Prime 75 180 120 90

A. 38.74 B. 23.97
C. 25.86 D. 16.24

Ans: option (B)
Sol: Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580
Revenue contributed by Prime = 75 + 180 + 120 +90 = 465
Total revenue of Mola = 895 + 580 + 465 = 1940
So, the percentage share =
465
1940
?100=23.97%

MECHANICAL ENGINEERING
1. A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by
application of pure bending moments at its ends. The Young?s modulus of the material of the
wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.
Ans: 50
Sol: Tensile stress
?? =
?? ?? ?? =
100?10
3
1
(
1
1000?2
)=50 ??????





5

2. In an electrical discharge machining process, the breakdown voltage across inter electrode gap
(IEG) is 200 V and the capacitance of the RC circuit is 50 ?F. The energy (in J) released per
spark across the IEG is __________
Ans: 1
Sol:
?? =
1
2
??????????????????????? ????????????? ?? 2

?? =0.5?50?10
?6
?200
2
=1 ??


3. If x is the mean of data 3, x, 2 and 4, then the mode is _________
Ans: 3
Sol: ?? =
3+?? +2+4
4

4??? =3+?? +2+4
4??? ??? =3+2+4=9
?? =3
Mode is 3. (Maximum repeated value)

4. The cold forming process in which a hardened tool is pressed against a workpiece (when there is
relative motion between the tool and the workpiece) to produce a roughened surface with a
regular pattern is
A. Strip rolling B. Knurling
C. Roll forming D. Chamfering
Ans: option (B)
Sol: We provide special pattern to prevent the relative motion between contact surface. This special
pattern is known as Knurling.


5. Endurance limit of a beam subjected to pure bending decreases with
A. increase in the surface roughness and increase in the size of the beam
B. decrease in the surface roughness and decrease in the size of the beam
C. decrease in the surface roughness and increase in the size of the beam
D. increase in the surface roughness and decrease in the size of the beam
Ans: option (A)
Sol: Formula for endurance limit
?? ?? =?? ?? ??? ?? ??? ?? ??? ?? ??? ?? ?

?? ???????
?? ?? ????????? ????????????
?? ?? ??????????????? ????????????
?? ?? ????????? ????????????
?? ?? ??????????????????????? ????????????
?? ?? ?
??????????????????? ?????????????? ?
Form above formula it is clear that the Endurance limit increases with increase in size,
surface, load, temp and endurance strength.







6

6. In matrix equation [A] {X} = {R}.
? ?
4 8 4 2
8 16 4 , 1
4 4 15 4
AX
? ? ? ?
?? ??
= ? = ??
??
????
??
??
?
? ? ? ?
and ? ?
32
16 .
64
R
??
??
=
??
??
??

One of the eigenvalues of matrix [A] is
A. 4 B. 15
C. 8 D. 16
Ans: option (D)
Sol: [A] {X} = {R}.

We know ???? = ???? ;?? ??????? ?? ??????????? ??????????

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}={
32
16
64
}

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}=16{
2
1
4
}

Hence, ?? =????

7. Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number
ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit.
The Reynolds number at the exit of the pipe is___________.
Ans: 500
Sol: Reynold?s Number
???? =
?? ?? ????
?? ??
Where: -
?? ??????????? ??????????????
?? ????
??????????????? ????????????????
?? ??????????????? ???? ????????
?? ? Dynamic viscosity of Fluid
?? ?? =(
?? ?? ????
?? ?? )=
(

?? (
?? ???????? ?? ???????? ) ?? ?? )


From above expiration, Reynold?s Number is independent of flow profile. Hence, Reynold?s
Number for parabolic flow profile is 500.

8. For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure
and temperature, respectively. As per Maxwell?s relations,
p
v
s
? ??
??
?
??
is equal to
A.
T
p
v
? ??
??
?
??
B.
p
s
T
? ??
??
?
??
C.
s
T
p
?? ?
??
?
??
D.
p
T
v
? ??
?
??
?
??

Ans: option (C)
Sol: From mathematical relation expiration



7

???? = ?????? +??????
? (
????
????
)
?? = (
????
????
)
??
???????? ?????????????? ????????????????
?? ?= ?????? +??????
? (
????
????
)
?? = (
????
????
)
??

9. Hardenability of steel is a measure of
A. the ability to harden when it is cold worked
B. the maximum hardness that can be obtained when it is austenitized and then quenched
C. the ability to retain its hardness when it is heated to elevated temperatures
D. the depth to which required hardening is obtained when it is austenitized and then quenched
Ans: option (D)
Sol: The depth to which required hardening is obtained when it is austenitized and then quenched.

10. The directional derivative of the function f(x, y) = x
2
+ y
2
along a line directed from (0, 0) to (1,
1), evaluated at the point x = 1, y = 1 is
A. 2 B. ?2
C. 4?2 D. 2?2
Ans: option (D)
Sol: Directional derivative of function along the line is the scalar value of derivative along the line. i.e.
we have to calculate value of derivative of function in the direction of given line vector
? ?? = ??? (
????
????
)+ ??? (
????
????
)
? ?? = 2???+ 2???
Now, calculating the value of ? ?? in 1???+ 1???
D.D of given function is (2???+ 2??? ) ?
(??? + ?? ?)
|??? + ?? ?|
= 2 ?2

11. A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is
A.
2 D
T
?
B.
T
D

C.
D
T
?
D.
D
T

Ans: option (C)
Sol: circular pitch =
????
??

12. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the
instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of
points P and R are VP and VR, in the x and y directions, respectively. The magnitude of the
angular velocity of the body is




8

A. /3
R
V B. /3
P
V
C. 2VR D. 2VP
Ans: option (C)
Sol: The given body is a rigid body; Hence the given body will not have any deformation, and the
possible motion is translation and angular motion. we know that the angular motion of the object is
always defined as the motion about the point. Hence, first we have to find a point parallel to both
velocity ?? ?? and ?? ?? .


? Angular velocity, ?? =
???????????????? ?????????????????????????? ????????????????
?? =
?? ?? ????
=
?? ?? ????

???? =
?3
2
????????? ???? ???????????????? =
?3
2
?1=
?3
2

???? =
1
2
????????? ???? ???????????????? =
1
2
?1=
1
2


?? =
2?? ?? ?3
=
2?? ?? 1


13. Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4
m. The view factor F12 is
A. 0.25 B. 0.0625
C. 1.0 D. 0.5
Ans: option (C)
Sol: ?? 12
=1

14. The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
A.
10
01
??
??
?
??
B.
01
10
? ??
??
?
??

C.
01
10
??
??
??
D.
10
01
???
??
??

Ans: option (C)
Sol: The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
01
10
??
??
??




S



9

15. The state of stress at a point in a component is represented by a Mohr?s circle of radius 100 MPa
centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the
normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same
point is ___________ MPa.
Ans: 80
Sol:


?? =?100
2
?60
2
=80 ??????

16. One-dimensional steady state heat conduction takes place through a solid whose cross-sectional
area varies linearly in the direction of heat transfer. Assume there is no heat generation in the
solid and the thermal conductivity of the material is constant and independent of temperature.
The temperature distribution in the solid is
A. Quadratic B. Exponential
C. Logarithmic D. Linear
Ans: option (C)
Sol: Let the given body cross-sectional area varies linearly, and heat is flowing from left to right.





If there is no heat generation,
?? ????
(?????
????
????
)=0

?
?? ????
(?????
????
????
)=?0

(?????
????
????
)=??

??? (?? 0
+?? ?? ?? )
????
????
=??
???? =
? ?? ????
?? (?? 0
+?? ?? ?? )


? ????
2
1
=?
? ?? ????
?? (?? 0
+?? ?? ?? )
2
1


?? 2
??? 1
= ?
?? ?? ln(
?? ?? ?? 2
+?? 0
?? ?? ?? 1
+?? 0
)



10

17. An analytic function f(z) of complex variable z = x + I y may be written as f(z) = u(x, y) + iv (x,
y). Then, u(x, y) and v(x, y) must satisfy
A.
uv
xy
??
=?
??
and
uv
yx
??
=
??

B.
uv
xy
??
=?
??
and
uv
yx
??
=?
??

C.
uv
xy
??
=
??
and
uv
yx
??
=?
??

D.
uv
xy
??
=
??
and
uv
yx
??
=
??

Ans: option (C)
Sol: If f(z) = u(x, y) + iv(x, y) is analytic function then it must satisfy the following relations.

????
????
=
????
????


????
????
=?
????
????


18. A thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is
losing heat to the surroundings by natural convection. The temperatures of the plate and the
surroundings, and the properties of the surrounding fluid, are constant. The relationship between
the average Nusselt and Rayleigh numbers is given as Nu = K Ra ?, where K is a constant. The
length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the
plate is increased to 16L keeping all other factors constant.

If the average heat transfer coefficient for the first plate is h1 and that for the second plate is h2,
the value of the ratio h1/h2 is____________.
Ans: 2
Sol: ?? ?? =?? (?? ?? )
1
4
We know that ?? ?? =?? ?? ?? ??
?? ?? =?? (?? ?? ?? ?? )
1
4
??? ?? ?(?? ?? )
1
4 ?(
???? ??? ?? 3
?? 2
)
1
4

??? ??? 3
4
???? ?
1
4
?
2
?
1
?(
?? 1
?? 2
)
1
4
=>
?
1
?
2
?(
?? 2
?? 1
)
1
4
=(16)
1
4=2



11


19. Which one of the following modifications of the simple ideal Rankine cycle increases the thermal
efficiency and reduces the moisture content of the steam at the turbine outlet?
A. Decreasing the condenser pressure.
B. Increasing the boiler pressure.
C. Decreasing the boiler pressure.
D. Increasing the turbine inlet temperature.
Ans: option (D)
Sol: Due to increase of the turbine inlet temperature, quality of the stream at outlet of the turbine
improves. Which increases the thermal efficiency and reduces the moisture content of the steam at the
turbine outlet.

20. Consider a linear rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of
100 MPa along the length direction. Assume plane stress conditions in the plane normal to the
thickness. The Young?s modulus E = 200 MPa and Poisson?s ratio v = 0.3 are given. The principal
strains in the plane of the sheet are
A. (0.5, 0.0) B. (0.35, -0.15)
C. (0.5, -0.5) D. (0.5, -0.15)
Ans: option (D)
Sol: ?
1
=
?? 1
?? ???
?? 2
?? =
100
200
?0.3?
0
200
=0.5

?
2
=
?? 2
?? ???
?? 1
?? =
0
200
?0.3?
100
200
=?0.15


21. The figure shows an idealized plane truss. If a horizontal force of 300 N is applied at point A,
then the magnitude of the force produced in member CD is ________N.

Ans: 0

Sol:



12



The momentum about the point A must be zero, because there is no deformation of any truss.
Hence, ?? ????
=0 [?? ????
is not passing through the point A]

22. The fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase
in
A. freezing range
B. surface tension
C. degree of superheat
D. viscosity
Ans: option (C)
Sol: Fluidity of molten metal of cast alloys increases with increase in degree of superheat.

23. The most common limit gage used for inspecting the hole diameter is
A. Ring gage B. Snap gage
C. Plug gage D. Master gage
Ans: option (C)
Sol: The most common limit gage used for inspecting the hole diameter is Plug gage.

24. The differential equation 45
dy
y
dx
+= is valid in the domain 0 ? x ? 1 with y(0) = 2.25. The
solution of the differential equation is
A. y = e
-4x
+ 1.25
B. y = e
4x
+ 5
C. y = e
4x
+ 1.25
D. y = e
-4x
+ 5
Ans: option (A)
Sol: The given equation is.



13

???? ???? +4?? =5
If Integration factor = ?? ?4????
=?? 4??
? ?? ????? =?5????? ???? +??
? ?? ??? 4?? =5?
?? 4?? 4
+??
? ?? ??? 4?? =5?
?? 4?? 4
+?? ?.( 1)
Now for at x=0,
? 2.25 =
5
4
+ ??
? ?? =1
? Using the value of C in equ (1)
? ?? ?
?? 4?? ?? 4?? =
5
?? 4?? ?
?? 4?? 4
+
?? ?? 4??
? ?? =1.25+ ?? ?4??

25. A two-dimensional incompressible frictionless flow field is given by
??
. u xi yj =? If ? is the density
of the fluid, the expression for pressure gradient vector at any point in the flow field is given as
A.
( )
22
??
x i y j ??+ B.
( )
??
xi yj ??+
C.
( )
??
xi yj ? + D.
( )
??
xi yj ? ?
Ans: option (B)
Sol: Euler?s Equation of motion in 2D.

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

As there is no extra force acting on the fluid.
?? ?? ?????? ?? ?? =0
Now form the given expiration, u=x & v=y
?
????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????


?0+ ?? ?1+0+0=0?
1
?? ????
????

0+ 0+?? ?1+0=0?
1
?? ????
????

??????????? ???????? ?????? =
????
????
???+
????
????
???= ??? (?? ???+?? ??? )




14

26. A short shoe external drum brake is shown in the figure. The diameter of the brake drum is 500
mm. The dimensions a = 1000 mm, b = 500 mm and c = 200 mm. The coefficient of friction
between the drum and the shoe is 0.35. The force applied on the lever F = 100 N as shown in
the figure. The drum is rotating anti-clockwise. The braking torque on the drum is _______N.m
(round off to two decimal places).

Ans: 20.34
Sol:

Applying momentum about point O.

??? ?? =0

?? ??? +?? ?? ?? ??? ??? ?? ??? =0
?? ?? =232.55
Breaking Torque = ?? ?? ?? ?? ?? = 20.34

27. A uniform disc with radius r and a mass of m kg is mounted centrally on a horizontal axle of
negligible mass and length of 1.5r. The disc spins counter-clockwise about the axle with angular
speed ?, when viewed from the right-hand side bearing, Q. The axle precesses about a vertical
axis at
?p = ?/10 in the clockwise direction when viewed from above. Let RP and RQ (positive upwards)
be the resultant reaction forces due to the mass and the gyroscopic effect, at bearings P and Q,
respectively. Assuming ?
2
r = 300 m/s
2
and g = 10 m/s
2
, the ratio of the larger to the smaller
bearing reaction force (considering appropriate signs) is __________.



15


Ans: -3
Sol: ?????????????????? ???????????? (???? )=???? ?? ??

Using: ?? ?? =
?? 10
and ?? 2
?? =300

???? =
?? ?? 2
2
?? 2
10
=15????

Reaction at P and Q due to gravity

?? ?? 1
+?? ?? 1
=???? =10??
?? ?? 1
=5??
??? ?? 1
= 5 ??

Reaction at P and Q due to GC

Taking momentum about point p.
?? ?? 2
?1.5?? ?15???? =0
?? ?? 2
=
15????
1.5?? =10 ??
??? ?? 2
= ?10 ??
?????? ,
?? ?? ?? ?? =
?? ?? 1
+?? ?? 2

?? ?? 1
+?? ?? 2
=
5+10
5?10
= ?3

28. The figure shows a pouring arrangement for casting of a metal block. Frictional losses are
negligible. The acceleration due to gravity is 9.81 m/s
2
. The time (in s, round off to two decimal
places) to fill up the mold cavity (of size 40 cm ? 30 cm ? 15 cm) is ____________



16


Ans: 29.84
Sol: ???????? ?????????????? ???????? =
?? ?? ?? ?? .?2?? ?

???????? =
0.40?0.30?0.15
?? 0.02
2
4
.?2?9.81?0.20
28.94 ??????

29. The activities of a project, their duration and the precedence relationships are given in the table.
For example, in a precedence relationship ?X < Y, Z? means that X is predecessor of activities Y
and Z. The time to complete the activities along the critical path is ____________ weeks.
Activity Duration
(Weeks)
Precedence
Relationship
A 5 A < B, C, D
B 7 B < E, F, G
C 10 C < I
D 6 D < G
E 3 E < H
F 9 F < I
G 7 G < I
H 4 H < I
I 2 ---
A. 21 B. 25
C. 23 D. 17
Ans: option (C)
Sol:



17


30. The crank of a slider-crank mechanism rotates counter-clockwise (CCW) with a constant angular
velocity ?, as shown. Assume the length of the crank to be r.

Using exact analysis, the acceleration of the slider in the y-direction, at the instant shown, where
the crank is parallel to x-axis, is given by
A. -?
2
r B. 2?
2
r
C. ?
2
r D. -2?
2
r
Ans: option (C)
Sol:


Velocity of point A, ?? ?? = ?? ???
The radial acceleration of point A, ?? ????
=?? ?? 2

Since, the inclination of line AB is 45 degree, the acceleration of the point B will be equal to the
acceleration of point A. i.e. ?? ?? 2


31. A gas tungsten arc welding operation is performed using a current of 250 A and an arc voltage of
20 V at a welding speed of 5 mm/s. Assuming that the arc efficiency is 70%, the net heat input
per unit length of the weld will be ________ kJ/mm (round off to one decimal place).
Ans: 0.7
Sol: ???????? ?????????? =??Power
elec

???????? ?????????? =0.7?250?20=3500 ????????

???????? ?????????? per unit length=
3500
5
=700
?? ????

=0.7 KJ/mm

32. Water flows through two different pipes A and B of the same circular cross-section but at
different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both
the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes
is same, the ratio of volume flow rates QB/QA is ______ (round off to two decimal places).
A
O
B



18

Ans: 0.5
Sol: Frictional losses of pipe

??? ? ????
?? ?? ?? ? ????
(
?? ?? )
?? ?? ?????
?? ?? ?? ??

?
????
?????
=
?? ?? ?? ?? ?? ?? 2
?? ?? ?? ?? ?? ?? 2
;?? ??????? ?? =
64
????



?? ?? 2
?? ?? 2
=
?
????
?? ?? ?? ?? ??? ?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? ?? ??

?? ?? ?? ?? =
?? ?? ?? ?? =0.5

33. Consider two concentric circular cylinders of different materials M and N in contact with each
other at r = b, as shown below. The interface at r = b is frictionless. The composite cylinder
system is subjected to internal pressure P. Let
( )
,
MM
r
uu
?
and
( )
,
MM
rr ??
?? denote the radial and
tangential displacement and stress components, respectively, in material M Similarly,
( )
,
NN
r
uu
?

and
( )
,
NN
rr ??
?? denote the radial and tangential displacement and stress components, respectively,
in material N. The boundary conditions that need to be satisfied at the frictionless interface
between the two cylinders are :

A.
MN
rr
uu = and
MN
rr rr
?? = and
MN
uu
??
= and
MN
? ? ? ?
?? =
B.
MN
rr rr
?? = and
MN
? ? ? ?
?? = only
C.
MN
uu
??
= and
MN
? ? ? ?
?? = only
D.
MN
rr
uu = and
MN
rr rr
?? = only
Ans: option (D)
Sol:



19



Internal pressure causes the stress in radial as well as circumferential direction.

At r=b i.e. interference of the cylinder can be frictionless if Stress in radial direction must be equal.
Velocity in radial direction must be equal. (This condition will make the normal force Zero)
As radius of the cylinder increases due to inside pressure, there will be relative velocity between
the contact surfaces in the circumferential direction.

34. The binary phase diagram of metals P and Q is shown in the figure. An alloy X containing 60% P
and 40% Q (by weight) is cooled from liquid to solid state. The fractions of solid and liquid (in
weight percent) at 1250
o
C, respectively, will be

A. 22.2% and 77.8%
B. 68.0% and 32.0%
C. 77.8% and 22.2%
D. 32.0% and 68.0%
Ans: option (A)
Sol: Mass fraction of liquid =
?? ?? ??? 0
?? ?? ??? ??
?? ?? =
68?40
68?32
= 0.778=77.8%
?? ?? =1??? ?? =0.222=22.2%

35. The annual demand of valves per year in a company is 10,000 units. The current order quantity
is 400 valves per order. The holding cost is Rs. 24 per valve per year and the ordering cost is Rs.
400 per order. If the current order quantity is changed to Economic Order Quantity, then the
saving in the total cost of inventory per year will be Rs. __________ (round off to two decimal
places).
Ans: 943.59
Sol:
Annual Demand (D) = 10000 nos



20

Order Quantities (Q) = 400 / order
Holding cost (?? ?
)= 24 /valve/year
Ordering Cost (?? 0
) = RS 400 /order
?????? =
?? ?? ?? 0
+
?? 2
?? ?


?????? =
10000
400
400+
10000
2
24=14800

?????? ?=?2?? ?? 0
?? ?


?????? ?=13856.41

???????????? =14800?13856.41=???? .?????? .????

36. A slender uniform rigid bar of mass m is hinged at O and supported by two springs, with
stiffnesses 3k and k, and a damper with damping coefficient c, as shown in the figure. For the
system to be critically damped, the ratio c/?km should be

A. 4 B. 2
C. 4?7 D. 2?7
Ans: option (C)
Sol:
?? ?????
=?;?? ????? ???????????? ???? ???????????????????? ????????????

Suppose that we apply a external force downward at horizontal road at spring constant 3K and
leave it freely for to and fro motion.
Therefore, moment about point ?O?; ? ?? 0
=0
?? 0
??
? +?? (
3?? 4
?? )(
3?? 4
)+ 3?? (
?? 4
?? )(
?? 4
)+?? (
?? 4
?? ? )(
?? 4
)=0
?? 0
??
? +?? (
9?? 2
16
?? )+3?? (
?? 2
16
?? )+?? (
?? 2

16
?? ? )=0
Now, moment of inertia of rod about the center of the rod is ?? ?? =
?? ?? 2
12

And moment of inertia about the hinged point is ?? 0
=?? ?? +?? ?? 2
=
?? ?? 2
12
+?? (
?? 4
)
2
=
7
48
?? ?? 2

7
48
?? ?? 2
??
? +
1
16
?? ?? 2
?? ?+
12
16
?? ?? 2
?? =0

As we know that for critical dumping, the root of the quadratic equation should be real and equal.



21

? ?? 2
?4???? =0
(
1
16
?? ?? 2
)
2
?4 (
7
48
?? ?? 2
)(
12
16
?? ?? 2
)=0

?? =?4 (
7
1
?? )(
4
1
?? )=4?7????
?
?? ?????
= 4?7

37. The probability that a part manufactured by a company will be defective is 0.05. If 15 such parts
are selected randomly and inspected, then the probability that at least two parts will be
defective is __________ (round off to two decimal places).
Ans: 0.17
Sol: Total no. of parts = 15
P[defective(p)] = 0.05
P[non-defective(q)] = 1 ? 0.05 = 0.95
P[at least 2 defective] = 1 ? [P(no defective)+P(1 defective)]
Using the binomial distribution,
P[at least 2 defective] = 1 ? [
15
C0p
0
q
15
+
15
C1p
1
q
14
]= 1 ? [0.05
0
0.95
15
+ 15?0.05?0.95
14
] = 1 ?
[0.4639 + 0.3657] = 1 ? 0.8296 = 0.1704


38. A four bar mechanism is shown in the figure. The link numbers are mentioned near the links.
Input link 2 is rotating anti-clockwise with a constant angular speed ?2. Length of different links
are :

2 4 2
4
,
2.
OO O A L
AB O B L
==
==

The magnitude of the angular speed of the output link 4 is ?4 at the instant when link 2 makes
an angle of 90
o
with O2O4 as shown. The ratio
4
2
?
?
is __________ (round off to two decimal
places).

Ans: 0.79
Sol: Using Instantaneous center method



22


?? 24
?? 12
?? 2
= ?? 24
?? 41
?? 4

?? 24
?? 12
=?? tan75
?? (???????? ? ?? 12
?? 23
?? 24
)
?? 24
?? 41
=?? +?? tan75
??
?
?? 4
?? 2
=
?? 24
?? 12
?? 24
?? 41
=
?? tan75
?? ?? +?? tan75
??
=0.788

39. Two masses A and B having mass ma and mb, respectively, lying in the plane of the figure
shown, are rigidly attached to a shaft which revolves about an axis through O perpendicular to
the figure. The radii of rotation of the masses ma and mb are ra and rb, respectively. The angle
between lines OA and OB is 90
o
. If ma = 10 kg, mb = 20 kg, ra = 200 mm and rb = 400 mm,
then the balance mass to be placed at a radius of 200 mm is _________ kg (round off to two
decimal places).

Ans: 41.23
Sol:
Let the balance mass be m
? ?? ?? =?? ?? ?? ?? ?????? 0?+?? ?? ?? ?? ?????? 90?+???????????? =0 -----(1)
? ?? ?? =?? ?? ?? ?? ?????? 0?+?? ?? ?? ?? ?????? 90?+???????????? =0------ (2)
From (1), ???????????? =?[?? ?? ?? ?? ?????? 0?+?? ?? ?? ?? ?????? 90?]
Or, ???????????? =?[10?200]=?2000
From (2), ???????????? =?[?? ?? ?? ?? ?????? 0+?? ?? ?? ?? ?????? 90?]
Or, ???????????? =?[20?400]=?8000
Using ?(???????????? )
2
+(???????????? )
2
=???? =?2000
2
+8000
2
=8246.21
Now, since the radius of the balance mass is 200mm, therefore ?? =
8246.21
200
? =41.23????

40. A prismatic, straight elastic, cantilever beam is subjected to a linearly distributed transverse load
as shown below. If the beam length is L, Young?s modulus E, and area moment of inertia I, the
magnitude of the maximum deflection is



23


A.
4
60
qL
EI
B.
4
30
qL
EI

C.
4
10
qL
EI
D.
4
15
qL
EI

Ans: option (B)
Sol: The maximum deflection of the cantilever beam subjected to uniformly varying load (UVL) is given
by
4
30
qL
EI


41. Given a vector
( )
3 3 3
1
? ??
3
u y i x j z k = ? + + and ? n as the unit normal vector to the surface of the
hemisphere (x
2
+ y
2
+ z
2
= 1;z ?0), the value of integral
( )
? u n dS ? ? ?
?
evaluated on the
curved surface of the hemisphere S is
A. ? B.
3
?

C.
2
?
D.
2
?
?
Ans: option (C)
Sol: Hemisphere (x
2
+ y
2
+ z
2
= 1;z ?0)



To find the integration of the given expiration, it is easy if we are using the stoke?s theorem.
Surface integral will become line integral.
?(?? ???? )???????? = ???? ?????

Now, putting the value of ?? in the above equation.
?(?? ???? )???????? =?
1
3
(??? 3
???? +?? 3
???? +?? 3
???? )
??

=?
1
3
(??? 3
???? +?? 3
???? )
?? ??? =0 ???? ???????? ????????????



24

=? (?? 2
???????? +?? 2
???????? )
?? [using green theorem]
=?(?? 2
+?? 2
)????????
Now converting the above equation into polar coordinate
?? 2
+?? 2
=?? 2


? ? ?? 2
?? ???? ????
1
?? =0
=
2?? ?? =0
? (? ?? 3
????
1
?? =0
)????
2?? ?? =0
=
?? 2



42. The thickness of a sheet is reduced by rolling (without any change in width) using 600 mm
diameter rolls. Neglect elastic deflection of the rolls and assume that the coefficient of friction at
the roll-workpiece interface is 0.05. The sheet enters the rotating rolls unaided. If the initial
sheet thickness is 2 mm, the minimum possible final thickness that can be produced by this
process in a single pass is ________ mm (round off to two decimal places).
Ans: 1.25
Sol: Draft = (??? )
?????? =?? 2
?? =0.05
2
?300=0.75????
Hence, final thickness of the sheet = 2 ? 0.75 = 1.25mm

43. A ball of mass 3 kg moving with a velocity of 4 m/s undergoes a perfectly-elastic direct-central
impact with a stationary ball of mass m. After the impact is over, the kinetic energy of the 3 kg
ball is 6 J. The possible value (s) of m is/are
A. 6 kg only B. 1 kg, 9 kg
C. 1 kg only D. 1 kg, 6 kg
Ans: option (D)
Sol: Conservation of momentum gives m1u1 + m2u2 = m1v1 + m2v2
?? 1
=3???? , ?? 1
=4?? /?? , ?? 2
=?? ???? , ?? 2
=0
Substituting in the above equation,
3?4+?? ?0=3??? 1
+?? ??? 2

Or, 12=3?? 1
+?? ?? 2
-------(1)
For perfectly-elastic impact,
?? =
?? 2
??? 1
?? 1
??? 2
=1
Or, ?? 2
??? 1
=?? 1
??? 2
=4?? /?? ------- (2)
Conservation of kinetic energy gives
1
2
?? 1
?? 1
2
+
1
2
?? 2
?? 2
2
=
1
2
?? 1
?? 1
2
+
1
2
?? 2
?? 2
2

Or,
1
2
3(4)
2
+0=6+
1
2
?? 2
?? 2
2

Or, ?? ?? 2
2
=36 ---------(3)
From equation (2), ?? 1
=?? 2
?4
Substituting in equation (1),
12=3(?? 2
?4)+?? ?? 2

Or 12=3?? 2
?12+ ?? ?? 2

Or ?? 2
(3+?? )=24
Or ?? 2
=
24
3+??
Substituting in equation (3)



25

?? (
24
3+?? )
2
=36
576?? =36(3+?? )
2

?16?? =9+?? 2
+6??
?? 2
?10?? +9=0
On solving, we get
?? =1,9
Therefore, possible values of m are 1 kg and 9 kg.


44. The derivative of f(x) = cos(x) can be estimated using the approximation
( )
( ) ( )
'.
2
f x h f x h
fx
h
+ ? ?
= The percentage error is calculated as
Exact value-Approximate value
100.
Exact value
??
?
??
??
The percentage error in the derivative of f(x) at x = ?/6
radian, choosing h = 0.1 radian, is
A. > 1% and < 5%
B. < 0.1%
C. > 0.1% and < 1%
D. > 5%
Ans: option (C)
Sol: f(x) = cos(x)
? f?(x) = -sin(x) = ?sin(
?? 6
? )=?0.5 (exact value)
Approximate value = ( )
( ) ( )
'.
2
f x h f x h
fx
h
+ ? ?
=
?? ?
(?? )=
cos(?? +?)?cos?? ??
2?

cos(?? +?)=?????????????? ???????????????? ?
?????? (?? ??)=?????????????? ?+?????????????? ?
So,
?? ?
(?? )=
?????????????? ???????????????? ??[?????????????? ?+?????????????? ?]
2?

=
?2?????????????? ?
2?
=
??????????????? ?
?

Or, ?? ?
(?? )=
?sin(
?? 6
)?????? (0.1)
0.1
=
?0.5?0.0998
0.1
=?0.4992

So, percentage error =
?0.5?(?0.4992)
?0.5
?100=0.166


45. The aerodynamic drag on a sports car depends on its shape. The car has a drag coefficient of 0.1
with the windows and the roof closed. With the windows and the roof open, the drag coefficient
becomes 0.8. The car travels at 44 km/h with the windows and roof closed. For the same
amount of power needed to overcome the aerodynamic drag, the speed of the car with the
windows and roof open (round off to two decimal places), is ________km/h (the density of air
and frontal area may be assumed to be constant).
Ans: 22



26

Sol: The power needed to overcome the aerodynamic drag is given by ?? ?? ???
Where, ?? ?? is the drag force given by
?? ?? =
1
2
? ?? ?? ???? ?? 2

For the power to remain same in both the cases of windows closed and open, then
(?? ?? ??? )
?????????????? ???????????? =(?? ?? ??? )
?????????????? ????????
Or,
(
1
2
? ?? ?? ???? ?? 3
)
?????????????? ???????????? =(
1
2
? ?? ?? ???? ?? 3
)
?????????????? ????????
Or, 0.1?44
3
=0.8??? 3

Or V = 22 km/h


46. An idealized centrifugal pump (blade outer radius of 50 mm) consumes 2 kW power while
running at 3000 rpm. The entry of the liquid into the pump is axial and exit from the pump is
radial with respect to impeller. If the losses are neglected, then the mass flow rate of the liquid
through the pump is ________ kg/s (round off to two decimal places).
Ans: 8.106
Sol: Diameter = 2????????????? ???? ?????????? =2?50=100???? =0.1 ??
?? =
?????? 60
=
?? ?0.1?3000
60
=15.71 ?? /??????
Now, power = mass flow rate ? ?? 2

?2000=?? ? ?(15.71)
2

Or, ?? ? =8.106


47. The figure shows a heat engine (HE) working between two reservoirs. The amount of heat (Q2)
rejected by the heat engine is drawn by a heat pump (HP). The heat pump receives the entire
work output (W) of the heat engine. If temperatures.
T1 > T3 > T2, then the relation between the efficiency (?) of the heat engine and the coefficient
of performance (COP) of the heat pump is

A. COP = ? B. OCP = 1 + ?
C. COP = ?
-1
D. COP = ?
-1
-1
Ans: option (C)
Sol: For heat engine, ?? =
?? ?? 1

For Heat engine, ?????? =
?? 3
??
Energy balance for Heat engine gives ?? 2
=?? 1
???
And energy balance for Heat pump gives ?? 3
=?? 2
+?? =?? 1
??? +?? =?? 1




27

Hence, ?????? =
?? 1
?? =
1
?? =?? ?1


48. Three sets of parallel plates LM, NR and PQ are given in Figures 1, 2 and 3. The view factor F U is
defined as the fraction of radiation leaving plate I that is intercepted by plate J. Assume that the
values of FLM and FNR are 0.8 and 0.4, respectively. The value of FPQ (round off to one decimal
place) is ___________.

Ans: 0.6
Sol:
?? ????
=?? ????
+
?? ????
??? ????
?? =?? .?? +
?? .?? ??? .?? ?? =?? .??


49. Hot and cold fluids enter a parallel flow double tube heat exchanger at 100
o
C and 15
o
C,
respectively. The heat capacity rates of hot and cold fluids are Ch = 2000 W/K and Cc = 1200
W/K, respectively. If the outlet temperature of the cold fluid is 45
o
C, the log mean temperature
difference (LMTD) of the heat exchanger is ________ K (round off to two decimal places).
Ans: option ()
Sol: Given data
?? ?
?? =100?, ?? ?? ?? =15?, ?? ?? ?? =45?
?? ?
=2000?? /?? , ?? ?? =1200?? /??
Using the energy balance equation for the heat exchanger
?? ?
(?? ?
?? ??? ?
?? )=?? ?? (?? ?? ?? ??? ?? ?? )
?2000(100??? ?
?? )=1200(45?15)
??? ?
?? =82?

??? ?? =?? ?
?? ??? ?? ?? =100?15=85?
??? ?? =?? ?
?? ??? ?? ?? =82?45=37?
???????? =
??? ?? ???? ?? ln
??? ?? ??? ?? =
85?37
ln
85
37
=57.71?


FirstRanker.com - FirstRanker's Choice



2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6




3

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of ?? =
8+6
2
=7

6. X is an online media provider. By offering unlimited and exclusive online content at attractive
prices for a loyalty membership, X is almost forcing its customers towards its loyalty
membership. If its loyalty membership continues to grow at its current rate, within the next
eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
A. Most households that subscribe to X?s loyalty membership discontinue watching cable
television
B. Non-members prefer to watch cable television
C. The X is cancelling accounts of non-members
D. Cable television operators don?t subscribe to X?s loyalty membership
Ans: option (A)
Sol: option A is the most appropriate solution

7. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased
by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.
A. 35.70 B. 10.00
C. 37.50 D. 25.00
Ans: option (C)
Sol: Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04??? =0.04??
And the fiscal deficit in 2016 = 0.05?1.1?? =0.055??
Increase in fiscal deficit = 0.055x ? 0.04x = 0.015x
So, the percentage increase in fiscal deficit =
0.015?? 0.04?? ?100=37.5%

8. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can
empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is
opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is
_________.
A. 16.50 B. 14.50
C. 15.50 D. 13.50
Ans: option (B)
Sol: 1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(
1
6
? ?
1
12
? )=
1
3
?
Tank filled by when Q and R works for another 6 hours = 6(
1
9
? ?
1
12
? )=
1
6
?
Total tank filled in these 10 hours =
1
3
? +
1
6
? =0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in
9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours




4

9. While teaching a creative writing class in India, I was surprised at receiving stories from the
students that were all set in distant places: in the American West with cowboys and in
Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave
the writers in the once-colonised countries the confidence to see the shabby lives around them
as worthy of being ?told?.
The writer of this passage is surprised by the creative writing assignments of his students,
because __________.
A. Some of the students had written about ice cubes and cowboys
B. None of the students had written about ice cubes and cowboys
C. Some of the students had written stories set in foreign places
D. None of the students had written stories set in India
Ans: option (C)
Sol: option C is the most appropriate solution

10. Mola is a digital platform for taxis in a city. It offers three types of rides ? Pool, Mini and Prime.
The Table below presents the number of rides for the past four months. The platform earns one
US dollar per ride. What is the percentage share of revenue contributed by Prime to the total
revenues of Mola, for the entire duration?
Type
Month
January February March April
Pool 170 320 215 190
Mini 110 220 180 70
Prime 75 180 120 90

A. 38.74 B. 23.97
C. 25.86 D. 16.24

Ans: option (B)
Sol: Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580
Revenue contributed by Prime = 75 + 180 + 120 +90 = 465
Total revenue of Mola = 895 + 580 + 465 = 1940
So, the percentage share =
465
1940
?100=23.97%

MECHANICAL ENGINEERING
1. A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by
application of pure bending moments at its ends. The Young?s modulus of the material of the
wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.
Ans: 50
Sol: Tensile stress
?? =
?? ?? ?? =
100?10
3
1
(
1
1000?2
)=50 ??????





5

2. In an electrical discharge machining process, the breakdown voltage across inter electrode gap
(IEG) is 200 V and the capacitance of the RC circuit is 50 ?F. The energy (in J) released per
spark across the IEG is __________
Ans: 1
Sol:
?? =
1
2
??????????????????????? ????????????? ?? 2

?? =0.5?50?10
?6
?200
2
=1 ??


3. If x is the mean of data 3, x, 2 and 4, then the mode is _________
Ans: 3
Sol: ?? =
3+?? +2+4
4

4??? =3+?? +2+4
4??? ??? =3+2+4=9
?? =3
Mode is 3. (Maximum repeated value)

4. The cold forming process in which a hardened tool is pressed against a workpiece (when there is
relative motion between the tool and the workpiece) to produce a roughened surface with a
regular pattern is
A. Strip rolling B. Knurling
C. Roll forming D. Chamfering
Ans: option (B)
Sol: We provide special pattern to prevent the relative motion between contact surface. This special
pattern is known as Knurling.


5. Endurance limit of a beam subjected to pure bending decreases with
A. increase in the surface roughness and increase in the size of the beam
B. decrease in the surface roughness and decrease in the size of the beam
C. decrease in the surface roughness and increase in the size of the beam
D. increase in the surface roughness and decrease in the size of the beam
Ans: option (A)
Sol: Formula for endurance limit
?? ?? =?? ?? ??? ?? ??? ?? ??? ?? ??? ?? ?

?? ???????
?? ?? ????????? ????????????
?? ?? ??????????????? ????????????
?? ?? ????????? ????????????
?? ?? ??????????????????????? ????????????
?? ?? ?
??????????????????? ?????????????? ?
Form above formula it is clear that the Endurance limit increases with increase in size,
surface, load, temp and endurance strength.







6

6. In matrix equation [A] {X} = {R}.
? ?
4 8 4 2
8 16 4 , 1
4 4 15 4
AX
? ? ? ?
?? ??
= ? = ??
??
????
??
??
?
? ? ? ?
and ? ?
32
16 .
64
R
??
??
=
??
??
??

One of the eigenvalues of matrix [A] is
A. 4 B. 15
C. 8 D. 16
Ans: option (D)
Sol: [A] {X} = {R}.

We know ???? = ???? ;?? ??????? ?? ??????????? ??????????

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}={
32
16
64
}

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}=16{
2
1
4
}

Hence, ?? =????

7. Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number
ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit.
The Reynolds number at the exit of the pipe is___________.
Ans: 500
Sol: Reynold?s Number
???? =
?? ?? ????
?? ??
Where: -
?? ??????????? ??????????????
?? ????
??????????????? ????????????????
?? ??????????????? ???? ????????
?? ? Dynamic viscosity of Fluid
?? ?? =(
?? ?? ????
?? ?? )=
(

?? (
?? ???????? ?? ???????? ) ?? ?? )


From above expiration, Reynold?s Number is independent of flow profile. Hence, Reynold?s
Number for parabolic flow profile is 500.

8. For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure
and temperature, respectively. As per Maxwell?s relations,
p
v
s
? ??
??
?
??
is equal to
A.
T
p
v
? ??
??
?
??
B.
p
s
T
? ??
??
?
??
C.
s
T
p
?? ?
??
?
??
D.
p
T
v
? ??
?
??
?
??

Ans: option (C)
Sol: From mathematical relation expiration



7

???? = ?????? +??????
? (
????
????
)
?? = (
????
????
)
??
???????? ?????????????? ????????????????
?? ?= ?????? +??????
? (
????
????
)
?? = (
????
????
)
??

9. Hardenability of steel is a measure of
A. the ability to harden when it is cold worked
B. the maximum hardness that can be obtained when it is austenitized and then quenched
C. the ability to retain its hardness when it is heated to elevated temperatures
D. the depth to which required hardening is obtained when it is austenitized and then quenched
Ans: option (D)
Sol: The depth to which required hardening is obtained when it is austenitized and then quenched.

10. The directional derivative of the function f(x, y) = x
2
+ y
2
along a line directed from (0, 0) to (1,
1), evaluated at the point x = 1, y = 1 is
A. 2 B. ?2
C. 4?2 D. 2?2
Ans: option (D)
Sol: Directional derivative of function along the line is the scalar value of derivative along the line. i.e.
we have to calculate value of derivative of function in the direction of given line vector
? ?? = ??? (
????
????
)+ ??? (
????
????
)
? ?? = 2???+ 2???
Now, calculating the value of ? ?? in 1???+ 1???
D.D of given function is (2???+ 2??? ) ?
(??? + ?? ?)
|??? + ?? ?|
= 2 ?2

11. A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is
A.
2 D
T
?
B.
T
D

C.
D
T
?
D.
D
T

Ans: option (C)
Sol: circular pitch =
????
??

12. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the
instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of
points P and R are VP and VR, in the x and y directions, respectively. The magnitude of the
angular velocity of the body is




8

A. /3
R
V B. /3
P
V
C. 2VR D. 2VP
Ans: option (C)
Sol: The given body is a rigid body; Hence the given body will not have any deformation, and the
possible motion is translation and angular motion. we know that the angular motion of the object is
always defined as the motion about the point. Hence, first we have to find a point parallel to both
velocity ?? ?? and ?? ?? .


? Angular velocity, ?? =
???????????????? ?????????????????????????? ????????????????
?? =
?? ?? ????
=
?? ?? ????

???? =
?3
2
????????? ???? ???????????????? =
?3
2
?1=
?3
2

???? =
1
2
????????? ???? ???????????????? =
1
2
?1=
1
2


?? =
2?? ?? ?3
=
2?? ?? 1


13. Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4
m. The view factor F12 is
A. 0.25 B. 0.0625
C. 1.0 D. 0.5
Ans: option (C)
Sol: ?? 12
=1

14. The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
A.
10
01
??
??
?
??
B.
01
10
? ??
??
?
??

C.
01
10
??
??
??
D.
10
01
???
??
??

Ans: option (C)
Sol: The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
01
10
??
??
??




S



9

15. The state of stress at a point in a component is represented by a Mohr?s circle of radius 100 MPa
centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the
normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same
point is ___________ MPa.
Ans: 80
Sol:


?? =?100
2
?60
2
=80 ??????

16. One-dimensional steady state heat conduction takes place through a solid whose cross-sectional
area varies linearly in the direction of heat transfer. Assume there is no heat generation in the
solid and the thermal conductivity of the material is constant and independent of temperature.
The temperature distribution in the solid is
A. Quadratic B. Exponential
C. Logarithmic D. Linear
Ans: option (C)
Sol: Let the given body cross-sectional area varies linearly, and heat is flowing from left to right.





If there is no heat generation,
?? ????
(?????
????
????
)=0

?
?? ????
(?????
????
????
)=?0

(?????
????
????
)=??

??? (?? 0
+?? ?? ?? )
????
????
=??
???? =
? ?? ????
?? (?? 0
+?? ?? ?? )


? ????
2
1
=?
? ?? ????
?? (?? 0
+?? ?? ?? )
2
1


?? 2
??? 1
= ?
?? ?? ln(
?? ?? ?? 2
+?? 0
?? ?? ?? 1
+?? 0
)



10

17. An analytic function f(z) of complex variable z = x + I y may be written as f(z) = u(x, y) + iv (x,
y). Then, u(x, y) and v(x, y) must satisfy
A.
uv
xy
??
=?
??
and
uv
yx
??
=
??

B.
uv
xy
??
=?
??
and
uv
yx
??
=?
??

C.
uv
xy
??
=
??
and
uv
yx
??
=?
??

D.
uv
xy
??
=
??
and
uv
yx
??
=
??

Ans: option (C)
Sol: If f(z) = u(x, y) + iv(x, y) is analytic function then it must satisfy the following relations.

????
????
=
????
????


????
????
=?
????
????


18. A thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is
losing heat to the surroundings by natural convection. The temperatures of the plate and the
surroundings, and the properties of the surrounding fluid, are constant. The relationship between
the average Nusselt and Rayleigh numbers is given as Nu = K Ra ?, where K is a constant. The
length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the
plate is increased to 16L keeping all other factors constant.

If the average heat transfer coefficient for the first plate is h1 and that for the second plate is h2,
the value of the ratio h1/h2 is____________.
Ans: 2
Sol: ?? ?? =?? (?? ?? )
1
4
We know that ?? ?? =?? ?? ?? ??
?? ?? =?? (?? ?? ?? ?? )
1
4
??? ?? ?(?? ?? )
1
4 ?(
???? ??? ?? 3
?? 2
)
1
4

??? ??? 3
4
???? ?
1
4
?
2
?
1
?(
?? 1
?? 2
)
1
4
=>
?
1
?
2
?(
?? 2
?? 1
)
1
4
=(16)
1
4=2



11


19. Which one of the following modifications of the simple ideal Rankine cycle increases the thermal
efficiency and reduces the moisture content of the steam at the turbine outlet?
A. Decreasing the condenser pressure.
B. Increasing the boiler pressure.
C. Decreasing the boiler pressure.
D. Increasing the turbine inlet temperature.
Ans: option (D)
Sol: Due to increase of the turbine inlet temperature, quality of the stream at outlet of the turbine
improves. Which increases the thermal efficiency and reduces the moisture content of the steam at the
turbine outlet.

20. Consider a linear rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of
100 MPa along the length direction. Assume plane stress conditions in the plane normal to the
thickness. The Young?s modulus E = 200 MPa and Poisson?s ratio v = 0.3 are given. The principal
strains in the plane of the sheet are
A. (0.5, 0.0) B. (0.35, -0.15)
C. (0.5, -0.5) D. (0.5, -0.15)
Ans: option (D)
Sol: ?
1
=
?? 1
?? ???
?? 2
?? =
100
200
?0.3?
0
200
=0.5

?
2
=
?? 2
?? ???
?? 1
?? =
0
200
?0.3?
100
200
=?0.15


21. The figure shows an idealized plane truss. If a horizontal force of 300 N is applied at point A,
then the magnitude of the force produced in member CD is ________N.

Ans: 0

Sol:



12



The momentum about the point A must be zero, because there is no deformation of any truss.
Hence, ?? ????
=0 [?? ????
is not passing through the point A]

22. The fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase
in
A. freezing range
B. surface tension
C. degree of superheat
D. viscosity
Ans: option (C)
Sol: Fluidity of molten metal of cast alloys increases with increase in degree of superheat.

23. The most common limit gage used for inspecting the hole diameter is
A. Ring gage B. Snap gage
C. Plug gage D. Master gage
Ans: option (C)
Sol: The most common limit gage used for inspecting the hole diameter is Plug gage.

24. The differential equation 45
dy
y
dx
+= is valid in the domain 0 ? x ? 1 with y(0) = 2.25. The
solution of the differential equation is
A. y = e
-4x
+ 1.25
B. y = e
4x
+ 5
C. y = e
4x
+ 1.25
D. y = e
-4x
+ 5
Ans: option (A)
Sol: The given equation is.



13

???? ???? +4?? =5
If Integration factor = ?? ?4????
=?? 4??
? ?? ????? =?5????? ???? +??
? ?? ??? 4?? =5?
?? 4?? 4
+??
? ?? ??? 4?? =5?
?? 4?? 4
+?? ?.( 1)
Now for at x=0,
? 2.25 =
5
4
+ ??
? ?? =1
? Using the value of C in equ (1)
? ?? ?
?? 4?? ?? 4?? =
5
?? 4?? ?
?? 4?? 4
+
?? ?? 4??
? ?? =1.25+ ?? ?4??

25. A two-dimensional incompressible frictionless flow field is given by
??
. u xi yj =? If ? is the density
of the fluid, the expression for pressure gradient vector at any point in the flow field is given as
A.
( )
22
??
x i y j ??+ B.
( )
??
xi yj ??+
C.
( )
??
xi yj ? + D.
( )
??
xi yj ? ?
Ans: option (B)
Sol: Euler?s Equation of motion in 2D.

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

As there is no extra force acting on the fluid.
?? ?? ?????? ?? ?? =0
Now form the given expiration, u=x & v=y
?
????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????


?0+ ?? ?1+0+0=0?
1
?? ????
????

0+ 0+?? ?1+0=0?
1
?? ????
????

??????????? ???????? ?????? =
????
????
???+
????
????
???= ??? (?? ???+?? ??? )




14

26. A short shoe external drum brake is shown in the figure. The diameter of the brake drum is 500
mm. The dimensions a = 1000 mm, b = 500 mm and c = 200 mm. The coefficient of friction
between the drum and the shoe is 0.35. The force applied on the lever F = 100 N as shown in
the figure. The drum is rotating anti-clockwise. The braking torque on the drum is _______N.m
(round off to two decimal places).

Ans: 20.34
Sol:

Applying momentum about point O.

??? ?? =0

?? ??? +?? ?? ?? ??? ??? ?? ??? =0
?? ?? =232.55
Breaking Torque = ?? ?? ?? ?? ?? = 20.34

27. A uniform disc with radius r and a mass of m kg is mounted centrally on a horizontal axle of
negligible mass and length of 1.5r. The disc spins counter-clockwise about the axle with angular
speed ?, when viewed from the right-hand side bearing, Q. The axle precesses about a vertical
axis at
?p = ?/10 in the clockwise direction when viewed from above. Let RP and RQ (positive upwards)
be the resultant reaction forces due to the mass and the gyroscopic effect, at bearings P and Q,
respectively. Assuming ?
2
r = 300 m/s
2
and g = 10 m/s
2
, the ratio of the larger to the smaller
bearing reaction force (considering appropriate signs) is __________.



15


Ans: -3
Sol: ?????????????????? ???????????? (???? )=???? ?? ??

Using: ?? ?? =
?? 10
and ?? 2
?? =300

???? =
?? ?? 2
2
?? 2
10
=15????

Reaction at P and Q due to gravity

?? ?? 1
+?? ?? 1
=???? =10??
?? ?? 1
=5??
??? ?? 1
= 5 ??

Reaction at P and Q due to GC

Taking momentum about point p.
?? ?? 2
?1.5?? ?15???? =0
?? ?? 2
=
15????
1.5?? =10 ??
??? ?? 2
= ?10 ??
?????? ,
?? ?? ?? ?? =
?? ?? 1
+?? ?? 2

?? ?? 1
+?? ?? 2
=
5+10
5?10
= ?3

28. The figure shows a pouring arrangement for casting of a metal block. Frictional losses are
negligible. The acceleration due to gravity is 9.81 m/s
2
. The time (in s, round off to two decimal
places) to fill up the mold cavity (of size 40 cm ? 30 cm ? 15 cm) is ____________



16


Ans: 29.84
Sol: ???????? ?????????????? ???????? =
?? ?? ?? ?? .?2?? ?

???????? =
0.40?0.30?0.15
?? 0.02
2
4
.?2?9.81?0.20
28.94 ??????

29. The activities of a project, their duration and the precedence relationships are given in the table.
For example, in a precedence relationship ?X < Y, Z? means that X is predecessor of activities Y
and Z. The time to complete the activities along the critical path is ____________ weeks.
Activity Duration
(Weeks)
Precedence
Relationship
A 5 A < B, C, D
B 7 B < E, F, G
C 10 C < I
D 6 D < G
E 3 E < H
F 9 F < I
G 7 G < I
H 4 H < I
I 2 ---
A. 21 B. 25
C. 23 D. 17
Ans: option (C)
Sol:



17


30. The crank of a slider-crank mechanism rotates counter-clockwise (CCW) with a constant angular
velocity ?, as shown. Assume the length of the crank to be r.

Using exact analysis, the acceleration of the slider in the y-direction, at the instant shown, where
the crank is parallel to x-axis, is given by
A. -?
2
r B. 2?
2
r
C. ?
2
r D. -2?
2
r
Ans: option (C)
Sol:


Velocity of point A, ?? ?? = ?? ???
The radial acceleration of point A, ?? ????
=?? ?? 2

Since, the inclination of line AB is 45 degree, the acceleration of the point B will be equal to the
acceleration of point A. i.e. ?? ?? 2


31. A gas tungsten arc welding operation is performed using a current of 250 A and an arc voltage of
20 V at a welding speed of 5 mm/s. Assuming that the arc efficiency is 70%, the net heat input
per unit length of the weld will be ________ kJ/mm (round off to one decimal place).
Ans: 0.7
Sol: ???????? ?????????? =??Power
elec

???????? ?????????? =0.7?250?20=3500 ????????

???????? ?????????? per unit length=
3500
5
=700
?? ????

=0.7 KJ/mm

32. Water flows through two different pipes A and B of the same circular cross-section but at
different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both
the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes
is same, the ratio of volume flow rates QB/QA is ______ (round off to two decimal places).
A
O
B



18

Ans: 0.5
Sol: Frictional losses of pipe

??? ? ????
?? ?? ?? ? ????
(
?? ?? )
?? ?? ?????
?? ?? ?? ??

?
????
?????
=
?? ?? ?? ?? ?? ?? 2
?? ?? ?? ?? ?? ?? 2
;?? ??????? ?? =
64
????



?? ?? 2
?? ?? 2
=
?
????
?? ?? ?? ?? ??? ?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? ?? ??

?? ?? ?? ?? =
?? ?? ?? ?? =0.5

33. Consider two concentric circular cylinders of different materials M and N in contact with each
other at r = b, as shown below. The interface at r = b is frictionless. The composite cylinder
system is subjected to internal pressure P. Let
( )
,
MM
r
uu
?
and
( )
,
MM
rr ??
?? denote the radial and
tangential displacement and stress components, respectively, in material M Similarly,
( )
,
NN
r
uu
?

and
( )
,
NN
rr ??
?? denote the radial and tangential displacement and stress components, respectively,
in material N. The boundary conditions that need to be satisfied at the frictionless interface
between the two cylinders are :

A.
MN
rr
uu = and
MN
rr rr
?? = and
MN
uu
??
= and
MN
? ? ? ?
?? =
B.
MN
rr rr
?? = and
MN
? ? ? ?
?? = only
C.
MN
uu
??
= and
MN
? ? ? ?
?? = only
D.
MN
rr
uu = and
MN
rr rr
?? = only
Ans: option (D)
Sol:



19



Internal pressure causes the stress in radial as well as circumferential direction.

At r=b i.e. interference of the cylinder can be frictionless if Stress in radial direction must be equal.
Velocity in radial direction must be equal. (This condition will make the normal force Zero)
As radius of the cylinder increases due to inside pressure, there will be relative velocity between
the contact surfaces in the circumferential direction.

34. The binary phase diagram of metals P and Q is shown in the figure. An alloy X containing 60% P
and 40% Q (by weight) is cooled from liquid to solid state. The fractions of solid and liquid (in
weight percent) at 1250
o
C, respectively, will be

A. 22.2% and 77.8%
B. 68.0% and 32.0%
C. 77.8% and 22.2%
D. 32.0% and 68.0%
Ans: option (A)
Sol: Mass fraction of liquid =
?? ?? ??? 0
?? ?? ??? ??
?? ?? =
68?40
68?32
= 0.778=77.8%
?? ?? =1??? ?? =0.222=22.2%

35. The annual demand of valves per year in a company is 10,000 units. The current order quantity
is 400 valves per order. The holding cost is Rs. 24 per valve per year and the ordering cost is Rs.
400 per order. If the current order quantity is changed to Economic Order Quantity, then the
saving in the total cost of inventory per year will be Rs. __________ (round off to two decimal
places).
Ans: 943.59
Sol:
Annual Demand (D) = 10000 nos



20

Order Quantities (Q) = 400 / order
Holding cost (?? ?
)= 24 /valve/year
Ordering Cost (?? 0
) = RS 400 /order
?????? =
?? ?? ?? 0
+
?? 2
?? ?


?????? =
10000
400
400+
10000
2
24=14800

?????? ?=?2?? ?? 0
?? ?


?????? ?=13856.41

???????????? =14800?13856.41=???? .?????? .????

36. A slender uniform rigid bar of mass m is hinged at O and supported by two springs, with
stiffnesses 3k and k, and a damper with damping coefficient c, as shown in the figure. For the
system to be critically damped, the ratio c/?km should be

A. 4 B. 2
C. 4?7 D. 2?7
Ans: option (C)
Sol:
?? ?????
=?;?? ????? ???????????? ???? ???????????????????? ????????????

Suppose that we apply a external force downward at horizontal road at spring constant 3K and
leave it freely for to and fro motion.
Therefore, moment about point ?O?; ? ?? 0
=0
?? 0
??
? +?? (
3?? 4
?? )(
3?? 4
)+ 3?? (
?? 4
?? )(
?? 4
)+?? (
?? 4
?? ? )(
?? 4
)=0
?? 0
??
? +?? (
9?? 2
16
?? )+3?? (
?? 2
16
?? )+?? (
?? 2

16
?? ? )=0
Now, moment of inertia of rod about the center of the rod is ?? ?? =
?? ?? 2
12

And moment of inertia about the hinged point is ?? 0
=?? ?? +?? ?? 2
=
?? ?? 2
12
+?? (
?? 4
)
2
=
7
48
?? ?? 2

7
48
?? ?? 2
??
? +
1
16
?? ?? 2
?? ?+
12
16
?? ?? 2
?? =0

As we know that for critical dumping, the root of the quadratic equation should be real and equal.



21

? ?? 2
?4???? =0
(
1
16
?? ?? 2
)
2
?4 (
7
48
?? ?? 2
)(
12
16
?? ?? 2
)=0

?? =?4 (
7
1
?? )(
4
1
?? )=4?7????
?
?? ?????
= 4?7

37. The probability that a part manufactured by a company will be defective is 0.05. If 15 such parts
are selected randomly and inspected, then the probability that at least two parts will be
defective is __________ (round off to two decimal places).
Ans: 0.17
Sol: Total no. of parts = 15
P[defective(p)] = 0.05
P[non-defective(q)] = 1 ? 0.05 = 0.95
P[at least 2 defective] = 1 ? [P(no defective)+P(1 defective)]
Using the binomial distribution,
P[at least 2 defective] = 1 ? [
15
C0p
0
q
15
+
15
C1p
1
q
14
]= 1 ? [0.05
0
0.95
15
+ 15?0.05?0.95
14
] = 1 ?
[0.4639 + 0.3657] = 1 ? 0.8296 = 0.1704


38. A four bar mechanism is shown in the figure. The link numbers are mentioned near the links.
Input link 2 is rotating anti-clockwise with a constant angular speed ?2. Length of different links
are :

2 4 2
4
,
2.
OO O A L
AB O B L
==
==

The magnitude of the angular speed of the output link 4 is ?4 at the instant when link 2 makes
an angle of 90
o
with O2O4 as shown. The ratio
4
2
?
?
is __________ (round off to two decimal
places).

Ans: 0.79
Sol: Using Instantaneous center method



22


?? 24
?? 12
?? 2
= ?? 24
?? 41
?? 4

?? 24
?? 12
=?? tan75
?? (???????? ? ?? 12
?? 23
?? 24
)
?? 24
?? 41
=?? +?? tan75
??
?
?? 4
?? 2
=
?? 24
?? 12
?? 24
?? 41
=
?? tan75
?? ?? +?? tan75
??
=0.788

39. Two masses A and B having mass ma and mb, respectively, lying in the plane of the figure
shown, are rigidly attached to a shaft which revolves about an axis through O perpendicular to
the figure. The radii of rotation of the masses ma and mb are ra and rb, respectively. The angle
between lines OA and OB is 90
o
. If ma = 10 kg, mb = 20 kg, ra = 200 mm and rb = 400 mm,
then the balance mass to be placed at a radius of 200 mm is _________ kg (round off to two
decimal places).

Ans: 41.23
Sol:
Let the balance mass be m
? ?? ?? =?? ?? ?? ?? ?????? 0?+?? ?? ?? ?? ?????? 90?+???????????? =0 -----(1)
? ?? ?? =?? ?? ?? ?? ?????? 0?+?? ?? ?? ?? ?????? 90?+???????????? =0------ (2)
From (1), ???????????? =?[?? ?? ?? ?? ?????? 0?+?? ?? ?? ?? ?????? 90?]
Or, ???????????? =?[10?200]=?2000
From (2), ???????????? =?[?? ?? ?? ?? ?????? 0+?? ?? ?? ?? ?????? 90?]
Or, ???????????? =?[20?400]=?8000
Using ?(???????????? )
2
+(???????????? )
2
=???? =?2000
2
+8000
2
=8246.21
Now, since the radius of the balance mass is 200mm, therefore ?? =
8246.21
200
? =41.23????

40. A prismatic, straight elastic, cantilever beam is subjected to a linearly distributed transverse load
as shown below. If the beam length is L, Young?s modulus E, and area moment of inertia I, the
magnitude of the maximum deflection is



23


A.
4
60
qL
EI
B.
4
30
qL
EI

C.
4
10
qL
EI
D.
4
15
qL
EI

Ans: option (B)
Sol: The maximum deflection of the cantilever beam subjected to uniformly varying load (UVL) is given
by
4
30
qL
EI


41. Given a vector
( )
3 3 3
1
? ??
3
u y i x j z k = ? + + and ? n as the unit normal vector to the surface of the
hemisphere (x
2
+ y
2
+ z
2
= 1;z ?0), the value of integral
( )
? u n dS ? ? ?
?
evaluated on the
curved surface of the hemisphere S is
A. ? B.
3
?

C.
2
?
D.
2
?
?
Ans: option (C)
Sol: Hemisphere (x
2
+ y
2
+ z
2
= 1;z ?0)



To find the integration of the given expiration, it is easy if we are using the stoke?s theorem.
Surface integral will become line integral.
?(?? ???? )???????? = ???? ?????

Now, putting the value of ?? in the above equation.
?(?? ???? )???????? =?
1
3
(??? 3
???? +?? 3
???? +?? 3
???? )
??

=?
1
3
(??? 3
???? +?? 3
???? )
?? ??? =0 ???? ???????? ????????????



24

=? (?? 2
???????? +?? 2
???????? )
?? [using green theorem]
=?(?? 2
+?? 2
)????????
Now converting the above equation into polar coordinate
?? 2
+?? 2
=?? 2


? ? ?? 2
?? ???? ????
1
?? =0
=
2?? ?? =0
? (? ?? 3
????
1
?? =0
)????
2?? ?? =0
=
?? 2



42. The thickness of a sheet is reduced by rolling (without any change in width) using 600 mm
diameter rolls. Neglect elastic deflection of the rolls and assume that the coefficient of friction at
the roll-workpiece interface is 0.05. The sheet enters the rotating rolls unaided. If the initial
sheet thickness is 2 mm, the minimum possible final thickness that can be produced by this
process in a single pass is ________ mm (round off to two decimal places).
Ans: 1.25
Sol: Draft = (??? )
?????? =?? 2
?? =0.05
2
?300=0.75????
Hence, final thickness of the sheet = 2 ? 0.75 = 1.25mm

43. A ball of mass 3 kg moving with a velocity of 4 m/s undergoes a perfectly-elastic direct-central
impact with a stationary ball of mass m. After the impact is over, the kinetic energy of the 3 kg
ball is 6 J. The possible value (s) of m is/are
A. 6 kg only B. 1 kg, 9 kg
C. 1 kg only D. 1 kg, 6 kg
Ans: option (D)
Sol: Conservation of momentum gives m1u1 + m2u2 = m1v1 + m2v2
?? 1
=3???? , ?? 1
=4?? /?? , ?? 2
=?? ???? , ?? 2
=0
Substituting in the above equation,
3?4+?? ?0=3??? 1
+?? ??? 2

Or, 12=3?? 1
+?? ?? 2
-------(1)
For perfectly-elastic impact,
?? =
?? 2
??? 1
?? 1
??? 2
=1
Or, ?? 2
??? 1
=?? 1
??? 2
=4?? /?? ------- (2)
Conservation of kinetic energy gives
1
2
?? 1
?? 1
2
+
1
2
?? 2
?? 2
2
=
1
2
?? 1
?? 1
2
+
1
2
?? 2
?? 2
2

Or,
1
2
3(4)
2
+0=6+
1
2
?? 2
?? 2
2

Or, ?? ?? 2
2
=36 ---------(3)
From equation (2), ?? 1
=?? 2
?4
Substituting in equation (1),
12=3(?? 2
?4)+?? ?? 2

Or 12=3?? 2
?12+ ?? ?? 2

Or ?? 2
(3+?? )=24
Or ?? 2
=
24
3+??
Substituting in equation (3)



25

?? (
24
3+?? )
2
=36
576?? =36(3+?? )
2

?16?? =9+?? 2
+6??
?? 2
?10?? +9=0
On solving, we get
?? =1,9
Therefore, possible values of m are 1 kg and 9 kg.


44. The derivative of f(x) = cos(x) can be estimated using the approximation
( )
( ) ( )
'.
2
f x h f x h
fx
h
+ ? ?
= The percentage error is calculated as
Exact value-Approximate value
100.
Exact value
??
?
??
??
The percentage error in the derivative of f(x) at x = ?/6
radian, choosing h = 0.1 radian, is
A. > 1% and < 5%
B. < 0.1%
C. > 0.1% and < 1%
D. > 5%
Ans: option (C)
Sol: f(x) = cos(x)
? f?(x) = -sin(x) = ?sin(
?? 6
? )=?0.5 (exact value)
Approximate value = ( )
( ) ( )
'.
2
f x h f x h
fx
h
+ ? ?
=
?? ?
(?? )=
cos(?? +?)?cos?? ??
2?

cos(?? +?)=?????????????? ???????????????? ?
?????? (?? ??)=?????????????? ?+?????????????? ?
So,
?? ?
(?? )=
?????????????? ???????????????? ??[?????????????? ?+?????????????? ?]
2?

=
?2?????????????? ?
2?
=
??????????????? ?
?

Or, ?? ?
(?? )=
?sin(
?? 6
)?????? (0.1)
0.1
=
?0.5?0.0998
0.1
=?0.4992

So, percentage error =
?0.5?(?0.4992)
?0.5
?100=0.166


45. The aerodynamic drag on a sports car depends on its shape. The car has a drag coefficient of 0.1
with the windows and the roof closed. With the windows and the roof open, the drag coefficient
becomes 0.8. The car travels at 44 km/h with the windows and roof closed. For the same
amount of power needed to overcome the aerodynamic drag, the speed of the car with the
windows and roof open (round off to two decimal places), is ________km/h (the density of air
and frontal area may be assumed to be constant).
Ans: 22



26

Sol: The power needed to overcome the aerodynamic drag is given by ?? ?? ???
Where, ?? ?? is the drag force given by
?? ?? =
1
2
? ?? ?? ???? ?? 2

For the power to remain same in both the cases of windows closed and open, then
(?? ?? ??? )
?????????????? ???????????? =(?? ?? ??? )
?????????????? ????????
Or,
(
1
2
? ?? ?? ???? ?? 3
)
?????????????? ???????????? =(
1
2
? ?? ?? ???? ?? 3
)
?????????????? ????????
Or, 0.1?44
3
=0.8??? 3

Or V = 22 km/h


46. An idealized centrifugal pump (blade outer radius of 50 mm) consumes 2 kW power while
running at 3000 rpm. The entry of the liquid into the pump is axial and exit from the pump is
radial with respect to impeller. If the losses are neglected, then the mass flow rate of the liquid
through the pump is ________ kg/s (round off to two decimal places).
Ans: 8.106
Sol: Diameter = 2????????????? ???? ?????????? =2?50=100???? =0.1 ??
?? =
?????? 60
=
?? ?0.1?3000
60
=15.71 ?? /??????
Now, power = mass flow rate ? ?? 2

?2000=?? ? ?(15.71)
2

Or, ?? ? =8.106


47. The figure shows a heat engine (HE) working between two reservoirs. The amount of heat (Q2)
rejected by the heat engine is drawn by a heat pump (HP). The heat pump receives the entire
work output (W) of the heat engine. If temperatures.
T1 > T3 > T2, then the relation between the efficiency (?) of the heat engine and the coefficient
of performance (COP) of the heat pump is

A. COP = ? B. OCP = 1 + ?
C. COP = ?
-1
D. COP = ?
-1
-1
Ans: option (C)
Sol: For heat engine, ?? =
?? ?? 1

For Heat engine, ?????? =
?? 3
??
Energy balance for Heat engine gives ?? 2
=?? 1
???
And energy balance for Heat pump gives ?? 3
=?? 2
+?? =?? 1
??? +?? =?? 1




27

Hence, ?????? =
?? 1
?? =
1
?? =?? ?1


48. Three sets of parallel plates LM, NR and PQ are given in Figures 1, 2 and 3. The view factor F U is
defined as the fraction of radiation leaving plate I that is intercepted by plate J. Assume that the
values of FLM and FNR are 0.8 and 0.4, respectively. The value of FPQ (round off to one decimal
place) is ___________.

Ans: 0.6
Sol:
?? ????
=?? ????
+
?? ????
??? ????
?? =?? .?? +
?? .?? ??? .?? ?? =?? .??


49. Hot and cold fluids enter a parallel flow double tube heat exchanger at 100
o
C and 15
o
C,
respectively. The heat capacity rates of hot and cold fluids are Ch = 2000 W/K and Cc = 1200
W/K, respectively. If the outlet temperature of the cold fluid is 45
o
C, the log mean temperature
difference (LMTD) of the heat exchanger is ________ K (round off to two decimal places).
Ans: option ()
Sol: Given data
?? ?
?? =100?, ?? ?? ?? =15?, ?? ?? ?? =45?
?? ?
=2000?? /?? , ?? ?? =1200?? /??
Using the energy balance equation for the heat exchanger
?? ?
(?? ?
?? ??? ?
?? )=?? ?? (?? ?? ?? ??? ?? ?? )
?2000(100??? ?
?? )=1200(45?15)
??? ?
?? =82?

??? ?? =?? ?
?? ??? ?? ?? =100?15=85?
??? ?? =?? ?
?? ??? ?? ?? =82?45=37?
???????? =
??? ?? ???? ?? ln
??? ?? ??? ?? =
85?37
ln
85
37
=57.71?





28

50. A differential equation is given as

2
2
2
2 2 4.
d y dy
x x y
dx dx
? + =
The solution of the differential equation in terms of arbitrary constants C1 and C2 is
A.
1
2 2
4
C
y C x
x
= + +
B.
2
12
4 y C x C x = + +
C.
2
12
2 y C x C x = + +
D.
1
2 2
2
C
y C x
x
= + +
Ans: option (D)
Sol: Given differential equation
(?? (?? ?1)?2?? +2)?? =4 ?? ??????? ?? =?? ??
Auxiliary equation, (?? ?2)(?? ?1)=0
?? =1,2
???? = ?? 1
?? 1?? + ?? 2
?? 2??
???? =
4
(?? ?2)(?? ?1)
= 2
?? = ???? + ????

??? = ?? 1
?? 1?? + ?? 2
?? 2?? +2


51. Water flowing at the rate of 1 kg/s through a system is heated using an electric heater such that
the specific enthalpy of the water increases by 2.50 kJ/kg and the specific entropy increases by
0.007 kJ/kg.K. The power input to the electric heater is 2.50 kW. There is no other work or heat
interaction between the system and the surroundings. Assuming an ambient temperature of 300
K, the irreversibility rate of the system is _________kW (round off to two decimal places).
Ans: 2.1
Sol: The entropy generation (?? ?????? ) is given by rise in entropy rise of the system (Since no heat
interaction is involved)
So, entropy generation (?? ?????? ) = ?? ? ????????????????? ?????????????? = 1?0.007=0.007 ???? /??
Now, according to Gouy Stodola theorem,
Irreversibility = ?? ?? ??? ?????? =300?0.007=2.1????

52. In an orthogonal machining with a single point cutting tool of rake angle 10
o
, the uncut chip
thickness and the chip thickness are 0.125 mm and 0.22 mm, respectively. Using Merchant?s
first solution for the condition of minimum cutting force, the coefficient of friction at the chip-tool
interface is ___________(round off to two decimal places).
Ans: 0.74
Sol: uncut chip thickness (t) = 0.125 mm
Cut chip thickness (tc) = 0.22 mm
So, ship thickness ratio =
?? ?? ?? =
0.125
0.22
=0.568
Rake angle (?? ) = 10?
tan?? =
?? cos?? 1??? sin?? =
0.568?cos10
1?0.568?sin10
=0.6206
FirstRanker.com - FirstRanker's Choice



2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6




3

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of ?? =
8+6
2
=7

6. X is an online media provider. By offering unlimited and exclusive online content at attractive
prices for a loyalty membership, X is almost forcing its customers towards its loyalty
membership. If its loyalty membership continues to grow at its current rate, within the next
eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
A. Most households that subscribe to X?s loyalty membership discontinue watching cable
television
B. Non-members prefer to watch cable television
C. The X is cancelling accounts of non-members
D. Cable television operators don?t subscribe to X?s loyalty membership
Ans: option (A)
Sol: option A is the most appropriate solution

7. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased
by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.
A. 35.70 B. 10.00
C. 37.50 D. 25.00
Ans: option (C)
Sol: Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04??? =0.04??
And the fiscal deficit in 2016 = 0.05?1.1?? =0.055??
Increase in fiscal deficit = 0.055x ? 0.04x = 0.015x
So, the percentage increase in fiscal deficit =
0.015?? 0.04?? ?100=37.5%

8. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can
empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is
opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is
_________.
A. 16.50 B. 14.50
C. 15.50 D. 13.50
Ans: option (B)
Sol: 1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(
1
6
? ?
1
12
? )=
1
3
?
Tank filled by when Q and R works for another 6 hours = 6(
1
9
? ?
1
12
? )=
1
6
?
Total tank filled in these 10 hours =
1
3
? +
1
6
? =0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in
9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours




4

9. While teaching a creative writing class in India, I was surprised at receiving stories from the
students that were all set in distant places: in the American West with cowboys and in
Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave
the writers in the once-colonised countries the confidence to see the shabby lives around them
as worthy of being ?told?.
The writer of this passage is surprised by the creative writing assignments of his students,
because __________.
A. Some of the students had written about ice cubes and cowboys
B. None of the students had written about ice cubes and cowboys
C. Some of the students had written stories set in foreign places
D. None of the students had written stories set in India
Ans: option (C)
Sol: option C is the most appropriate solution

10. Mola is a digital platform for taxis in a city. It offers three types of rides ? Pool, Mini and Prime.
The Table below presents the number of rides for the past four months. The platform earns one
US dollar per ride. What is the percentage share of revenue contributed by Prime to the total
revenues of Mola, for the entire duration?
Type
Month
January February March April
Pool 170 320 215 190
Mini 110 220 180 70
Prime 75 180 120 90

A. 38.74 B. 23.97
C. 25.86 D. 16.24

Ans: option (B)
Sol: Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580
Revenue contributed by Prime = 75 + 180 + 120 +90 = 465
Total revenue of Mola = 895 + 580 + 465 = 1940
So, the percentage share =
465
1940
?100=23.97%

MECHANICAL ENGINEERING
1. A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by
application of pure bending moments at its ends. The Young?s modulus of the material of the
wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.
Ans: 50
Sol: Tensile stress
?? =
?? ?? ?? =
100?10
3
1
(
1
1000?2
)=50 ??????





5

2. In an electrical discharge machining process, the breakdown voltage across inter electrode gap
(IEG) is 200 V and the capacitance of the RC circuit is 50 ?F. The energy (in J) released per
spark across the IEG is __________
Ans: 1
Sol:
?? =
1
2
??????????????????????? ????????????? ?? 2

?? =0.5?50?10
?6
?200
2
=1 ??


3. If x is the mean of data 3, x, 2 and 4, then the mode is _________
Ans: 3
Sol: ?? =
3+?? +2+4
4

4??? =3+?? +2+4
4??? ??? =3+2+4=9
?? =3
Mode is 3. (Maximum repeated value)

4. The cold forming process in which a hardened tool is pressed against a workpiece (when there is
relative motion between the tool and the workpiece) to produce a roughened surface with a
regular pattern is
A. Strip rolling B. Knurling
C. Roll forming D. Chamfering
Ans: option (B)
Sol: We provide special pattern to prevent the relative motion between contact surface. This special
pattern is known as Knurling.


5. Endurance limit of a beam subjected to pure bending decreases with
A. increase in the surface roughness and increase in the size of the beam
B. decrease in the surface roughness and decrease in the size of the beam
C. decrease in the surface roughness and increase in the size of the beam
D. increase in the surface roughness and decrease in the size of the beam
Ans: option (A)
Sol: Formula for endurance limit
?? ?? =?? ?? ??? ?? ??? ?? ??? ?? ??? ?? ?

?? ???????
?? ?? ????????? ????????????
?? ?? ??????????????? ????????????
?? ?? ????????? ????????????
?? ?? ??????????????????????? ????????????
?? ?? ?
??????????????????? ?????????????? ?
Form above formula it is clear that the Endurance limit increases with increase in size,
surface, load, temp and endurance strength.







6

6. In matrix equation [A] {X} = {R}.
? ?
4 8 4 2
8 16 4 , 1
4 4 15 4
AX
? ? ? ?
?? ??
= ? = ??
??
????
??
??
?
? ? ? ?
and ? ?
32
16 .
64
R
??
??
=
??
??
??

One of the eigenvalues of matrix [A] is
A. 4 B. 15
C. 8 D. 16
Ans: option (D)
Sol: [A] {X} = {R}.

We know ???? = ???? ;?? ??????? ?? ??????????? ??????????

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}={
32
16
64
}

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}=16{
2
1
4
}

Hence, ?? =????

7. Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number
ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit.
The Reynolds number at the exit of the pipe is___________.
Ans: 500
Sol: Reynold?s Number
???? =
?? ?? ????
?? ??
Where: -
?? ??????????? ??????????????
?? ????
??????????????? ????????????????
?? ??????????????? ???? ????????
?? ? Dynamic viscosity of Fluid
?? ?? =(
?? ?? ????
?? ?? )=
(

?? (
?? ???????? ?? ???????? ) ?? ?? )


From above expiration, Reynold?s Number is independent of flow profile. Hence, Reynold?s
Number for parabolic flow profile is 500.

8. For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure
and temperature, respectively. As per Maxwell?s relations,
p
v
s
? ??
??
?
??
is equal to
A.
T
p
v
? ??
??
?
??
B.
p
s
T
? ??
??
?
??
C.
s
T
p
?? ?
??
?
??
D.
p
T
v
? ??
?
??
?
??

Ans: option (C)
Sol: From mathematical relation expiration



7

???? = ?????? +??????
? (
????
????
)
?? = (
????
????
)
??
???????? ?????????????? ????????????????
?? ?= ?????? +??????
? (
????
????
)
?? = (
????
????
)
??

9. Hardenability of steel is a measure of
A. the ability to harden when it is cold worked
B. the maximum hardness that can be obtained when it is austenitized and then quenched
C. the ability to retain its hardness when it is heated to elevated temperatures
D. the depth to which required hardening is obtained when it is austenitized and then quenched
Ans: option (D)
Sol: The depth to which required hardening is obtained when it is austenitized and then quenched.

10. The directional derivative of the function f(x, y) = x
2
+ y
2
along a line directed from (0, 0) to (1,
1), evaluated at the point x = 1, y = 1 is
A. 2 B. ?2
C. 4?2 D. 2?2
Ans: option (D)
Sol: Directional derivative of function along the line is the scalar value of derivative along the line. i.e.
we have to calculate value of derivative of function in the direction of given line vector
? ?? = ??? (
????
????
)+ ??? (
????
????
)
? ?? = 2???+ 2???
Now, calculating the value of ? ?? in 1???+ 1???
D.D of given function is (2???+ 2??? ) ?
(??? + ?? ?)
|??? + ?? ?|
= 2 ?2

11. A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is
A.
2 D
T
?
B.
T
D

C.
D
T
?
D.
D
T

Ans: option (C)
Sol: circular pitch =
????
??

12. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the
instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of
points P and R are VP and VR, in the x and y directions, respectively. The magnitude of the
angular velocity of the body is




8

A. /3
R
V B. /3
P
V
C. 2VR D. 2VP
Ans: option (C)
Sol: The given body is a rigid body; Hence the given body will not have any deformation, and the
possible motion is translation and angular motion. we know that the angular motion of the object is
always defined as the motion about the point. Hence, first we have to find a point parallel to both
velocity ?? ?? and ?? ?? .


? Angular velocity, ?? =
???????????????? ?????????????????????????? ????????????????
?? =
?? ?? ????
=
?? ?? ????

???? =
?3
2
????????? ???? ???????????????? =
?3
2
?1=
?3
2

???? =
1
2
????????? ???? ???????????????? =
1
2
?1=
1
2


?? =
2?? ?? ?3
=
2?? ?? 1


13. Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4
m. The view factor F12 is
A. 0.25 B. 0.0625
C. 1.0 D. 0.5
Ans: option (C)
Sol: ?? 12
=1

14. The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
A.
10
01
??
??
?
??
B.
01
10
? ??
??
?
??

C.
01
10
??
??
??
D.
10
01
???
??
??

Ans: option (C)
Sol: The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
01
10
??
??
??




S



9

15. The state of stress at a point in a component is represented by a Mohr?s circle of radius 100 MPa
centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the
normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same
point is ___________ MPa.
Ans: 80
Sol:


?? =?100
2
?60
2
=80 ??????

16. One-dimensional steady state heat conduction takes place through a solid whose cross-sectional
area varies linearly in the direction of heat transfer. Assume there is no heat generation in the
solid and the thermal conductivity of the material is constant and independent of temperature.
The temperature distribution in the solid is
A. Quadratic B. Exponential
C. Logarithmic D. Linear
Ans: option (C)
Sol: Let the given body cross-sectional area varies linearly, and heat is flowing from left to right.





If there is no heat generation,
?? ????
(?????
????
????
)=0

?
?? ????
(?????
????
????
)=?0

(?????
????
????
)=??

??? (?? 0
+?? ?? ?? )
????
????
=??
???? =
? ?? ????
?? (?? 0
+?? ?? ?? )


? ????
2
1
=?
? ?? ????
?? (?? 0
+?? ?? ?? )
2
1


?? 2
??? 1
= ?
?? ?? ln(
?? ?? ?? 2
+?? 0
?? ?? ?? 1
+?? 0
)



10

17. An analytic function f(z) of complex variable z = x + I y may be written as f(z) = u(x, y) + iv (x,
y). Then, u(x, y) and v(x, y) must satisfy
A.
uv
xy
??
=?
??
and
uv
yx
??
=
??

B.
uv
xy
??
=?
??
and
uv
yx
??
=?
??

C.
uv
xy
??
=
??
and
uv
yx
??
=?
??

D.
uv
xy
??
=
??
and
uv
yx
??
=
??

Ans: option (C)
Sol: If f(z) = u(x, y) + iv(x, y) is analytic function then it must satisfy the following relations.

????
????
=
????
????


????
????
=?
????
????


18. A thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is
losing heat to the surroundings by natural convection. The temperatures of the plate and the
surroundings, and the properties of the surrounding fluid, are constant. The relationship between
the average Nusselt and Rayleigh numbers is given as Nu = K Ra ?, where K is a constant. The
length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the
plate is increased to 16L keeping all other factors constant.

If the average heat transfer coefficient for the first plate is h1 and that for the second plate is h2,
the value of the ratio h1/h2 is____________.
Ans: 2
Sol: ?? ?? =?? (?? ?? )
1
4
We know that ?? ?? =?? ?? ?? ??
?? ?? =?? (?? ?? ?? ?? )
1
4
??? ?? ?(?? ?? )
1
4 ?(
???? ??? ?? 3
?? 2
)
1
4

??? ??? 3
4
???? ?
1
4
?
2
?
1
?(
?? 1
?? 2
)
1
4
=>
?
1
?
2
?(
?? 2
?? 1
)
1
4
=(16)
1
4=2



11


19. Which one of the following modifications of the simple ideal Rankine cycle increases the thermal
efficiency and reduces the moisture content of the steam at the turbine outlet?
A. Decreasing the condenser pressure.
B. Increasing the boiler pressure.
C. Decreasing the boiler pressure.
D. Increasing the turbine inlet temperature.
Ans: option (D)
Sol: Due to increase of the turbine inlet temperature, quality of the stream at outlet of the turbine
improves. Which increases the thermal efficiency and reduces the moisture content of the steam at the
turbine outlet.

20. Consider a linear rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of
100 MPa along the length direction. Assume plane stress conditions in the plane normal to the
thickness. The Young?s modulus E = 200 MPa and Poisson?s ratio v = 0.3 are given. The principal
strains in the plane of the sheet are
A. (0.5, 0.0) B. (0.35, -0.15)
C. (0.5, -0.5) D. (0.5, -0.15)
Ans: option (D)
Sol: ?
1
=
?? 1
?? ???
?? 2
?? =
100
200
?0.3?
0
200
=0.5

?
2
=
?? 2
?? ???
?? 1
?? =
0
200
?0.3?
100
200
=?0.15


21. The figure shows an idealized plane truss. If a horizontal force of 300 N is applied at point A,
then the magnitude of the force produced in member CD is ________N.

Ans: 0

Sol:



12



The momentum about the point A must be zero, because there is no deformation of any truss.
Hence, ?? ????
=0 [?? ????
is not passing through the point A]

22. The fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase
in
A. freezing range
B. surface tension
C. degree of superheat
D. viscosity
Ans: option (C)
Sol: Fluidity of molten metal of cast alloys increases with increase in degree of superheat.

23. The most common limit gage used for inspecting the hole diameter is
A. Ring gage B. Snap gage
C. Plug gage D. Master gage
Ans: option (C)
Sol: The most common limit gage used for inspecting the hole diameter is Plug gage.

24. The differential equation 45
dy
y
dx
+= is valid in the domain 0 ? x ? 1 with y(0) = 2.25. The
solution of the differential equation is
A. y = e
-4x
+ 1.25
B. y = e
4x
+ 5
C. y = e
4x
+ 1.25
D. y = e
-4x
+ 5
Ans: option (A)
Sol: The given equation is.



13

???? ???? +4?? =5
If Integration factor = ?? ?4????
=?? 4??
? ?? ????? =?5????? ???? +??
? ?? ??? 4?? =5?
?? 4?? 4
+??
? ?? ??? 4?? =5?
?? 4?? 4
+?? ?.( 1)
Now for at x=0,
? 2.25 =
5
4
+ ??
? ?? =1
? Using the value of C in equ (1)
? ?? ?
?? 4?? ?? 4?? =
5
?? 4?? ?
?? 4?? 4
+
?? ?? 4??
? ?? =1.25+ ?? ?4??

25. A two-dimensional incompressible frictionless flow field is given by
??
. u xi yj =? If ? is the density
of the fluid, the expression for pressure gradient vector at any point in the flow field is given as
A.
( )
22
??
x i y j ??+ B.
( )
??
xi yj ??+
C.
( )
??
xi yj ? + D.
( )
??
xi yj ? ?
Ans: option (B)
Sol: Euler?s Equation of motion in 2D.

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

As there is no extra force acting on the fluid.
?? ?? ?????? ?? ?? =0
Now form the given expiration, u=x & v=y
?
????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????


?0+ ?? ?1+0+0=0?
1
?? ????
????

0+ 0+?? ?1+0=0?
1
?? ????
????

??????????? ???????? ?????? =
????
????
???+
????
????
???= ??? (?? ???+?? ??? )




14

26. A short shoe external drum brake is shown in the figure. The diameter of the brake drum is 500
mm. The dimensions a = 1000 mm, b = 500 mm and c = 200 mm. The coefficient of friction
between the drum and the shoe is 0.35. The force applied on the lever F = 100 N as shown in
the figure. The drum is rotating anti-clockwise. The braking torque on the drum is _______N.m
(round off to two decimal places).

Ans: 20.34
Sol:

Applying momentum about point O.

??? ?? =0

?? ??? +?? ?? ?? ??? ??? ?? ??? =0
?? ?? =232.55
Breaking Torque = ?? ?? ?? ?? ?? = 20.34

27. A uniform disc with radius r and a mass of m kg is mounted centrally on a horizontal axle of
negligible mass and length of 1.5r. The disc spins counter-clockwise about the axle with angular
speed ?, when viewed from the right-hand side bearing, Q. The axle precesses about a vertical
axis at
?p = ?/10 in the clockwise direction when viewed from above. Let RP and RQ (positive upwards)
be the resultant reaction forces due to the mass and the gyroscopic effect, at bearings P and Q,
respectively. Assuming ?
2
r = 300 m/s
2
and g = 10 m/s
2
, the ratio of the larger to the smaller
bearing reaction force (considering appropriate signs) is __________.



15


Ans: -3
Sol: ?????????????????? ???????????? (???? )=???? ?? ??

Using: ?? ?? =
?? 10
and ?? 2
?? =300

???? =
?? ?? 2
2
?? 2
10
=15????

Reaction at P and Q due to gravity

?? ?? 1
+?? ?? 1
=???? =10??
?? ?? 1
=5??
??? ?? 1
= 5 ??

Reaction at P and Q due to GC

Taking momentum about point p.
?? ?? 2
?1.5?? ?15???? =0
?? ?? 2
=
15????
1.5?? =10 ??
??? ?? 2
= ?10 ??
?????? ,
?? ?? ?? ?? =
?? ?? 1
+?? ?? 2

?? ?? 1
+?? ?? 2
=
5+10
5?10
= ?3

28. The figure shows a pouring arrangement for casting of a metal block. Frictional losses are
negligible. The acceleration due to gravity is 9.81 m/s
2
. The time (in s, round off to two decimal
places) to fill up the mold cavity (of size 40 cm ? 30 cm ? 15 cm) is ____________



16


Ans: 29.84
Sol: ???????? ?????????????? ???????? =
?? ?? ?? ?? .?2?? ?

???????? =
0.40?0.30?0.15
?? 0.02
2
4
.?2?9.81?0.20
28.94 ??????

29. The activities of a project, their duration and the precedence relationships are given in the table.
For example, in a precedence relationship ?X < Y, Z? means that X is predecessor of activities Y
and Z. The time to complete the activities along the critical path is ____________ weeks.
Activity Duration
(Weeks)
Precedence
Relationship
A 5 A < B, C, D
B 7 B < E, F, G
C 10 C < I
D 6 D < G
E 3 E < H
F 9 F < I
G 7 G < I
H 4 H < I
I 2 ---
A. 21 B. 25
C. 23 D. 17
Ans: option (C)
Sol:



17


30. The crank of a slider-crank mechanism rotates counter-clockwise (CCW) with a constant angular
velocity ?, as shown. Assume the length of the crank to be r.

Using exact analysis, the acceleration of the slider in the y-direction, at the instant shown, where
the crank is parallel to x-axis, is given by
A. -?
2
r B. 2?
2
r
C. ?
2
r D. -2?
2
r
Ans: option (C)
Sol:


Velocity of point A, ?? ?? = ?? ???
The radial acceleration of point A, ?? ????
=?? ?? 2

Since, the inclination of line AB is 45 degree, the acceleration of the point B will be equal to the
acceleration of point A. i.e. ?? ?? 2


31. A gas tungsten arc welding operation is performed using a current of 250 A and an arc voltage of
20 V at a welding speed of 5 mm/s. Assuming that the arc efficiency is 70%, the net heat input
per unit length of the weld will be ________ kJ/mm (round off to one decimal place).
Ans: 0.7
Sol: ???????? ?????????? =??Power
elec

???????? ?????????? =0.7?250?20=3500 ????????

???????? ?????????? per unit length=
3500
5
=700
?? ????

=0.7 KJ/mm

32. Water flows through two different pipes A and B of the same circular cross-section but at
different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both
the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes
is same, the ratio of volume flow rates QB/QA is ______ (round off to two decimal places).
A
O
B



18

Ans: 0.5
Sol: Frictional losses of pipe

??? ? ????
?? ?? ?? ? ????
(
?? ?? )
?? ?? ?????
?? ?? ?? ??

?
????
?????
=
?? ?? ?? ?? ?? ?? 2
?? ?? ?? ?? ?? ?? 2
;?? ??????? ?? =
64
????



?? ?? 2
?? ?? 2
=
?
????
?? ?? ?? ?? ??? ?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? ?? ??

?? ?? ?? ?? =
?? ?? ?? ?? =0.5

33. Consider two concentric circular cylinders of different materials M and N in contact with each
other at r = b, as shown below. The interface at r = b is frictionless. The composite cylinder
system is subjected to internal pressure P. Let
( )
,
MM
r
uu
?
and
( )
,
MM
rr ??
?? denote the radial and
tangential displacement and stress components, respectively, in material M Similarly,
( )
,
NN
r
uu
?

and
( )
,
NN
rr ??
?? denote the radial and tangential displacement and stress components, respectively,
in material N. The boundary conditions that need to be satisfied at the frictionless interface
between the two cylinders are :

A.
MN
rr
uu = and
MN
rr rr
?? = and
MN
uu
??
= and
MN
? ? ? ?
?? =
B.
MN
rr rr
?? = and
MN
? ? ? ?
?? = only
C.
MN
uu
??
= and
MN
? ? ? ?
?? = only
D.
MN
rr
uu = and
MN
rr rr
?? = only
Ans: option (D)
Sol:



19



Internal pressure causes the stress in radial as well as circumferential direction.

At r=b i.e. interference of the cylinder can be frictionless if Stress in radial direction must be equal.
Velocity in radial direction must be equal. (This condition will make the normal force Zero)
As radius of the cylinder increases due to inside pressure, there will be relative velocity between
the contact surfaces in the circumferential direction.

34. The binary phase diagram of metals P and Q is shown in the figure. An alloy X containing 60% P
and 40% Q (by weight) is cooled from liquid to solid state. The fractions of solid and liquid (in
weight percent) at 1250
o
C, respectively, will be

A. 22.2% and 77.8%
B. 68.0% and 32.0%
C. 77.8% and 22.2%
D. 32.0% and 68.0%
Ans: option (A)
Sol: Mass fraction of liquid =
?? ?? ??? 0
?? ?? ??? ??
?? ?? =
68?40
68?32
= 0.778=77.8%
?? ?? =1??? ?? =0.222=22.2%

35. The annual demand of valves per year in a company is 10,000 units. The current order quantity
is 400 valves per order. The holding cost is Rs. 24 per valve per year and the ordering cost is Rs.
400 per order. If the current order quantity is changed to Economic Order Quantity, then the
saving in the total cost of inventory per year will be Rs. __________ (round off to two decimal
places).
Ans: 943.59
Sol:
Annual Demand (D) = 10000 nos



20

Order Quantities (Q) = 400 / order
Holding cost (?? ?
)= 24 /valve/year
Ordering Cost (?? 0
) = RS 400 /order
?????? =
?? ?? ?? 0
+
?? 2
?? ?


?????? =
10000
400
400+
10000
2
24=14800

?????? ?=?2?? ?? 0
?? ?


?????? ?=13856.41

???????????? =14800?13856.41=???? .?????? .????

36. A slender uniform rigid bar of mass m is hinged at O and supported by two springs, with
stiffnesses 3k and k, and a damper with damping coefficient c, as shown in the figure. For the
system to be critically damped, the ratio c/?km should be

A. 4 B. 2
C. 4?7 D. 2?7
Ans: option (C)
Sol:
?? ?????
=?;?? ????? ???????????? ???? ???????????????????? ????????????

Suppose that we apply a external force downward at horizontal road at spring constant 3K and
leave it freely for to and fro motion.
Therefore, moment about point ?O?; ? ?? 0
=0
?? 0
??
? +?? (
3?? 4
?? )(
3?? 4
)+ 3?? (
?? 4
?? )(
?? 4
)+?? (
?? 4
?? ? )(
?? 4
)=0
?? 0
??
? +?? (
9?? 2
16
?? )+3?? (
?? 2
16
?? )+?? (
?? 2

16
?? ? )=0
Now, moment of inertia of rod about the center of the rod is ?? ?? =
?? ?? 2
12

And moment of inertia about the hinged point is ?? 0
=?? ?? +?? ?? 2
=
?? ?? 2
12
+?? (
?? 4
)
2
=
7
48
?? ?? 2

7
48
?? ?? 2
??
? +
1
16
?? ?? 2
?? ?+
12
16
?? ?? 2
?? =0

As we know that for critical dumping, the root of the quadratic equation should be real and equal.



21

? ?? 2
?4???? =0
(
1
16
?? ?? 2
)
2
?4 (
7
48
?? ?? 2
)(
12
16
?? ?? 2
)=0

?? =?4 (
7
1
?? )(
4
1
?? )=4?7????
?
?? ?????
= 4?7

37. The probability that a part manufactured by a company will be defective is 0.05. If 15 such parts
are selected randomly and inspected, then the probability that at least two parts will be
defective is __________ (round off to two decimal places).
Ans: 0.17
Sol: Total no. of parts = 15
P[defective(p)] = 0.05
P[non-defective(q)] = 1 ? 0.05 = 0.95
P[at least 2 defective] = 1 ? [P(no defective)+P(1 defective)]
Using the binomial distribution,
P[at least 2 defective] = 1 ? [
15
C0p
0
q
15
+
15
C1p
1
q
14
]= 1 ? [0.05
0
0.95
15
+ 15?0.05?0.95
14
] = 1 ?
[0.4639 + 0.3657] = 1 ? 0.8296 = 0.1704


38. A four bar mechanism is shown in the figure. The link numbers are mentioned near the links.
Input link 2 is rotating anti-clockwise with a constant angular speed ?2. Length of different links
are :

2 4 2
4
,
2.
OO O A L
AB O B L
==
==

The magnitude of the angular speed of the output link 4 is ?4 at the instant when link 2 makes
an angle of 90
o
with O2O4 as shown. The ratio
4
2
?
?
is __________ (round off to two decimal
places).

Ans: 0.79
Sol: Using Instantaneous center method



22


?? 24
?? 12
?? 2
= ?? 24
?? 41
?? 4

?? 24
?? 12
=?? tan75
?? (???????? ? ?? 12
?? 23
?? 24
)
?? 24
?? 41
=?? +?? tan75
??
?
?? 4
?? 2
=
?? 24
?? 12
?? 24
?? 41
=
?? tan75
?? ?? +?? tan75
??
=0.788

39. Two masses A and B having mass ma and mb, respectively, lying in the plane of the figure
shown, are rigidly attached to a shaft which revolves about an axis through O perpendicular to
the figure. The radii of rotation of the masses ma and mb are ra and rb, respectively. The angle
between lines OA and OB is 90
o
. If ma = 10 kg, mb = 20 kg, ra = 200 mm and rb = 400 mm,
then the balance mass to be placed at a radius of 200 mm is _________ kg (round off to two
decimal places).

Ans: 41.23
Sol:
Let the balance mass be m
? ?? ?? =?? ?? ?? ?? ?????? 0?+?? ?? ?? ?? ?????? 90?+???????????? =0 -----(1)
? ?? ?? =?? ?? ?? ?? ?????? 0?+?? ?? ?? ?? ?????? 90?+???????????? =0------ (2)
From (1), ???????????? =?[?? ?? ?? ?? ?????? 0?+?? ?? ?? ?? ?????? 90?]
Or, ???????????? =?[10?200]=?2000
From (2), ???????????? =?[?? ?? ?? ?? ?????? 0+?? ?? ?? ?? ?????? 90?]
Or, ???????????? =?[20?400]=?8000
Using ?(???????????? )
2
+(???????????? )
2
=???? =?2000
2
+8000
2
=8246.21
Now, since the radius of the balance mass is 200mm, therefore ?? =
8246.21
200
? =41.23????

40. A prismatic, straight elastic, cantilever beam is subjected to a linearly distributed transverse load
as shown below. If the beam length is L, Young?s modulus E, and area moment of inertia I, the
magnitude of the maximum deflection is



23


A.
4
60
qL
EI
B.
4
30
qL
EI

C.
4
10
qL
EI
D.
4
15
qL
EI

Ans: option (B)
Sol: The maximum deflection of the cantilever beam subjected to uniformly varying load (UVL) is given
by
4
30
qL
EI


41. Given a vector
( )
3 3 3
1
? ??
3
u y i x j z k = ? + + and ? n as the unit normal vector to the surface of the
hemisphere (x
2
+ y
2
+ z
2
= 1;z ?0), the value of integral
( )
? u n dS ? ? ?
?
evaluated on the
curved surface of the hemisphere S is
A. ? B.
3
?

C.
2
?
D.
2
?
?
Ans: option (C)
Sol: Hemisphere (x
2
+ y
2
+ z
2
= 1;z ?0)



To find the integration of the given expiration, it is easy if we are using the stoke?s theorem.
Surface integral will become line integral.
?(?? ???? )???????? = ???? ?????

Now, putting the value of ?? in the above equation.
?(?? ???? )???????? =?
1
3
(??? 3
???? +?? 3
???? +?? 3
???? )
??

=?
1
3
(??? 3
???? +?? 3
???? )
?? ??? =0 ???? ???????? ????????????



24

=? (?? 2
???????? +?? 2
???????? )
?? [using green theorem]
=?(?? 2
+?? 2
)????????
Now converting the above equation into polar coordinate
?? 2
+?? 2
=?? 2


? ? ?? 2
?? ???? ????
1
?? =0
=
2?? ?? =0
? (? ?? 3
????
1
?? =0
)????
2?? ?? =0
=
?? 2



42. The thickness of a sheet is reduced by rolling (without any change in width) using 600 mm
diameter rolls. Neglect elastic deflection of the rolls and assume that the coefficient of friction at
the roll-workpiece interface is 0.05. The sheet enters the rotating rolls unaided. If the initial
sheet thickness is 2 mm, the minimum possible final thickness that can be produced by this
process in a single pass is ________ mm (round off to two decimal places).
Ans: 1.25
Sol: Draft = (??? )
?????? =?? 2
?? =0.05
2
?300=0.75????
Hence, final thickness of the sheet = 2 ? 0.75 = 1.25mm

43. A ball of mass 3 kg moving with a velocity of 4 m/s undergoes a perfectly-elastic direct-central
impact with a stationary ball of mass m. After the impact is over, the kinetic energy of the 3 kg
ball is 6 J. The possible value (s) of m is/are
A. 6 kg only B. 1 kg, 9 kg
C. 1 kg only D. 1 kg, 6 kg
Ans: option (D)
Sol: Conservation of momentum gives m1u1 + m2u2 = m1v1 + m2v2
?? 1
=3???? , ?? 1
=4?? /?? , ?? 2
=?? ???? , ?? 2
=0
Substituting in the above equation,
3?4+?? ?0=3??? 1
+?? ??? 2

Or, 12=3?? 1
+?? ?? 2
-------(1)
For perfectly-elastic impact,
?? =
?? 2
??? 1
?? 1
??? 2
=1
Or, ?? 2
??? 1
=?? 1
??? 2
=4?? /?? ------- (2)
Conservation of kinetic energy gives
1
2
?? 1
?? 1
2
+
1
2
?? 2
?? 2
2
=
1
2
?? 1
?? 1
2
+
1
2
?? 2
?? 2
2

Or,
1
2
3(4)
2
+0=6+
1
2
?? 2
?? 2
2

Or, ?? ?? 2
2
=36 ---------(3)
From equation (2), ?? 1
=?? 2
?4
Substituting in equation (1),
12=3(?? 2
?4)+?? ?? 2

Or 12=3?? 2
?12+ ?? ?? 2

Or ?? 2
(3+?? )=24
Or ?? 2
=
24
3+??
Substituting in equation (3)



25

?? (
24
3+?? )
2
=36
576?? =36(3+?? )
2

?16?? =9+?? 2
+6??
?? 2
?10?? +9=0
On solving, we get
?? =1,9
Therefore, possible values of m are 1 kg and 9 kg.


44. The derivative of f(x) = cos(x) can be estimated using the approximation
( )
( ) ( )
'.
2
f x h f x h
fx
h
+ ? ?
= The percentage error is calculated as
Exact value-Approximate value
100.
Exact value
??
?
??
??
The percentage error in the derivative of f(x) at x = ?/6
radian, choosing h = 0.1 radian, is
A. > 1% and < 5%
B. < 0.1%
C. > 0.1% and < 1%
D. > 5%
Ans: option (C)
Sol: f(x) = cos(x)
? f?(x) = -sin(x) = ?sin(
?? 6
? )=?0.5 (exact value)
Approximate value = ( )
( ) ( )
'.
2
f x h f x h
fx
h
+ ? ?
=
?? ?
(?? )=
cos(?? +?)?cos?? ??
2?

cos(?? +?)=?????????????? ???????????????? ?
?????? (?? ??)=?????????????? ?+?????????????? ?
So,
?? ?
(?? )=
?????????????? ???????????????? ??[?????????????? ?+?????????????? ?]
2?

=
?2?????????????? ?
2?
=
??????????????? ?
?

Or, ?? ?
(?? )=
?sin(
?? 6
)?????? (0.1)
0.1
=
?0.5?0.0998
0.1
=?0.4992

So, percentage error =
?0.5?(?0.4992)
?0.5
?100=0.166


45. The aerodynamic drag on a sports car depends on its shape. The car has a drag coefficient of 0.1
with the windows and the roof closed. With the windows and the roof open, the drag coefficient
becomes 0.8. The car travels at 44 km/h with the windows and roof closed. For the same
amount of power needed to overcome the aerodynamic drag, the speed of the car with the
windows and roof open (round off to two decimal places), is ________km/h (the density of air
and frontal area may be assumed to be constant).
Ans: 22



26

Sol: The power needed to overcome the aerodynamic drag is given by ?? ?? ???
Where, ?? ?? is the drag force given by
?? ?? =
1
2
? ?? ?? ???? ?? 2

For the power to remain same in both the cases of windows closed and open, then
(?? ?? ??? )
?????????????? ???????????? =(?? ?? ??? )
?????????????? ????????
Or,
(
1
2
? ?? ?? ???? ?? 3
)
?????????????? ???????????? =(
1
2
? ?? ?? ???? ?? 3
)
?????????????? ????????
Or, 0.1?44
3
=0.8??? 3

Or V = 22 km/h


46. An idealized centrifugal pump (blade outer radius of 50 mm) consumes 2 kW power while
running at 3000 rpm. The entry of the liquid into the pump is axial and exit from the pump is
radial with respect to impeller. If the losses are neglected, then the mass flow rate of the liquid
through the pump is ________ kg/s (round off to two decimal places).
Ans: 8.106
Sol: Diameter = 2????????????? ???? ?????????? =2?50=100???? =0.1 ??
?? =
?????? 60
=
?? ?0.1?3000
60
=15.71 ?? /??????
Now, power = mass flow rate ? ?? 2

?2000=?? ? ?(15.71)
2

Or, ?? ? =8.106


47. The figure shows a heat engine (HE) working between two reservoirs. The amount of heat (Q2)
rejected by the heat engine is drawn by a heat pump (HP). The heat pump receives the entire
work output (W) of the heat engine. If temperatures.
T1 > T3 > T2, then the relation between the efficiency (?) of the heat engine and the coefficient
of performance (COP) of the heat pump is

A. COP = ? B. OCP = 1 + ?
C. COP = ?
-1
D. COP = ?
-1
-1
Ans: option (C)
Sol: For heat engine, ?? =
?? ?? 1

For Heat engine, ?????? =
?? 3
??
Energy balance for Heat engine gives ?? 2
=?? 1
???
And energy balance for Heat pump gives ?? 3
=?? 2
+?? =?? 1
??? +?? =?? 1




27

Hence, ?????? =
?? 1
?? =
1
?? =?? ?1


48. Three sets of parallel plates LM, NR and PQ are given in Figures 1, 2 and 3. The view factor F U is
defined as the fraction of radiation leaving plate I that is intercepted by plate J. Assume that the
values of FLM and FNR are 0.8 and 0.4, respectively. The value of FPQ (round off to one decimal
place) is ___________.

Ans: 0.6
Sol:
?? ????
=?? ????
+
?? ????
??? ????
?? =?? .?? +
?? .?? ??? .?? ?? =?? .??


49. Hot and cold fluids enter a parallel flow double tube heat exchanger at 100
o
C and 15
o
C,
respectively. The heat capacity rates of hot and cold fluids are Ch = 2000 W/K and Cc = 1200
W/K, respectively. If the outlet temperature of the cold fluid is 45
o
C, the log mean temperature
difference (LMTD) of the heat exchanger is ________ K (round off to two decimal places).
Ans: option ()
Sol: Given data
?? ?
?? =100?, ?? ?? ?? =15?, ?? ?? ?? =45?
?? ?
=2000?? /?? , ?? ?? =1200?? /??
Using the energy balance equation for the heat exchanger
?? ?
(?? ?
?? ??? ?
?? )=?? ?? (?? ?? ?? ??? ?? ?? )
?2000(100??? ?
?? )=1200(45?15)
??? ?
?? =82?

??? ?? =?? ?
?? ??? ?? ?? =100?15=85?
??? ?? =?? ?
?? ??? ?? ?? =82?45=37?
???????? =
??? ?? ???? ?? ln
??? ?? ??? ?? =
85?37
ln
85
37
=57.71?





28

50. A differential equation is given as

2
2
2
2 2 4.
d y dy
x x y
dx dx
? + =
The solution of the differential equation in terms of arbitrary constants C1 and C2 is
A.
1
2 2
4
C
y C x
x
= + +
B.
2
12
4 y C x C x = + +
C.
2
12
2 y C x C x = + +
D.
1
2 2
2
C
y C x
x
= + +
Ans: option (D)
Sol: Given differential equation
(?? (?? ?1)?2?? +2)?? =4 ?? ??????? ?? =?? ??
Auxiliary equation, (?? ?2)(?? ?1)=0
?? =1,2
???? = ?? 1
?? 1?? + ?? 2
?? 2??
???? =
4
(?? ?2)(?? ?1)
= 2
?? = ???? + ????

??? = ?? 1
?? 1?? + ?? 2
?? 2?? +2


51. Water flowing at the rate of 1 kg/s through a system is heated using an electric heater such that
the specific enthalpy of the water increases by 2.50 kJ/kg and the specific entropy increases by
0.007 kJ/kg.K. The power input to the electric heater is 2.50 kW. There is no other work or heat
interaction between the system and the surroundings. Assuming an ambient temperature of 300
K, the irreversibility rate of the system is _________kW (round off to two decimal places).
Ans: 2.1
Sol: The entropy generation (?? ?????? ) is given by rise in entropy rise of the system (Since no heat
interaction is involved)
So, entropy generation (?? ?????? ) = ?? ? ????????????????? ?????????????? = 1?0.007=0.007 ???? /??
Now, according to Gouy Stodola theorem,
Irreversibility = ?? ?? ??? ?????? =300?0.007=2.1????

52. In an orthogonal machining with a single point cutting tool of rake angle 10
o
, the uncut chip
thickness and the chip thickness are 0.125 mm and 0.22 mm, respectively. Using Merchant?s
first solution for the condition of minimum cutting force, the coefficient of friction at the chip-tool
interface is ___________(round off to two decimal places).
Ans: 0.74
Sol: uncut chip thickness (t) = 0.125 mm
Cut chip thickness (tc) = 0.22 mm
So, ship thickness ratio =
?? ?? ?? =
0.125
0.22
=0.568
Rake angle (?? ) = 10?
tan?? =
?? cos?? 1??? sin?? =
0.568?cos10
1?0.568?sin10
=0.6206



29

Or shear angle (?? ) = 31.82?
According to Merchant?s theory, we have
2?? +?? ??? =
?? 2

So, ?? =90??63.64+10=36.36?
Now, ???????? =?? (?????????????????????? ???? ???????????????? )
Therefore, coefficient of friction = ?????? 36.36?=0.74

53. An air standard Otto cycle has thermal efficiency of 0.5 and the mean effective pressure of the
cycle is 1000 kPa. For air, assume specific heat ratio ? = 1.4 and specific gas constant R = 0.287
kJ/kg.K, If the pressure and temperature at the beginning of the compression stroke are 100
kPa and 300 K, respectively, then the specific net work output of the cycle is ___________kJ/kg
(round off to two decimal places).
Ans: 708.8
Sol:

Given data
P1 = 100kPa, T1 = 300K, mep = 1000 kPa, ?? =1.4, efficiency(?? )=0.5, R = 0.287 kJ/kg-K
Using P1V1 = RT1
V1 =
0.287?300
100
=0.861?? 3
/????
Efficiency(?? )=1?
1
(?? )
?? ?1
where, r is the compression ratio = V1/V2
1?
1
(?? )
?? ?1
=0.5
1?
1
(?? )
1.4?1
=0.5
Or, r = 5.657
V1/V2 = 5.657
??? 2
=0.1522 m
3
/kg
Swept volume = V1 ? V2 = 0.861 ? 0.1522 = 0.7088 m
3
/kg
Went = Swept volume ??????? = 0.7088 ? 1000 = 708.8 kJ/kg

54. A through hole is drilled in an aluminum alloy plate of 15 mm thickness with a drill bit of
diameter 10 mm, at a feed of 0.25 mm/rev and a spindle speed of 1200 rpm. If the specific
energy required for cutting this material is 0.7 N.m/mm
3
, the power required for drilling is
_________W (round off to two decimal places).
Ans: 274.89
Sol: ?????? =
?? ?? 2
4
????????? ??????? ?????? ?????? =
?? (10)
2
4
?0.25?
1200
60
=125?? mm
3

Specific energy = 0.7 Nm/mm
3
So, power required for drilling = 0.7?125?? =274.89??

FirstRanker.com - FirstRanker's Choice



2

General Aptitude
1. A final examination is the __________ of a series of evaluations that a student has to go
through.
A. desperation B. insinuation C. consultation D. culmination
Ans: option (D)
Sol: A final examination is the culmination of a series of evaluations that a student has to go
through.
Meaning of culmination is the highest or climactic point of something, especially as attained after a
long time
Hence, it is the most appropriate word

2. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.
A. JDC B. JCD
C. JDE D. JED
Ans: option (D)
Sol: I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

3. Are there enough seats here? There are __________ people here than I expected.
A. many B. most
C. more D. least
Ans: option (C)
Sol: Comparison is made here between the number of people and number of seats, hence, more is
the most appropriate word

4. Once the team of analysts identify the problem, we ________ in a better position to comment
on the issue.
Which one of the following choices CANNOT fill the given blank?
A. might be B. are going to be
C. will be D. were to be
Ans: option (C)
Sol: Future is being discussed here, hence will be is the most appropriate phrase

5. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of
X and Y. What is the minimum possible value of P?
A. 7 B. 6
C. 8 D. 9.5
Ans: option (A)
Sol: XYZ = 192 and Z = 4
So, XY = 48
?? =
?? +?? 2

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows
X Y
48 1
24 2
16 3
12 4
8 6




3

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of ?? =
8+6
2
=7

6. X is an online media provider. By offering unlimited and exclusive online content at attractive
prices for a loyalty membership, X is almost forcing its customers towards its loyalty
membership. If its loyalty membership continues to grow at its current rate, within the next
eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
A. Most households that subscribe to X?s loyalty membership discontinue watching cable
television
B. Non-members prefer to watch cable television
C. The X is cancelling accounts of non-members
D. Cable television operators don?t subscribe to X?s loyalty membership
Ans: option (A)
Sol: option A is the most appropriate solution

7. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased
by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.
A. 35.70 B. 10.00
C. 37.50 D. 25.00
Ans: option (C)
Sol: Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04??? =0.04??
And the fiscal deficit in 2016 = 0.05?1.1?? =0.055??
Increase in fiscal deficit = 0.055x ? 0.04x = 0.015x
So, the percentage increase in fiscal deficit =
0.015?? 0.04?? ?100=37.5%

8. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can
empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is
opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is
_________.
A. 16.50 B. 14.50
C. 15.50 D. 13.50
Ans: option (B)
Sol: 1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours = 4(
1
6
? ?
1
12
? )=
1
3
?
Tank filled by when Q and R works for another 6 hours = 6(
1
9
? ?
1
12
? )=
1
6
?
Total tank filled in these 10 hours =
1
3
? +
1
6
? =0.5
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in
9 hours)
Therefore, total time required to fill the tank = 4 + 6 + 4.5 = 14.5 hours




4

9. While teaching a creative writing class in India, I was surprised at receiving stories from the
students that were all set in distant places: in the American West with cowboys and in
Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave
the writers in the once-colonised countries the confidence to see the shabby lives around them
as worthy of being ?told?.
The writer of this passage is surprised by the creative writing assignments of his students,
because __________.
A. Some of the students had written about ice cubes and cowboys
B. None of the students had written about ice cubes and cowboys
C. Some of the students had written stories set in foreign places
D. None of the students had written stories set in India
Ans: option (C)
Sol: option C is the most appropriate solution

10. Mola is a digital platform for taxis in a city. It offers three types of rides ? Pool, Mini and Prime.
The Table below presents the number of rides for the past four months. The platform earns one
US dollar per ride. What is the percentage share of revenue contributed by Prime to the total
revenues of Mola, for the entire duration?
Type
Month
January February March April
Pool 170 320 215 190
Mini 110 220 180 70
Prime 75 180 120 90

A. 38.74 B. 23.97
C. 25.86 D. 16.24

Ans: option (B)
Sol: Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580
Revenue contributed by Prime = 75 + 180 + 120 +90 = 465
Total revenue of Mola = 895 + 580 + 465 = 1940
So, the percentage share =
465
1940
?100=23.97%

MECHANICAL ENGINEERING
1. A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by
application of pure bending moments at its ends. The Young?s modulus of the material of the
wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.
Ans: 50
Sol: Tensile stress
?? =
?? ?? ?? =
100?10
3
1
(
1
1000?2
)=50 ??????





5

2. In an electrical discharge machining process, the breakdown voltage across inter electrode gap
(IEG) is 200 V and the capacitance of the RC circuit is 50 ?F. The energy (in J) released per
spark across the IEG is __________
Ans: 1
Sol:
?? =
1
2
??????????????????????? ????????????? ?? 2

?? =0.5?50?10
?6
?200
2
=1 ??


3. If x is the mean of data 3, x, 2 and 4, then the mode is _________
Ans: 3
Sol: ?? =
3+?? +2+4
4

4??? =3+?? +2+4
4??? ??? =3+2+4=9
?? =3
Mode is 3. (Maximum repeated value)

4. The cold forming process in which a hardened tool is pressed against a workpiece (when there is
relative motion between the tool and the workpiece) to produce a roughened surface with a
regular pattern is
A. Strip rolling B. Knurling
C. Roll forming D. Chamfering
Ans: option (B)
Sol: We provide special pattern to prevent the relative motion between contact surface. This special
pattern is known as Knurling.


5. Endurance limit of a beam subjected to pure bending decreases with
A. increase in the surface roughness and increase in the size of the beam
B. decrease in the surface roughness and decrease in the size of the beam
C. decrease in the surface roughness and increase in the size of the beam
D. increase in the surface roughness and decrease in the size of the beam
Ans: option (A)
Sol: Formula for endurance limit
?? ?? =?? ?? ??? ?? ??? ?? ??? ?? ??? ?? ?

?? ???????
?? ?? ????????? ????????????
?? ?? ??????????????? ????????????
?? ?? ????????? ????????????
?? ?? ??????????????????????? ????????????
?? ?? ?
??????????????????? ?????????????? ?
Form above formula it is clear that the Endurance limit increases with increase in size,
surface, load, temp and endurance strength.







6

6. In matrix equation [A] {X} = {R}.
? ?
4 8 4 2
8 16 4 , 1
4 4 15 4
AX
? ? ? ?
?? ??
= ? = ??
??
????
??
??
?
? ? ? ?
and ? ?
32
16 .
64
R
??
??
=
??
??
??

One of the eigenvalues of matrix [A] is
A. 4 B. 15
C. 8 D. 16
Ans: option (D)
Sol: [A] {X} = {R}.

We know ???? = ???? ;?? ??????? ?? ??????????? ??????????

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}={
32
16
64
}

[
4 8 4
8 16 ?4
4 ?4 15
]{
2
1
4
}=16{
2
1
4
}

Hence, ?? =????

7. Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number
ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit.
The Reynolds number at the exit of the pipe is___________.
Ans: 500
Sol: Reynold?s Number
???? =
?? ?? ????
?? ??
Where: -
?? ??????????? ??????????????
?? ????
??????????????? ????????????????
?? ??????????????? ???? ????????
?? ? Dynamic viscosity of Fluid
?? ?? =(
?? ?? ????
?? ?? )=
(

?? (
?? ???????? ?? ???????? ) ?? ?? )


From above expiration, Reynold?s Number is independent of flow profile. Hence, Reynold?s
Number for parabolic flow profile is 500.

8. For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure
and temperature, respectively. As per Maxwell?s relations,
p
v
s
? ??
??
?
??
is equal to
A.
T
p
v
? ??
??
?
??
B.
p
s
T
? ??
??
?
??
C.
s
T
p
?? ?
??
?
??
D.
p
T
v
? ??
?
??
?
??

Ans: option (C)
Sol: From mathematical relation expiration



7

???? = ?????? +??????
? (
????
????
)
?? = (
????
????
)
??
???????? ?????????????? ????????????????
?? ?= ?????? +??????
? (
????
????
)
?? = (
????
????
)
??

9. Hardenability of steel is a measure of
A. the ability to harden when it is cold worked
B. the maximum hardness that can be obtained when it is austenitized and then quenched
C. the ability to retain its hardness when it is heated to elevated temperatures
D. the depth to which required hardening is obtained when it is austenitized and then quenched
Ans: option (D)
Sol: The depth to which required hardening is obtained when it is austenitized and then quenched.

10. The directional derivative of the function f(x, y) = x
2
+ y
2
along a line directed from (0, 0) to (1,
1), evaluated at the point x = 1, y = 1 is
A. 2 B. ?2
C. 4?2 D. 2?2
Ans: option (D)
Sol: Directional derivative of function along the line is the scalar value of derivative along the line. i.e.
we have to calculate value of derivative of function in the direction of given line vector
? ?? = ??? (
????
????
)+ ??? (
????
????
)
? ?? = 2???+ 2???
Now, calculating the value of ? ?? in 1???+ 1???
D.D of given function is (2???+ 2??? ) ?
(??? + ?? ?)
|??? + ?? ?|
= 2 ?2

11. A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is
A.
2 D
T
?
B.
T
D

C.
D
T
?
D.
D
T

Ans: option (C)
Sol: circular pitch =
????
??

12. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the
instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of
points P and R are VP and VR, in the x and y directions, respectively. The magnitude of the
angular velocity of the body is




8

A. /3
R
V B. /3
P
V
C. 2VR D. 2VP
Ans: option (C)
Sol: The given body is a rigid body; Hence the given body will not have any deformation, and the
possible motion is translation and angular motion. we know that the angular motion of the object is
always defined as the motion about the point. Hence, first we have to find a point parallel to both
velocity ?? ?? and ?? ?? .


? Angular velocity, ?? =
???????????????? ?????????????????????????? ????????????????
?? =
?? ?? ????
=
?? ?? ????

???? =
?3
2
????????? ???? ???????????????? =
?3
2
?1=
?3
2

???? =
1
2
????????? ???? ???????????????? =
1
2
?1=
1
2


?? =
2?? ?? ?3
=
2?? ?? 1


13. Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4
m. The view factor F12 is
A. 0.25 B. 0.0625
C. 1.0 D. 0.5
Ans: option (C)
Sol: ?? 12
=1

14. The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
A.
10
01
??
??
?
??
B.
01
10
? ??
??
?
??

C.
01
10
??
??
??
D.
10
01
???
??
??

Ans: option (C)
Sol: The transformation matrix for mirroring a point in x ? y plane about the line y = x is given by
01
10
??
??
??




S



9

15. The state of stress at a point in a component is represented by a Mohr?s circle of radius 100 MPa
centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the
normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same
point is ___________ MPa.
Ans: 80
Sol:


?? =?100
2
?60
2
=80 ??????

16. One-dimensional steady state heat conduction takes place through a solid whose cross-sectional
area varies linearly in the direction of heat transfer. Assume there is no heat generation in the
solid and the thermal conductivity of the material is constant and independent of temperature.
The temperature distribution in the solid is
A. Quadratic B. Exponential
C. Logarithmic D. Linear
Ans: option (C)
Sol: Let the given body cross-sectional area varies linearly, and heat is flowing from left to right.





If there is no heat generation,
?? ????
(?????
????
????
)=0

?
?? ????
(?????
????
????
)=?0

(?????
????
????
)=??

??? (?? 0
+?? ?? ?? )
????
????
=??
???? =
? ?? ????
?? (?? 0
+?? ?? ?? )


? ????
2
1
=?
? ?? ????
?? (?? 0
+?? ?? ?? )
2
1


?? 2
??? 1
= ?
?? ?? ln(
?? ?? ?? 2
+?? 0
?? ?? ?? 1
+?? 0
)



10

17. An analytic function f(z) of complex variable z = x + I y may be written as f(z) = u(x, y) + iv (x,
y). Then, u(x, y) and v(x, y) must satisfy
A.
uv
xy
??
=?
??
and
uv
yx
??
=
??

B.
uv
xy
??
=?
??
and
uv
yx
??
=?
??

C.
uv
xy
??
=
??
and
uv
yx
??
=?
??

D.
uv
xy
??
=
??
and
uv
yx
??
=
??

Ans: option (C)
Sol: If f(z) = u(x, y) + iv(x, y) is analytic function then it must satisfy the following relations.

????
????
=
????
????


????
????
=?
????
????


18. A thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is
losing heat to the surroundings by natural convection. The temperatures of the plate and the
surroundings, and the properties of the surrounding fluid, are constant. The relationship between
the average Nusselt and Rayleigh numbers is given as Nu = K Ra ?, where K is a constant. The
length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the
plate is increased to 16L keeping all other factors constant.

If the average heat transfer coefficient for the first plate is h1 and that for the second plate is h2,
the value of the ratio h1/h2 is____________.
Ans: 2
Sol: ?? ?? =?? (?? ?? )
1
4
We know that ?? ?? =?? ?? ?? ??
?? ?? =?? (?? ?? ?? ?? )
1
4
??? ?? ?(?? ?? )
1
4 ?(
???? ??? ?? 3
?? 2
)
1
4

??? ??? 3
4
???? ?
1
4
?
2
?
1
?(
?? 1
?? 2
)
1
4
=>
?
1
?
2
?(
?? 2
?? 1
)
1
4
=(16)
1
4=2



11


19. Which one of the following modifications of the simple ideal Rankine cycle increases the thermal
efficiency and reduces the moisture content of the steam at the turbine outlet?
A. Decreasing the condenser pressure.
B. Increasing the boiler pressure.
C. Decreasing the boiler pressure.
D. Increasing the turbine inlet temperature.
Ans: option (D)
Sol: Due to increase of the turbine inlet temperature, quality of the stream at outlet of the turbine
improves. Which increases the thermal efficiency and reduces the moisture content of the steam at the
turbine outlet.

20. Consider a linear rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of
100 MPa along the length direction. Assume plane stress conditions in the plane normal to the
thickness. The Young?s modulus E = 200 MPa and Poisson?s ratio v = 0.3 are given. The principal
strains in the plane of the sheet are
A. (0.5, 0.0) B. (0.35, -0.15)
C. (0.5, -0.5) D. (0.5, -0.15)
Ans: option (D)
Sol: ?
1
=
?? 1
?? ???
?? 2
?? =
100
200
?0.3?
0
200
=0.5

?
2
=
?? 2
?? ???
?? 1
?? =
0
200
?0.3?
100
200
=?0.15


21. The figure shows an idealized plane truss. If a horizontal force of 300 N is applied at point A,
then the magnitude of the force produced in member CD is ________N.

Ans: 0

Sol:



12



The momentum about the point A must be zero, because there is no deformation of any truss.
Hence, ?? ????
=0 [?? ????
is not passing through the point A]

22. The fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase
in
A. freezing range
B. surface tension
C. degree of superheat
D. viscosity
Ans: option (C)
Sol: Fluidity of molten metal of cast alloys increases with increase in degree of superheat.

23. The most common limit gage used for inspecting the hole diameter is
A. Ring gage B. Snap gage
C. Plug gage D. Master gage
Ans: option (C)
Sol: The most common limit gage used for inspecting the hole diameter is Plug gage.

24. The differential equation 45
dy
y
dx
+= is valid in the domain 0 ? x ? 1 with y(0) = 2.25. The
solution of the differential equation is
A. y = e
-4x
+ 1.25
B. y = e
4x
+ 5
C. y = e
4x
+ 1.25
D. y = e
-4x
+ 5
Ans: option (A)
Sol: The given equation is.



13

???? ???? +4?? =5
If Integration factor = ?? ?4????
=?? 4??
? ?? ????? =?5????? ???? +??
? ?? ??? 4?? =5?
?? 4?? 4
+??
? ?? ??? 4?? =5?
?? 4?? 4
+?? ?.( 1)
Now for at x=0,
? 2.25 =
5
4
+ ??
? ?? =1
? Using the value of C in equ (1)
? ?? ?
?? 4?? ?? 4?? =
5
?? 4?? ?
?? 4?? 4
+
?? ?? 4??
? ?? =1.25+ ?? ?4??

25. A two-dimensional incompressible frictionless flow field is given by
??
. u xi yj =? If ? is the density
of the fluid, the expression for pressure gradient vector at any point in the flow field is given as
A.
( )
22
??
x i y j ??+ B.
( )
??
xi yj ??+
C.
( )
??
xi yj ? + D.
( )
??
xi yj ? ?
Ans: option (B)
Sol: Euler?s Equation of motion in 2D.

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=?? ?? ?
1
?? ????
????

As there is no extra force acting on the fluid.
?? ?? ?????? ?? ?? =0
Now form the given expiration, u=x & v=y
?
????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????

????
????
+ ?? ????
????
+?? ????
????
+?? ????
????
=0?
1
?? ????
????


?0+ ?? ?1+0+0=0?
1
?? ????
????

0+ 0+?? ?1+0=0?
1
?? ????
????

??????????? ???????? ?????? =
????
????
???+
????
????
???= ??? (?? ???+?? ??? )




14

26. A short shoe external drum brake is shown in the figure. The diameter of the brake drum is 500
mm. The dimensions a = 1000 mm, b = 500 mm and c = 200 mm. The coefficient of friction
between the drum and the shoe is 0.35. The force applied on the lever F = 100 N as shown in
the figure. The drum is rotating anti-clockwise. The braking torque on the drum is _______N.m
(round off to two decimal places).

Ans: 20.34
Sol:

Applying momentum about point O.

??? ?? =0

?? ??? +?? ?? ?? ??? ??? ?? ??? =0
?? ?? =232.55
Breaking Torque = ?? ?? ?? ?? ?? = 20.34

27. A uniform disc with radius r and a mass of m kg is mounted centrally on a horizontal axle of
negligible mass and length of 1.5r. The disc spins counter-clockwise about the axle with angular
speed ?, when viewed from the right-hand side bearing, Q. The axle precesses about a vertical
axis at
?p = ?/10 in the clockwise direction when viewed from above. Let RP and RQ (positive upwards)
be the resultant reaction forces due to the mass and the gyroscopic effect, at bearings P and Q,
respectively. Assuming ?
2
r = 300 m/s
2
and g = 10 m/s
2
, the ratio of the larger to the smaller
bearing reaction force (considering appropriate signs) is __________.



15


Ans: -3
Sol: ?????????????????? ???????????? (???? )=???? ?? ??

Using: ?? ?? =
?? 10
and ?? 2
?? =300

???? =
?? ?? 2
2
?? 2
10
=15????

Reaction at P and Q due to gravity

?? ?? 1
+?? ?? 1
=???? =10??
?? ?? 1
=5??
??? ?? 1
= 5 ??

Reaction at P and Q due to GC

Taking momentum about point p.
?? ?? 2
?1.5?? ?15???? =0
?? ?? 2
=
15????
1.5?? =10 ??
??? ?? 2
= ?10 ??
?????? ,
?? ?? ?? ?? =
?? ?? 1
+?? ?? 2

?? ?? 1
+?? ?? 2
=
5+10
5?10
= ?3

28. The figure shows a pouring arrangement for casting of a metal block. Frictional losses are
negligible. The acceleration due to gravity is 9.81 m/s
2
. The time (in s, round off to two decimal
places) to fill up the mold cavity (of size 40 cm ? 30 cm ? 15 cm) is ____________



16


Ans: 29.84
Sol: ???????? ?????????????? ???????? =
?? ?? ?? ?? .?2?? ?

???????? =
0.40?0.30?0.15
?? 0.02
2
4
.?2?9.81?0.20
28.94 ??????

29. The activities of a project, their duration and the precedence relationships are given in the table.
For example, in a precedence relationship ?X < Y, Z? means that X is predecessor of activities Y
and Z. The time to complete the activities along the critical path is ____________ weeks.
Activity Duration
(Weeks)
Precedence
Relationship
A 5 A < B, C, D
B 7 B < E, F, G
C 10 C < I
D 6 D < G
E 3 E < H
F 9 F < I
G 7 G < I
H 4 H < I
I 2 ---
A. 21 B. 25
C. 23 D. 17
Ans: option (C)
Sol:



17


30. The crank of a slider-crank mechanism rotates counter-clockwise (CCW) with a constant angular
velocity ?, as shown. Assume the length of the crank to be r.

Using exact analysis, the acceleration of the slider in the y-direction, at the instant shown, where
the crank is parallel to x-axis, is given by
A. -?
2
r B. 2?
2
r
C. ?
2
r D. -2?
2
r
Ans: option (C)
Sol:


Velocity of point A, ?? ?? = ?? ???
The radial acceleration of point A, ?? ????
=?? ?? 2

Since, the inclination of line AB is 45 degree, the acceleration of the point B will be equal to the
acceleration of point A. i.e. ?? ?? 2


31. A gas tungsten arc welding operation is performed using a current of 250 A and an arc voltage of
20 V at a welding speed of 5 mm/s. Assuming that the arc efficiency is 70%, the net heat input
per unit length of the weld will be ________ kJ/mm (round off to one decimal place).
Ans: 0.7
Sol: ???????? ?????????? =??Power
elec

???????? ?????????? =0.7?250?20=3500 ????????

???????? ?????????? per unit length=
3500
5
=700
?? ????

=0.7 KJ/mm

32. Water flows through two different pipes A and B of the same circular cross-section but at
different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both
the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes
is same, the ratio of volume flow rates QB/QA is ______ (round off to two decimal places).
A
O
B



18

Ans: 0.5
Sol: Frictional losses of pipe

??? ? ????
?? ?? ?? ? ????
(
?? ?? )
?? ?? ?????
?? ?? ?? ??

?
????
?????
=
?? ?? ?? ?? ?? ?? 2
?? ?? ?? ?? ?? ?? 2
;?? ??????? ?? =
64
????



?? ?? 2
?? ?? 2
=
?
????
?? ?? ?? ?? ??? ?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? ?? ??

?? ?? ?? ?? =
?? ?? ?? ?? =0.5

33. Consider two concentric circular cylinders of different materials M and N in contact with each
other at r = b, as shown below. The interface at r = b is frictionless. The composite cylinder
system is subjected to internal pressure P. Let
( )
,
MM
r
uu
?
and
( )
,
MM
rr ??
?? denote the radial and
tangential displacement and stress components, respectively, in material M Similarly,
( )
,
NN
r
uu
?

and
( )
,
NN
rr ??
?? denote the radial and tangential displacement and stress components, respectively,
in material N. The boundary conditions that need to be satisfied at the frictionless interface
between the two cylinders are :

A.
MN
rr
uu = and
MN
rr rr
?? = and
MN
uu
??
= and
MN
? ? ? ?
?? =
B.
MN
rr rr
?? = and
MN
? ? ? ?
?? = only
C.
MN
uu
??
= and
MN
? ? ? ?
?? = only
D.
MN
rr
uu = and
MN
rr rr
?? = only
Ans: option (D)
Sol:



19



Internal pressure causes the stress in radial as well as circumferential direction.

At r=b i.e. interference of the cylinder can be frictionless if Stress in radial direction must be equal.
Velocity in radial direction must be equal. (This condition will make the normal force Zero)
As radius of the cylinder increases due to inside pressure, there will be relative velocity between
the contact surfaces in the circumferential direction.

34. The binary phase diagram of metals P and Q is shown in the figure. An alloy X containing 60% P
and 40% Q (by weight) is cooled from liquid to solid state. The fractions of solid and liquid (in
weight percent) at 1250
o
C, respectively, will be

A. 22.2% and 77.8%
B. 68.0% and 32.0%
C. 77.8% and 22.2%
D. 32.0% and 68.0%
Ans: option (A)
Sol: Mass fraction of liquid =
?? ?? ??? 0
?? ?? ??? ??
?? ?? =
68?40
68?32
= 0.778=77.8%
?? ?? =1??? ?? =0.222=22.2%

35. The annual demand of valves per year in a company is 10,000 units. The current order quantity
is 400 valves per order. The holding cost is Rs. 24 per valve per year and the ordering cost is Rs.
400 per order. If the current order quantity is changed to Economic Order Quantity, then the
saving in the total cost of inventory per year will be Rs. __________ (round off to two decimal
places).
Ans: 943.59
Sol:
Annual Demand (D) = 10000 nos



20

Order Quantities (Q) = 400 / order
Holding cost (?? ?
)= 24 /valve/year
Ordering Cost (?? 0
) = RS 400 /order
?????? =
?? ?? ?? 0
+
?? 2
?? ?


?????? =
10000
400
400+
10000
2
24=14800

?????? ?=?2?? ?? 0
?? ?


?????? ?=13856.41

???????????? =14800?13856.41=???? .?????? .????

36. A slender uniform rigid bar of mass m is hinged at O and supported by two springs, with
stiffnesses 3k and k, and a damper with damping coefficient c, as shown in the figure. For the
system to be critically damped, the ratio c/?km should be

A. 4 B. 2
C. 4?7 D. 2?7
Ans: option (C)
Sol:
?? ?????
=?;?? ????? ???????????? ???? ???????????????????? ????????????

Suppose that we apply a external force downward at horizontal road at spring constant 3K and
leave it freely for to and fro motion.
Therefore, moment about point ?O?; ? ?? 0
=0
?? 0
??
? +?? (
3?? 4
?? )(
3?? 4
)+ 3?? (
?? 4
?? )(
?? 4
)+?? (
?? 4
?? ? )(
?? 4
)=0
?? 0
??
? +?? (
9?? 2
16
?? )+3?? (
?? 2
16
?? )+?? (
?? 2

16
?? ? )=0
Now, moment of inertia of rod about the center of the rod is ?? ?? =
?? ?? 2
12

And moment of inertia about the hinged point is ?? 0
=?? ?? +?? ?? 2
=
?? ?? 2
12
+?? (
?? 4
)
2
=
7
48
?? ?? 2

7
48
?? ?? 2
??
? +
1
16
?? ?? 2
?? ?+
12
16
?? ?? 2
?? =0

As we know that for critical dumping, the root of the quadratic equation should be real and equal.



21

? ?? 2
?4???? =0
(
1
16
?? ?? 2
)
2
?4 (
7
48
?? ?? 2
)(
12
16
?? ?? 2
)=0

?? =?4 (
7
1
?? )(
4
1
?? )=4?7????
?
?? ?????
= 4?7

37. The probability that a part manufactured by a company will be defective is 0.05. If 15 such parts
are selected randomly and inspected, then the probability that at least two parts will be
defective is __________ (round off to two decimal places).
Ans: 0.17
Sol: Total no. of parts = 15
P[defective(p)] = 0.05
P[non-defective(q)] = 1 ? 0.05 = 0.95
P[at least 2 defective] = 1 ? [P(no defective)+P(1 defective)]
Using the binomial distribution,
P[at least 2 defective] = 1 ? [
15
C0p
0
q
15
+
15
C1p
1
q
14
]= 1 ? [0.05
0
0.95
15
+ 15?0.05?0.95
14
] = 1 ?
[0.4639 + 0.3657] = 1 ? 0.8296 = 0.1704


38. A four bar mechanism is shown in the figure. The link numbers are mentioned near the links.
Input link 2 is rotating anti-clockwise with a constant angular speed ?2. Length of different links
are :

2 4 2
4
,
2.
OO O A L
AB O B L
==
==

The magnitude of the angular speed of the output link 4 is ?4 at the instant when link 2 makes
an angle of 90
o
with O2O4 as shown. The ratio
4
2
?
?
is __________ (round off to two decimal
places).

Ans: 0.79
Sol: Using Instantaneous center method



22


?? 24
?? 12
?? 2
= ?? 24
?? 41
?? 4

?? 24
?? 12
=?? tan75
?? (???????? ? ?? 12
?? 23
?? 24
)
?? 24
?? 41
=?? +?? tan75
??
?
?? 4
?? 2
=
?? 24
?? 12
?? 24
?? 41
=
?? tan75
?? ?? +?? tan75
??
=0.788

39. Two masses A and B having mass ma and mb, respectively, lying in the plane of the figure
shown, are rigidly attached to a shaft which revolves about an axis through O perpendicular to
the figure. The radii of rotation of the masses ma and mb are ra and rb, respectively. The angle
between lines OA and OB is 90
o
. If ma = 10 kg, mb = 20 kg, ra = 200 mm and rb = 400 mm,
then the balance mass to be placed at a radius of 200 mm is _________ kg (round off to two
decimal places).

Ans: 41.23
Sol:
Let the balance mass be m
? ?? ?? =?? ?? ?? ?? ?????? 0?+?? ?? ?? ?? ?????? 90?+???????????? =0 -----(1)
? ?? ?? =?? ?? ?? ?? ?????? 0?+?? ?? ?? ?? ?????? 90?+???????????? =0------ (2)
From (1), ???????????? =?[?? ?? ?? ?? ?????? 0?+?? ?? ?? ?? ?????? 90?]
Or, ???????????? =?[10?200]=?2000
From (2), ???????????? =?[?? ?? ?? ?? ?????? 0+?? ?? ?? ?? ?????? 90?]
Or, ???????????? =?[20?400]=?8000
Using ?(???????????? )
2
+(???????????? )
2
=???? =?2000
2
+8000
2
=8246.21
Now, since the radius of the balance mass is 200mm, therefore ?? =
8246.21
200
? =41.23????

40. A prismatic, straight elastic, cantilever beam is subjected to a linearly distributed transverse load
as shown below. If the beam length is L, Young?s modulus E, and area moment of inertia I, the
magnitude of the maximum deflection is



23


A.
4
60
qL
EI
B.
4
30
qL
EI

C.
4
10
qL
EI
D.
4
15
qL
EI

Ans: option (B)
Sol: The maximum deflection of the cantilever beam subjected to uniformly varying load (UVL) is given
by
4
30
qL
EI


41. Given a vector
( )
3 3 3
1
? ??
3
u y i x j z k = ? + + and ? n as the unit normal vector to the surface of the
hemisphere (x
2
+ y
2
+ z
2
= 1;z ?0), the value of integral
( )
? u n dS ? ? ?
?
evaluated on the
curved surface of the hemisphere S is
A. ? B.
3
?

C.
2
?
D.
2
?
?
Ans: option (C)
Sol: Hemisphere (x
2
+ y
2
+ z
2
= 1;z ?0)



To find the integration of the given expiration, it is easy if we are using the stoke?s theorem.
Surface integral will become line integral.
?(?? ???? )???????? = ???? ?????

Now, putting the value of ?? in the above equation.
?(?? ???? )???????? =?
1
3
(??? 3
???? +?? 3
???? +?? 3
???? )
??

=?
1
3
(??? 3
???? +?? 3
???? )
?? ??? =0 ???? ???????? ????????????



24

=? (?? 2
???????? +?? 2
???????? )
?? [using green theorem]
=?(?? 2
+?? 2
)????????
Now converting the above equation into polar coordinate
?? 2
+?? 2
=?? 2


? ? ?? 2
?? ???? ????
1
?? =0
=
2?? ?? =0
? (? ?? 3
????
1
?? =0
)????
2?? ?? =0
=
?? 2



42. The thickness of a sheet is reduced by rolling (without any change in width) using 600 mm
diameter rolls. Neglect elastic deflection of the rolls and assume that the coefficient of friction at
the roll-workpiece interface is 0.05. The sheet enters the rotating rolls unaided. If the initial
sheet thickness is 2 mm, the minimum possible final thickness that can be produced by this
process in a single pass is ________ mm (round off to two decimal places).
Ans: 1.25
Sol: Draft = (??? )
?????? =?? 2
?? =0.05
2
?300=0.75????
Hence, final thickness of the sheet = 2 ? 0.75 = 1.25mm

43. A ball of mass 3 kg moving with a velocity of 4 m/s undergoes a perfectly-elastic direct-central
impact with a stationary ball of mass m. After the impact is over, the kinetic energy of the 3 kg
ball is 6 J. The possible value (s) of m is/are
A. 6 kg only B. 1 kg, 9 kg
C. 1 kg only D. 1 kg, 6 kg
Ans: option (D)
Sol: Conservation of momentum gives m1u1 + m2u2 = m1v1 + m2v2
?? 1
=3???? , ?? 1
=4?? /?? , ?? 2
=?? ???? , ?? 2
=0
Substituting in the above equation,
3?4+?? ?0=3??? 1
+?? ??? 2

Or, 12=3?? 1
+?? ?? 2
-------(1)
For perfectly-elastic impact,
?? =
?? 2
??? 1
?? 1
??? 2
=1
Or, ?? 2
??? 1
=?? 1
??? 2
=4?? /?? ------- (2)
Conservation of kinetic energy gives
1
2
?? 1
?? 1
2
+
1
2
?? 2
?? 2
2
=
1
2
?? 1
?? 1
2
+
1
2
?? 2
?? 2
2

Or,
1
2
3(4)
2
+0=6+
1
2
?? 2
?? 2
2

Or, ?? ?? 2
2
=36 ---------(3)
From equation (2), ?? 1
=?? 2
?4
Substituting in equation (1),
12=3(?? 2
?4)+?? ?? 2

Or 12=3?? 2
?12+ ?? ?? 2

Or ?? 2
(3+?? )=24
Or ?? 2
=
24
3+??
Substituting in equation (3)



25

?? (
24
3+?? )
2
=36
576?? =36(3+?? )
2

?16?? =9+?? 2
+6??
?? 2
?10?? +9=0
On solving, we get
?? =1,9
Therefore, possible values of m are 1 kg and 9 kg.


44. The derivative of f(x) = cos(x) can be estimated using the approximation
( )
( ) ( )
'.
2
f x h f x h
fx
h
+ ? ?
= The percentage error is calculated as
Exact value-Approximate value
100.
Exact value
??
?
??
??
The percentage error in the derivative of f(x) at x = ?/6
radian, choosing h = 0.1 radian, is
A. > 1% and < 5%
B. < 0.1%
C. > 0.1% and < 1%
D. > 5%
Ans: option (C)
Sol: f(x) = cos(x)
? f?(x) = -sin(x) = ?sin(
?? 6
? )=?0.5 (exact value)
Approximate value = ( )
( ) ( )
'.
2
f x h f x h
fx
h
+ ? ?
=
?? ?
(?? )=
cos(?? +?)?cos?? ??
2?

cos(?? +?)=?????????????? ???????????????? ?
?????? (?? ??)=?????????????? ?+?????????????? ?
So,
?? ?
(?? )=
?????????????? ???????????????? ??[?????????????? ?+?????????????? ?]
2?

=
?2?????????????? ?
2?
=
??????????????? ?
?

Or, ?? ?
(?? )=
?sin(
?? 6
)?????? (0.1)
0.1
=
?0.5?0.0998
0.1
=?0.4992

So, percentage error =
?0.5?(?0.4992)
?0.5
?100=0.166


45. The aerodynamic drag on a sports car depends on its shape. The car has a drag coefficient of 0.1
with the windows and the roof closed. With the windows and the roof open, the drag coefficient
becomes 0.8. The car travels at 44 km/h with the windows and roof closed. For the same
amount of power needed to overcome the aerodynamic drag, the speed of the car with the
windows and roof open (round off to two decimal places), is ________km/h (the density of air
and frontal area may be assumed to be constant).
Ans: 22



26

Sol: The power needed to overcome the aerodynamic drag is given by ?? ?? ???
Where, ?? ?? is the drag force given by
?? ?? =
1
2
? ?? ?? ???? ?? 2

For the power to remain same in both the cases of windows closed and open, then
(?? ?? ??? )
?????????????? ???????????? =(?? ?? ??? )
?????????????? ????????
Or,
(
1
2
? ?? ?? ???? ?? 3
)
?????????????? ???????????? =(
1
2
? ?? ?? ???? ?? 3
)
?????????????? ????????
Or, 0.1?44
3
=0.8??? 3

Or V = 22 km/h


46. An idealized centrifugal pump (blade outer radius of 50 mm) consumes 2 kW power while
running at 3000 rpm. The entry of the liquid into the pump is axial and exit from the pump is
radial with respect to impeller. If the losses are neglected, then the mass flow rate of the liquid
through the pump is ________ kg/s (round off to two decimal places).
Ans: 8.106
Sol: Diameter = 2????????????? ???? ?????????? =2?50=100???? =0.1 ??
?? =
?????? 60
=
?? ?0.1?3000
60
=15.71 ?? /??????
Now, power = mass flow rate ? ?? 2

?2000=?? ? ?(15.71)
2

Or, ?? ? =8.106


47. The figure shows a heat engine (HE) working between two reservoirs. The amount of heat (Q2)
rejected by the heat engine is drawn by a heat pump (HP). The heat pump receives the entire
work output (W) of the heat engine. If temperatures.
T1 > T3 > T2, then the relation between the efficiency (?) of the heat engine and the coefficient
of performance (COP) of the heat pump is

A. COP = ? B. OCP = 1 + ?
C. COP = ?
-1
D. COP = ?
-1
-1
Ans: option (C)
Sol: For heat engine, ?? =
?? ?? 1

For Heat engine, ?????? =
?? 3
??
Energy balance for Heat engine gives ?? 2
=?? 1
???
And energy balance for Heat pump gives ?? 3
=?? 2
+?? =?? 1
??? +?? =?? 1




27

Hence, ?????? =
?? 1
?? =
1
?? =?? ?1


48. Three sets of parallel plates LM, NR and PQ are given in Figures 1, 2 and 3. The view factor F U is
defined as the fraction of radiation leaving plate I that is intercepted by plate J. Assume that the
values of FLM and FNR are 0.8 and 0.4, respectively. The value of FPQ (round off to one decimal
place) is ___________.

Ans: 0.6
Sol:
?? ????
=?? ????
+
?? ????
??? ????
?? =?? .?? +
?? .?? ??? .?? ?? =?? .??


49. Hot and cold fluids enter a parallel flow double tube heat exchanger at 100
o
C and 15
o
C,
respectively. The heat capacity rates of hot and cold fluids are Ch = 2000 W/K and Cc = 1200
W/K, respectively. If the outlet temperature of the cold fluid is 45
o
C, the log mean temperature
difference (LMTD) of the heat exchanger is ________ K (round off to two decimal places).
Ans: option ()
Sol: Given data
?? ?
?? =100?, ?? ?? ?? =15?, ?? ?? ?? =45?
?? ?
=2000?? /?? , ?? ?? =1200?? /??
Using the energy balance equation for the heat exchanger
?? ?
(?? ?
?? ??? ?
?? )=?? ?? (?? ?? ?? ??? ?? ?? )
?2000(100??? ?
?? )=1200(45?15)
??? ?
?? =82?

??? ?? =?? ?
?? ??? ?? ?? =100?15=85?
??? ?? =?? ?
?? ??? ?? ?? =82?45=37?
???????? =
??? ?? ???? ?? ln
??? ?? ??? ?? =
85?37
ln
85
37
=57.71?





28

50. A differential equation is given as

2
2
2
2 2 4.
d y dy
x x y
dx dx
? + =
The solution of the differential equation in terms of arbitrary constants C1 and C2 is
A.
1
2 2
4
C
y C x
x
= + +
B.
2
12
4 y C x C x = + +
C.
2
12
2 y C x C x = + +
D.
1
2 2
2
C
y C x
x
= + +
Ans: option (D)
Sol: Given differential equation
(?? (?? ?1)?2?? +2)?? =4 ?? ??????? ?? =?? ??
Auxiliary equation, (?? ?2)(?? ?1)=0
?? =1,2
???? = ?? 1
?? 1?? + ?? 2
?? 2??
???? =
4
(?? ?2)(?? ?1)
= 2
?? = ???? + ????

??? = ?? 1
?? 1?? + ?? 2
?? 2?? +2


51. Water flowing at the rate of 1 kg/s through a system is heated using an electric heater such that
the specific enthalpy of the water increases by 2.50 kJ/kg and the specific entropy increases by
0.007 kJ/kg.K. The power input to the electric heater is 2.50 kW. There is no other work or heat
interaction between the system and the surroundings. Assuming an ambient temperature of 300
K, the irreversibility rate of the system is _________kW (round off to two decimal places).
Ans: 2.1
Sol: The entropy generation (?? ?????? ) is given by rise in entropy rise of the system (Since no heat
interaction is involved)
So, entropy generation (?? ?????? ) = ?? ? ????????????????? ?????????????? = 1?0.007=0.007 ???? /??
Now, according to Gouy Stodola theorem,
Irreversibility = ?? ?? ??? ?????? =300?0.007=2.1????

52. In an orthogonal machining with a single point cutting tool of rake angle 10
o
, the uncut chip
thickness and the chip thickness are 0.125 mm and 0.22 mm, respectively. Using Merchant?s
first solution for the condition of minimum cutting force, the coefficient of friction at the chip-tool
interface is ___________(round off to two decimal places).
Ans: 0.74
Sol: uncut chip thickness (t) = 0.125 mm
Cut chip thickness (tc) = 0.22 mm
So, ship thickness ratio =
?? ?? ?? =
0.125
0.22
=0.568
Rake angle (?? ) = 10?
tan?? =
?? cos?? 1??? sin?? =
0.568?cos10
1?0.568?sin10
=0.6206



29

Or shear angle (?? ) = 31.82?
According to Merchant?s theory, we have
2?? +?? ??? =
?? 2

So, ?? =90??63.64+10=36.36?
Now, ???????? =?? (?????????????????????? ???? ???????????????? )
Therefore, coefficient of friction = ?????? 36.36?=0.74

53. An air standard Otto cycle has thermal efficiency of 0.5 and the mean effective pressure of the
cycle is 1000 kPa. For air, assume specific heat ratio ? = 1.4 and specific gas constant R = 0.287
kJ/kg.K, If the pressure and temperature at the beginning of the compression stroke are 100
kPa and 300 K, respectively, then the specific net work output of the cycle is ___________kJ/kg
(round off to two decimal places).
Ans: 708.8
Sol:

Given data
P1 = 100kPa, T1 = 300K, mep = 1000 kPa, ?? =1.4, efficiency(?? )=0.5, R = 0.287 kJ/kg-K
Using P1V1 = RT1
V1 =
0.287?300
100
=0.861?? 3
/????
Efficiency(?? )=1?
1
(?? )
?? ?1
where, r is the compression ratio = V1/V2
1?
1
(?? )
?? ?1
=0.5
1?
1
(?? )
1.4?1
=0.5
Or, r = 5.657
V1/V2 = 5.657
??? 2
=0.1522 m
3
/kg
Swept volume = V1 ? V2 = 0.861 ? 0.1522 = 0.7088 m
3
/kg
Went = Swept volume ??????? = 0.7088 ? 1000 = 708.8 kJ/kg

54. A through hole is drilled in an aluminum alloy plate of 15 mm thickness with a drill bit of
diameter 10 mm, at a feed of 0.25 mm/rev and a spindle speed of 1200 rpm. If the specific
energy required for cutting this material is 0.7 N.m/mm
3
, the power required for drilling is
_________W (round off to two decimal places).
Ans: 274.89
Sol: ?????? =
?? ?? 2
4
????????? ??????? ?????? ?????? =
?? (10)
2
4
?0.25?
1200
60
=125?? mm
3

Specific energy = 0.7 Nm/mm
3
So, power required for drilling = 0.7?125?? =274.89??




30

55. A horizontal cantilever beam of circular cross-section, length 1.0 m and flexural rigidity EI = 200
N.m
2
is subjected to an applied moment MA = 1.0 N-m at the free end as shown in the figure.
The magnitude of the vertical deflection of the free end is _____________mm (round off to one
decimal place).

Ans: 2.5
Sol: When the cantilever beam is subjected to moment at the free end, then the deflection at the free
end is given by
?? (???????? ?????? )
=
?? ?? 2
2????

So,
?? (???????? ?????? )
=
1?1
2
2?200
=2.5?10
?3
?? =2.5 ????


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