GATE SOLVED PAPER-ME GATE-2016-SET-1 Mechanical Engineering Notes | EduRev

ISRO, GATE & IES/ESE Mechanical Previous Year Solved Papers

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Mechanical Engineering : GATE SOLVED PAPER-ME GATE-2016-SET-1 Mechanical Engineering Notes | EduRev

 Page 1


Mechanical Paper Set-1 2016  Page 1
2016 paper set-I
Q.1-Q.5 carry one mark each.
Q1 Which of the following is CORRECT with respect 
to grammar and usage?
Mount Everest is ______.
(A) the highest peak in the world
(B) highest peak in the world
(C) one of highest peak in the world
(D) one of the highest peak in the world
s1 Correct option is (A)
Before superlative article ‘the’ has to be used. “one of” 
the expression should take plural noun and so option ‘C’ 
and ‘D’ can’t be the answer.
Q2 The policeman asked the victim of a theft, “What 
did you ______?”
(A) loose
(B) lose
(C) loss
(D) louse
s1 Correct option is (B)
‘lose’ is verb
Q3 Despite the new medicine’s ______ in treating 
diabetes, it is not ______ widely.
(A) effectiveness - prescribed
(B) availability - used
(C) prescription - available
(D) acceptance - proscribed
s1 Correct option is (A)
‘effectiveness’ is noun and ‘prescribed’ is verb. These 
words are apt and befitting with the word medicine’.
Q4 In a huge pile of apples and oranges, both ripe and 
unripe mixed together, 15% are unripe fruits. Of the 
unripe fruits, 45% are apples. Of the ripe ones, 66% are 
oranges. If the pile contains a total of 5692000 fruits, how 
many of them are apples?
(A) 2029198
(B) 2467482
(C) 2789080
(D) 3577422
s1 Correct option is (A)
 Total no. of fruits 5692000 =
  
100
45
100
15
5692000
##
=
  384210 =
 Ripe type of apples 
100
34
100
85
5692000
##
=
  1644988 =
` Total no. of apples 384210 1644988 =+
  2029198 =
Q5 Michael lives 10 km away from where I live. Ahmed 
lives 5 km away and Susan lives 7 km away from where 
I live. Arun is farther away than Ahmed but closer than 
Susan from where I live. From the information provided 
here, what is one possible distance (in km) at which I live 
from Arun’s place?
(A) 3.00
(B) 4.99
(C) 6.02
(D) 7.01
s1 Correct option is (C)
From given data, the following diagram is possible
 I = I live
 AH = Ahmed lives
 M = Michael lives
 S = Susan lives
 A = Arun lives
Q.6 to Q.10 carry two marks each.
Q6 A person moving through a tuberculosis prone zone 
has a 50% probability of becoming infected. However, 
only 30% of infected people develop the disease. What 
percentage of people moving through a tuberculosis prone 
zone remains infected but does not show symptoms of 
disease?
(A) 15
(B) 33
(C) 35
(D) 37
s1 Correct option is (C)
Page 2


Mechanical Paper Set-1 2016  Page 1
2016 paper set-I
Q.1-Q.5 carry one mark each.
Q1 Which of the following is CORRECT with respect 
to grammar and usage?
Mount Everest is ______.
(A) the highest peak in the world
(B) highest peak in the world
(C) one of highest peak in the world
(D) one of the highest peak in the world
s1 Correct option is (A)
Before superlative article ‘the’ has to be used. “one of” 
the expression should take plural noun and so option ‘C’ 
and ‘D’ can’t be the answer.
Q2 The policeman asked the victim of a theft, “What 
did you ______?”
(A) loose
(B) lose
(C) loss
(D) louse
s1 Correct option is (B)
‘lose’ is verb
Q3 Despite the new medicine’s ______ in treating 
diabetes, it is not ______ widely.
(A) effectiveness - prescribed
(B) availability - used
(C) prescription - available
(D) acceptance - proscribed
s1 Correct option is (A)
‘effectiveness’ is noun and ‘prescribed’ is verb. These 
words are apt and befitting with the word medicine’.
Q4 In a huge pile of apples and oranges, both ripe and 
unripe mixed together, 15% are unripe fruits. Of the 
unripe fruits, 45% are apples. Of the ripe ones, 66% are 
oranges. If the pile contains a total of 5692000 fruits, how 
many of them are apples?
(A) 2029198
(B) 2467482
(C) 2789080
(D) 3577422
s1 Correct option is (A)
 Total no. of fruits 5692000 =
  
100
45
100
15
5692000
##
=
  384210 =
 Ripe type of apples 
100
34
100
85
5692000
##
=
  1644988 =
` Total no. of apples 384210 1644988 =+
  2029198 =
Q5 Michael lives 10 km away from where I live. Ahmed 
lives 5 km away and Susan lives 7 km away from where 
I live. Arun is farther away than Ahmed but closer than 
Susan from where I live. From the information provided 
here, what is one possible distance (in km) at which I live 
from Arun’s place?
(A) 3.00
(B) 4.99
(C) 6.02
(D) 7.01
s1 Correct option is (C)
From given data, the following diagram is possible
 I = I live
 AH = Ahmed lives
 M = Michael lives
 S = Susan lives
 A = Arun lives
Q.6 to Q.10 carry two marks each.
Q6 A person moving through a tuberculosis prone zone 
has a 50% probability of becoming infected. However, 
only 30% of infected people develop the disease. What 
percentage of people moving through a tuberculosis prone 
zone remains infected but does not show symptoms of 
disease?
(A) 15
(B) 33
(C) 35
(D) 37
s1 Correct option is (C)
Page 2  Mechanical Paper Set-1 2016
  
100
70
100
50
#
=
100
35
&
  35 = %
` Option ‘C’ is correct.
Q7 In a world filled with uncertainty, he was glad to have 
many good friends. He had always assisted them in times 
of need and was confident that they would reciprocate. 
However, the events of the last week proved him wrong. 
Which of the following inference(s) is/are logically valid 
and can be inferred from the above passage?
(i) His friends were always asking him to help him.
(ii) He felt that when in need of help, his friends would 
let him down.
(iii) He was sure that his friends would help him when in 
need.
(iv) His friends did not help him last week.
(A) (i) and (ii)
(B) (iii) and (iv)
(C) (iii) only
(D) (iv) only
s1 Correct option is (B)
The words ‘was confident that they would reciprocate’ 
and ‘last week proved him wrong’ lead to statements (iii) 
and (iv) as logically valid inferences.
Q8 Leela is older than her cousin Pavithra. Pavithra’s 
brother Shiva is older than Leela. When Pavithra and 
Shiva are visiting Leela, all three like to play chess. 
Pavithra wins more often than Leela does.
Which one of the following statements must be True based 
on the above?
(A) When Shiva plays chess with Leela and Pavithra, he 
often loses.
(B) Leela is the oldest of the three.
(C) Shiva is a better chess player than Pavithra.
(D) Pavithra is the youngest of the three.
s1 Correct option is (D)
From given data, the following arrangement is possible.
Shiva
Leela
Pavithra
Among four alternatives, option (D) is TRUE.
Q9 if q
a
r
1
=
-
 and r
b
s
1
=
-
 and S
c
q
1
=
-
, the value of abc 
is ______ 
(A) rqs
1 -
^h
(B) 0
(C) 1
(D) rq s ++
s1 Correct option is (C)
 q
a -
 
r
1
=
q
1
a
&
  
r
1
= q
a
&
  r =
 r
b -
 
S
1
=
r
1
b
&
  
S
1
= S &
  r
b
=
 S
c -
 
q
1
=
s
1
c
&
  
q
1
= S
c
&
  q =
 q
a
 r = S
c a
& ^h
  r = S
ac
&
  r =
 S
ac b
^h S = S
abc
&
  S
1
=
` abc 1 =
` Option (C) is correct.
Q10 ,, PQ R and S are working on a project. Q can finish 
the task in 25 days, working alone for 12 hours a day. R 
can finish the task in 50 days, working alone for 12 hours 
per day. Q worked 12 hours a day but took sick leave in 
the beginning for two days. R worked 18 hours a day on 
all days. What is the ratio of work done by Q and R after 
7 days from the start of the project?
(A) 10:11
(B) 11:10
(C) 20:21
(D) 21:20
s1 Correct option is (C)
 Q can finish the task 25 = days, 12 hrs/day
  300 = hrs 1 & hr
  
300
1
= th
 R can finish the task 50 = days, 12 hrs/day
  50 12
#
=
  600 = hrs 1 & hr
  
600
1
= th
 Q Working hours 72 12 &
#
- ^h
  60 = hrs
 R Working hours 718 &
#
  126 = hrs
After 7 days, the ratio of Work done by Q and R.
 Q : R
Page 3


Mechanical Paper Set-1 2016  Page 1
2016 paper set-I
Q.1-Q.5 carry one mark each.
Q1 Which of the following is CORRECT with respect 
to grammar and usage?
Mount Everest is ______.
(A) the highest peak in the world
(B) highest peak in the world
(C) one of highest peak in the world
(D) one of the highest peak in the world
s1 Correct option is (A)
Before superlative article ‘the’ has to be used. “one of” 
the expression should take plural noun and so option ‘C’ 
and ‘D’ can’t be the answer.
Q2 The policeman asked the victim of a theft, “What 
did you ______?”
(A) loose
(B) lose
(C) loss
(D) louse
s1 Correct option is (B)
‘lose’ is verb
Q3 Despite the new medicine’s ______ in treating 
diabetes, it is not ______ widely.
(A) effectiveness - prescribed
(B) availability - used
(C) prescription - available
(D) acceptance - proscribed
s1 Correct option is (A)
‘effectiveness’ is noun and ‘prescribed’ is verb. These 
words are apt and befitting with the word medicine’.
Q4 In a huge pile of apples and oranges, both ripe and 
unripe mixed together, 15% are unripe fruits. Of the 
unripe fruits, 45% are apples. Of the ripe ones, 66% are 
oranges. If the pile contains a total of 5692000 fruits, how 
many of them are apples?
(A) 2029198
(B) 2467482
(C) 2789080
(D) 3577422
s1 Correct option is (A)
 Total no. of fruits 5692000 =
  
100
45
100
15
5692000
##
=
  384210 =
 Ripe type of apples 
100
34
100
85
5692000
##
=
  1644988 =
` Total no. of apples 384210 1644988 =+
  2029198 =
Q5 Michael lives 10 km away from where I live. Ahmed 
lives 5 km away and Susan lives 7 km away from where 
I live. Arun is farther away than Ahmed but closer than 
Susan from where I live. From the information provided 
here, what is one possible distance (in km) at which I live 
from Arun’s place?
(A) 3.00
(B) 4.99
(C) 6.02
(D) 7.01
s1 Correct option is (C)
From given data, the following diagram is possible
 I = I live
 AH = Ahmed lives
 M = Michael lives
 S = Susan lives
 A = Arun lives
Q.6 to Q.10 carry two marks each.
Q6 A person moving through a tuberculosis prone zone 
has a 50% probability of becoming infected. However, 
only 30% of infected people develop the disease. What 
percentage of people moving through a tuberculosis prone 
zone remains infected but does not show symptoms of 
disease?
(A) 15
(B) 33
(C) 35
(D) 37
s1 Correct option is (C)
Page 2  Mechanical Paper Set-1 2016
  
100
70
100
50
#
=
100
35
&
  35 = %
` Option ‘C’ is correct.
Q7 In a world filled with uncertainty, he was glad to have 
many good friends. He had always assisted them in times 
of need and was confident that they would reciprocate. 
However, the events of the last week proved him wrong. 
Which of the following inference(s) is/are logically valid 
and can be inferred from the above passage?
(i) His friends were always asking him to help him.
(ii) He felt that when in need of help, his friends would 
let him down.
(iii) He was sure that his friends would help him when in 
need.
(iv) His friends did not help him last week.
(A) (i) and (ii)
(B) (iii) and (iv)
(C) (iii) only
(D) (iv) only
s1 Correct option is (B)
The words ‘was confident that they would reciprocate’ 
and ‘last week proved him wrong’ lead to statements (iii) 
and (iv) as logically valid inferences.
Q8 Leela is older than her cousin Pavithra. Pavithra’s 
brother Shiva is older than Leela. When Pavithra and 
Shiva are visiting Leela, all three like to play chess. 
Pavithra wins more often than Leela does.
Which one of the following statements must be True based 
on the above?
(A) When Shiva plays chess with Leela and Pavithra, he 
often loses.
(B) Leela is the oldest of the three.
(C) Shiva is a better chess player than Pavithra.
(D) Pavithra is the youngest of the three.
s1 Correct option is (D)
From given data, the following arrangement is possible.
Shiva
Leela
Pavithra
Among four alternatives, option (D) is TRUE.
Q9 if q
a
r
1
=
-
 and r
b
s
1
=
-
 and S
c
q
1
=
-
, the value of abc 
is ______ 
(A) rqs
1 -
^h
(B) 0
(C) 1
(D) rq s ++
s1 Correct option is (C)
 q
a -
 
r
1
=
q
1
a
&
  
r
1
= q
a
&
  r =
 r
b -
 
S
1
=
r
1
b
&
  
S
1
= S &
  r
b
=
 S
c -
 
q
1
=
s
1
c
&
  
q
1
= S
c
&
  q =
 q
a
 r = S
c a
& ^h
  r = S
ac
&
  r =
 S
ac b
^h S = S
abc
&
  S
1
=
` abc 1 =
` Option (C) is correct.
Q10 ,, PQ R and S are working on a project. Q can finish 
the task in 25 days, working alone for 12 hours a day. R 
can finish the task in 50 days, working alone for 12 hours 
per day. Q worked 12 hours a day but took sick leave in 
the beginning for two days. R worked 18 hours a day on 
all days. What is the ratio of work done by Q and R after 
7 days from the start of the project?
(A) 10:11
(B) 11:10
(C) 20:21
(D) 21:20
s1 Correct option is (C)
 Q can finish the task 25 = days, 12 hrs/day
  300 = hrs 1 & hr
  
300
1
= th
 R can finish the task 50 = days, 12 hrs/day
  50 12
#
=
  600 = hrs 1 & hr
  
600
1
= th
 Q Working hours 72 12 &
#
- ^h
  60 = hrs
 R Working hours 718 &
#
  126 = hrs
After 7 days, the ratio of Work done by Q and R.
 Q : R
Mechanical Paper Set-1 2016  Page 3
 
300
60
 : 
600
126
  20 :  21
Q.11-Q.35 carry one mark each.
Q11 The solution to the system of equation is
 
x
y
2
4
5
3 -
>H*4 
2
30
=
-
)3 is 
(A) 6, 2
(B) , 62 -
(C) , 62 --
(D) , 62 -
s1 Correct option is (D)
 x 6 = , y 2 =- is the solution of equation
 xy 25 + 2 = and xy 43 -+ 30 =-
Q12 If ft ^h is a function defined for all t 0 > , its Laplace 
transform Fs ^h is defined as
(A) ef tdt
st
0
3
^h #
(B) ef tdt
st
0
3
-
^h #
(C) ef tdt
ist
0
3
^h #
(D) ef tdt
ist
0
3
-
^h #
s1 Correct option is (B)
By the definition of Laplace transform of ft t 0 > 6 ^h , we 
have
 Fs _i Lf t = ^h #-
  ef tdt
st
0
=
3
-
^h #
Q13 ,, fz ux yivx y =+ _ ^^ i hh is an analytic function of 
complex variable zx iy =+ where i 1 =- . If , ux y ^h
xy 2 = , then , vx y ^h may be expressed as
(A) xy
22
-+ + constant
(B) xy
22
-+ constant
(C) xy
22
++ constant
(D) xy
22
-+ + _i constant
s1 Correct option is (A)
Given u xy 2 = , ? v =
The Cauchy-Riemann equation
 u
x
 v
y
= & vu
xy
=- 
         are satisfying with option (A) xy
22
-+ + constant.
` , Vx y ^h xy
22
=- ++ constant.
Q14 Consider a Poisson distribution for the tossing of 
a biased coin. The mean for this distribution is µ . The 
standard deviation for this distribution is given by
(A) µ 
(B) 
2
µ 
(C) µ 
(D) 
1
µ 
s1 Correct option is (A)
For Poisson distribution mean =variance
 Given mean µ =
`  Variance µ =
` standard deviation µ =
Q15 Solve the equation cos x
x
10 = ^h using the Newton-
Raphson method. The initial guess is x
4
=
p 
. The value of 
the predicted root after the first iteration, up to second 
decimal, is ______
s1 Correct answer is 1.564
Let fx ^h cos xx 10 =-
^h
 & X
0
4
p 
= ak
Then fx l^h sin x 110 =+ ^h
 x
1
 x
fx
fx
0
0
0
=-
^
^
h
h
  
4
1
2
10
4
2
10
p 
=-
+
-
p 
_
_
i
i
  
.
.
4
8 0711
6 2857
&
p 
+
^
^
h
h
` x
1
 . 1 5641 =
Q16 A rigid ball of weight 100 N is suspended with the 
help of a string. The ball is pulled by a horizontal force 
F such that the string makes an angle of 30c with the 
vertical. The magnitude of force F (in N) is ______
s1 Correct answer is 57.735 N
By Lami’s theorem
 
sin
F
150c
 
sin120
100
c
= . 57 735 & N
Page 4


Mechanical Paper Set-1 2016  Page 1
2016 paper set-I
Q.1-Q.5 carry one mark each.
Q1 Which of the following is CORRECT with respect 
to grammar and usage?
Mount Everest is ______.
(A) the highest peak in the world
(B) highest peak in the world
(C) one of highest peak in the world
(D) one of the highest peak in the world
s1 Correct option is (A)
Before superlative article ‘the’ has to be used. “one of” 
the expression should take plural noun and so option ‘C’ 
and ‘D’ can’t be the answer.
Q2 The policeman asked the victim of a theft, “What 
did you ______?”
(A) loose
(B) lose
(C) loss
(D) louse
s1 Correct option is (B)
‘lose’ is verb
Q3 Despite the new medicine’s ______ in treating 
diabetes, it is not ______ widely.
(A) effectiveness - prescribed
(B) availability - used
(C) prescription - available
(D) acceptance - proscribed
s1 Correct option is (A)
‘effectiveness’ is noun and ‘prescribed’ is verb. These 
words are apt and befitting with the word medicine’.
Q4 In a huge pile of apples and oranges, both ripe and 
unripe mixed together, 15% are unripe fruits. Of the 
unripe fruits, 45% are apples. Of the ripe ones, 66% are 
oranges. If the pile contains a total of 5692000 fruits, how 
many of them are apples?
(A) 2029198
(B) 2467482
(C) 2789080
(D) 3577422
s1 Correct option is (A)
 Total no. of fruits 5692000 =
  
100
45
100
15
5692000
##
=
  384210 =
 Ripe type of apples 
100
34
100
85
5692000
##
=
  1644988 =
` Total no. of apples 384210 1644988 =+
  2029198 =
Q5 Michael lives 10 km away from where I live. Ahmed 
lives 5 km away and Susan lives 7 km away from where 
I live. Arun is farther away than Ahmed but closer than 
Susan from where I live. From the information provided 
here, what is one possible distance (in km) at which I live 
from Arun’s place?
(A) 3.00
(B) 4.99
(C) 6.02
(D) 7.01
s1 Correct option is (C)
From given data, the following diagram is possible
 I = I live
 AH = Ahmed lives
 M = Michael lives
 S = Susan lives
 A = Arun lives
Q.6 to Q.10 carry two marks each.
Q6 A person moving through a tuberculosis prone zone 
has a 50% probability of becoming infected. However, 
only 30% of infected people develop the disease. What 
percentage of people moving through a tuberculosis prone 
zone remains infected but does not show symptoms of 
disease?
(A) 15
(B) 33
(C) 35
(D) 37
s1 Correct option is (C)
Page 2  Mechanical Paper Set-1 2016
  
100
70
100
50
#
=
100
35
&
  35 = %
` Option ‘C’ is correct.
Q7 In a world filled with uncertainty, he was glad to have 
many good friends. He had always assisted them in times 
of need and was confident that they would reciprocate. 
However, the events of the last week proved him wrong. 
Which of the following inference(s) is/are logically valid 
and can be inferred from the above passage?
(i) His friends were always asking him to help him.
(ii) He felt that when in need of help, his friends would 
let him down.
(iii) He was sure that his friends would help him when in 
need.
(iv) His friends did not help him last week.
(A) (i) and (ii)
(B) (iii) and (iv)
(C) (iii) only
(D) (iv) only
s1 Correct option is (B)
The words ‘was confident that they would reciprocate’ 
and ‘last week proved him wrong’ lead to statements (iii) 
and (iv) as logically valid inferences.
Q8 Leela is older than her cousin Pavithra. Pavithra’s 
brother Shiva is older than Leela. When Pavithra and 
Shiva are visiting Leela, all three like to play chess. 
Pavithra wins more often than Leela does.
Which one of the following statements must be True based 
on the above?
(A) When Shiva plays chess with Leela and Pavithra, he 
often loses.
(B) Leela is the oldest of the three.
(C) Shiva is a better chess player than Pavithra.
(D) Pavithra is the youngest of the three.
s1 Correct option is (D)
From given data, the following arrangement is possible.
Shiva
Leela
Pavithra
Among four alternatives, option (D) is TRUE.
Q9 if q
a
r
1
=
-
 and r
b
s
1
=
-
 and S
c
q
1
=
-
, the value of abc 
is ______ 
(A) rqs
1 -
^h
(B) 0
(C) 1
(D) rq s ++
s1 Correct option is (C)
 q
a -
 
r
1
=
q
1
a
&
  
r
1
= q
a
&
  r =
 r
b -
 
S
1
=
r
1
b
&
  
S
1
= S &
  r
b
=
 S
c -
 
q
1
=
s
1
c
&
  
q
1
= S
c
&
  q =
 q
a
 r = S
c a
& ^h
  r = S
ac
&
  r =
 S
ac b
^h S = S
abc
&
  S
1
=
` abc 1 =
` Option (C) is correct.
Q10 ,, PQ R and S are working on a project. Q can finish 
the task in 25 days, working alone for 12 hours a day. R 
can finish the task in 50 days, working alone for 12 hours 
per day. Q worked 12 hours a day but took sick leave in 
the beginning for two days. R worked 18 hours a day on 
all days. What is the ratio of work done by Q and R after 
7 days from the start of the project?
(A) 10:11
(B) 11:10
(C) 20:21
(D) 21:20
s1 Correct option is (C)
 Q can finish the task 25 = days, 12 hrs/day
  300 = hrs 1 & hr
  
300
1
= th
 R can finish the task 50 = days, 12 hrs/day
  50 12
#
=
  600 = hrs 1 & hr
  
600
1
= th
 Q Working hours 72 12 &
#
- ^h
  60 = hrs
 R Working hours 718 &
#
  126 = hrs
After 7 days, the ratio of Work done by Q and R.
 Q : R
Mechanical Paper Set-1 2016  Page 3
 
300
60
 : 
600
126
  20 :  21
Q.11-Q.35 carry one mark each.
Q11 The solution to the system of equation is
 
x
y
2
4
5
3 -
>H*4 
2
30
=
-
)3 is 
(A) 6, 2
(B) , 62 -
(C) , 62 --
(D) , 62 -
s1 Correct option is (D)
 x 6 = , y 2 =- is the solution of equation
 xy 25 + 2 = and xy 43 -+ 30 =-
Q12 If ft ^h is a function defined for all t 0 > , its Laplace 
transform Fs ^h is defined as
(A) ef tdt
st
0
3
^h #
(B) ef tdt
st
0
3
-
^h #
(C) ef tdt
ist
0
3
^h #
(D) ef tdt
ist
0
3
-
^h #
s1 Correct option is (B)
By the definition of Laplace transform of ft t 0 > 6 ^h , we 
have
 Fs _i Lf t = ^h #-
  ef tdt
st
0
=
3
-
^h #
Q13 ,, fz ux yivx y =+ _ ^^ i hh is an analytic function of 
complex variable zx iy =+ where i 1 =- . If , ux y ^h
xy 2 = , then , vx y ^h may be expressed as
(A) xy
22
-+ + constant
(B) xy
22
-+ constant
(C) xy
22
++ constant
(D) xy
22
-+ + _i constant
s1 Correct option is (A)
Given u xy 2 = , ? v =
The Cauchy-Riemann equation
 u
x
 v
y
= & vu
xy
=- 
         are satisfying with option (A) xy
22
-+ + constant.
` , Vx y ^h xy
22
=- ++ constant.
Q14 Consider a Poisson distribution for the tossing of 
a biased coin. The mean for this distribution is µ . The 
standard deviation for this distribution is given by
(A) µ 
(B) 
2
µ 
(C) µ 
(D) 
1
µ 
s1 Correct option is (A)
For Poisson distribution mean =variance
 Given mean µ =
`  Variance µ =
` standard deviation µ =
Q15 Solve the equation cos x
x
10 = ^h using the Newton-
Raphson method. The initial guess is x
4
=
p 
. The value of 
the predicted root after the first iteration, up to second 
decimal, is ______
s1 Correct answer is 1.564
Let fx ^h cos xx 10 =-
^h
 & X
0
4
p 
= ak
Then fx l^h sin x 110 =+ ^h
 x
1
 x
fx
fx
0
0
0
=-
^
^
h
h
  
4
1
2
10
4
2
10
p 
=-
+
-
p 
_
_
i
i
  
.
.
4
8 0711
6 2857
&
p 
+
^
^
h
h
` x
1
 . 1 5641 =
Q16 A rigid ball of weight 100 N is suspended with the 
help of a string. The ball is pulled by a horizontal force 
F such that the string makes an angle of 30c with the 
vertical. The magnitude of force F (in N) is ______
s1 Correct answer is 57.735 N
By Lami’s theorem
 
sin
F
150c
 
sin120
100
c
= . 57 735 & N
Page 4  Mechanical Paper Set-1 2016
Q17 A point mass M is released from rest and slides 
down a spherical bowl (or radius R) from a height H 
as shown in the figure below. The surface of the bowl 
is smooth (no friction). The velocity of the mass at the 
bottom of the bowl is
(A) gH
(B) gR 2
(C) gH 2
(D) 0
s1 Correct option is (C)
By Energy Conservation
 mgH mv
2
1 2
=
  V &
  gH 2 =
Q18 The cross sections of two hollow bars made of the 
same material are concentric circles as shown in the figure. 
It is given that rr >
31
 and rr >
42
, and that the areas of 
the cross-sections are the same. J
1
 and J
2
 are the torsional 
rigidities of the bars on the left and right, respectively. 
The ratio 
J
J
1
2
 is
(A) >1
(B) <0.5
(C) =1
(D) between 0.5 and 1
s1 Correct option is (A)
Given, r
3
 r >
1
, rr >
42
 A
1
 = Area of cross section of bar 1 -
 A
2
 = Area of cross section of bar 2 -
 A
1
 A
2
=
 rr
2
2
1
2
& - 6@ rr
4
2
3
2
p =- 7A
` rr
2
2
1
2
- rr
4
2
3
2
=- rr
3
2
1
2
& -
  rr
4
2
2
2
=-
` 
J
J
1
2
 
rr
rr
2
4
1
4
2
4
4
3
4
=
-
-
p 
7
7
A
A
  
rr rr
rr rr
2
2
1
2
2
2
1
2
4
2
3
2
4
2
3
2
=
+-
+-
^^
^^
hh
hh
  
rr
rr
2
2
1
2
4
2
3
2
=
+
+
 rr rr
4
2
3
2
2
2
1
2
` -=- 7A
 
J
J
1
2
 1 > & rr rr >>
42 31
` 6@
Q19 A cantilever beam having square cross-section of 
side a is subjected to an end load. If a is increased by 
19%, the tip deflection decrease approximately by
(A) 19%
(B) 29%
(C) 41%
(D) 50%
s1 Correct option is (D)
 
1
d  
EI
W
3
1
3
=
 
1
2
d
d
 
. a
a
12
119
12
4
4
=
_
^
^
i
h
h
  
. 119
1
4
=
^h
  . 05 =
 
2
d  . 05
1
d = ^h
  
2
d  reduced by 50%
Q20 A car is moving on a curved horizontal road of radius 
100 m with a speed of 20 m/s. The rotating masses of the 
engine have an angular speed of 100 rad/s in clockwise 
direction when viewed from the front of the car. The 
combined moment of inertia of the rotating masses is 
10 kg-m
2
. The magnitude of the gyroscopic moment (in 
N-m) is ______
s1 Correct answer is 200
 R 100 = m,
 v 20 = m/sec
 
p
?  
R
v
=
  .
sec
rad
02 =
 
s
?  100 = rad/sec
 I Kg m 10
2
-
=
Page 5


Mechanical Paper Set-1 2016  Page 1
2016 paper set-I
Q.1-Q.5 carry one mark each.
Q1 Which of the following is CORRECT with respect 
to grammar and usage?
Mount Everest is ______.
(A) the highest peak in the world
(B) highest peak in the world
(C) one of highest peak in the world
(D) one of the highest peak in the world
s1 Correct option is (A)
Before superlative article ‘the’ has to be used. “one of” 
the expression should take plural noun and so option ‘C’ 
and ‘D’ can’t be the answer.
Q2 The policeman asked the victim of a theft, “What 
did you ______?”
(A) loose
(B) lose
(C) loss
(D) louse
s1 Correct option is (B)
‘lose’ is verb
Q3 Despite the new medicine’s ______ in treating 
diabetes, it is not ______ widely.
(A) effectiveness - prescribed
(B) availability - used
(C) prescription - available
(D) acceptance - proscribed
s1 Correct option is (A)
‘effectiveness’ is noun and ‘prescribed’ is verb. These 
words are apt and befitting with the word medicine’.
Q4 In a huge pile of apples and oranges, both ripe and 
unripe mixed together, 15% are unripe fruits. Of the 
unripe fruits, 45% are apples. Of the ripe ones, 66% are 
oranges. If the pile contains a total of 5692000 fruits, how 
many of them are apples?
(A) 2029198
(B) 2467482
(C) 2789080
(D) 3577422
s1 Correct option is (A)
 Total no. of fruits 5692000 =
  
100
45
100
15
5692000
##
=
  384210 =
 Ripe type of apples 
100
34
100
85
5692000
##
=
  1644988 =
` Total no. of apples 384210 1644988 =+
  2029198 =
Q5 Michael lives 10 km away from where I live. Ahmed 
lives 5 km away and Susan lives 7 km away from where 
I live. Arun is farther away than Ahmed but closer than 
Susan from where I live. From the information provided 
here, what is one possible distance (in km) at which I live 
from Arun’s place?
(A) 3.00
(B) 4.99
(C) 6.02
(D) 7.01
s1 Correct option is (C)
From given data, the following diagram is possible
 I = I live
 AH = Ahmed lives
 M = Michael lives
 S = Susan lives
 A = Arun lives
Q.6 to Q.10 carry two marks each.
Q6 A person moving through a tuberculosis prone zone 
has a 50% probability of becoming infected. However, 
only 30% of infected people develop the disease. What 
percentage of people moving through a tuberculosis prone 
zone remains infected but does not show symptoms of 
disease?
(A) 15
(B) 33
(C) 35
(D) 37
s1 Correct option is (C)
Page 2  Mechanical Paper Set-1 2016
  
100
70
100
50
#
=
100
35
&
  35 = %
` Option ‘C’ is correct.
Q7 In a world filled with uncertainty, he was glad to have 
many good friends. He had always assisted them in times 
of need and was confident that they would reciprocate. 
However, the events of the last week proved him wrong. 
Which of the following inference(s) is/are logically valid 
and can be inferred from the above passage?
(i) His friends were always asking him to help him.
(ii) He felt that when in need of help, his friends would 
let him down.
(iii) He was sure that his friends would help him when in 
need.
(iv) His friends did not help him last week.
(A) (i) and (ii)
(B) (iii) and (iv)
(C) (iii) only
(D) (iv) only
s1 Correct option is (B)
The words ‘was confident that they would reciprocate’ 
and ‘last week proved him wrong’ lead to statements (iii) 
and (iv) as logically valid inferences.
Q8 Leela is older than her cousin Pavithra. Pavithra’s 
brother Shiva is older than Leela. When Pavithra and 
Shiva are visiting Leela, all three like to play chess. 
Pavithra wins more often than Leela does.
Which one of the following statements must be True based 
on the above?
(A) When Shiva plays chess with Leela and Pavithra, he 
often loses.
(B) Leela is the oldest of the three.
(C) Shiva is a better chess player than Pavithra.
(D) Pavithra is the youngest of the three.
s1 Correct option is (D)
From given data, the following arrangement is possible.
Shiva
Leela
Pavithra
Among four alternatives, option (D) is TRUE.
Q9 if q
a
r
1
=
-
 and r
b
s
1
=
-
 and S
c
q
1
=
-
, the value of abc 
is ______ 
(A) rqs
1 -
^h
(B) 0
(C) 1
(D) rq s ++
s1 Correct option is (C)
 q
a -
 
r
1
=
q
1
a
&
  
r
1
= q
a
&
  r =
 r
b -
 
S
1
=
r
1
b
&
  
S
1
= S &
  r
b
=
 S
c -
 
q
1
=
s
1
c
&
  
q
1
= S
c
&
  q =
 q
a
 r = S
c a
& ^h
  r = S
ac
&
  r =
 S
ac b
^h S = S
abc
&
  S
1
=
` abc 1 =
` Option (C) is correct.
Q10 ,, PQ R and S are working on a project. Q can finish 
the task in 25 days, working alone for 12 hours a day. R 
can finish the task in 50 days, working alone for 12 hours 
per day. Q worked 12 hours a day but took sick leave in 
the beginning for two days. R worked 18 hours a day on 
all days. What is the ratio of work done by Q and R after 
7 days from the start of the project?
(A) 10:11
(B) 11:10
(C) 20:21
(D) 21:20
s1 Correct option is (C)
 Q can finish the task 25 = days, 12 hrs/day
  300 = hrs 1 & hr
  
300
1
= th
 R can finish the task 50 = days, 12 hrs/day
  50 12
#
=
  600 = hrs 1 & hr
  
600
1
= th
 Q Working hours 72 12 &
#
- ^h
  60 = hrs
 R Working hours 718 &
#
  126 = hrs
After 7 days, the ratio of Work done by Q and R.
 Q : R
Mechanical Paper Set-1 2016  Page 3
 
300
60
 : 
600
126
  20 :  21
Q.11-Q.35 carry one mark each.
Q11 The solution to the system of equation is
 
x
y
2
4
5
3 -
>H*4 
2
30
=
-
)3 is 
(A) 6, 2
(B) , 62 -
(C) , 62 --
(D) , 62 -
s1 Correct option is (D)
 x 6 = , y 2 =- is the solution of equation
 xy 25 + 2 = and xy 43 -+ 30 =-
Q12 If ft ^h is a function defined for all t 0 > , its Laplace 
transform Fs ^h is defined as
(A) ef tdt
st
0
3
^h #
(B) ef tdt
st
0
3
-
^h #
(C) ef tdt
ist
0
3
^h #
(D) ef tdt
ist
0
3
-
^h #
s1 Correct option is (B)
By the definition of Laplace transform of ft t 0 > 6 ^h , we 
have
 Fs _i Lf t = ^h #-
  ef tdt
st
0
=
3
-
^h #
Q13 ,, fz ux yivx y =+ _ ^^ i hh is an analytic function of 
complex variable zx iy =+ where i 1 =- . If , ux y ^h
xy 2 = , then , vx y ^h may be expressed as
(A) xy
22
-+ + constant
(B) xy
22
-+ constant
(C) xy
22
++ constant
(D) xy
22
-+ + _i constant
s1 Correct option is (A)
Given u xy 2 = , ? v =
The Cauchy-Riemann equation
 u
x
 v
y
= & vu
xy
=- 
         are satisfying with option (A) xy
22
-+ + constant.
` , Vx y ^h xy
22
=- ++ constant.
Q14 Consider a Poisson distribution for the tossing of 
a biased coin. The mean for this distribution is µ . The 
standard deviation for this distribution is given by
(A) µ 
(B) 
2
µ 
(C) µ 
(D) 
1
µ 
s1 Correct option is (A)
For Poisson distribution mean =variance
 Given mean µ =
`  Variance µ =
` standard deviation µ =
Q15 Solve the equation cos x
x
10 = ^h using the Newton-
Raphson method. The initial guess is x
4
=
p 
. The value of 
the predicted root after the first iteration, up to second 
decimal, is ______
s1 Correct answer is 1.564
Let fx ^h cos xx 10 =-
^h
 & X
0
4
p 
= ak
Then fx l^h sin x 110 =+ ^h
 x
1
 x
fx
fx
0
0
0
=-
^
^
h
h
  
4
1
2
10
4
2
10
p 
=-
+
-
p 
_
_
i
i
  
.
.
4
8 0711
6 2857
&
p 
+
^
^
h
h
` x
1
 . 1 5641 =
Q16 A rigid ball of weight 100 N is suspended with the 
help of a string. The ball is pulled by a horizontal force 
F such that the string makes an angle of 30c with the 
vertical. The magnitude of force F (in N) is ______
s1 Correct answer is 57.735 N
By Lami’s theorem
 
sin
F
150c
 
sin120
100
c
= . 57 735 & N
Page 4  Mechanical Paper Set-1 2016
Q17 A point mass M is released from rest and slides 
down a spherical bowl (or radius R) from a height H 
as shown in the figure below. The surface of the bowl 
is smooth (no friction). The velocity of the mass at the 
bottom of the bowl is
(A) gH
(B) gR 2
(C) gH 2
(D) 0
s1 Correct option is (C)
By Energy Conservation
 mgH mv
2
1 2
=
  V &
  gH 2 =
Q18 The cross sections of two hollow bars made of the 
same material are concentric circles as shown in the figure. 
It is given that rr >
31
 and rr >
42
, and that the areas of 
the cross-sections are the same. J
1
 and J
2
 are the torsional 
rigidities of the bars on the left and right, respectively. 
The ratio 
J
J
1
2
 is
(A) >1
(B) <0.5
(C) =1
(D) between 0.5 and 1
s1 Correct option is (A)
Given, r
3
 r >
1
, rr >
42
 A
1
 = Area of cross section of bar 1 -
 A
2
 = Area of cross section of bar 2 -
 A
1
 A
2
=
 rr
2
2
1
2
& - 6@ rr
4
2
3
2
p =- 7A
` rr
2
2
1
2
- rr
4
2
3
2
=- rr
3
2
1
2
& -
  rr
4
2
2
2
=-
` 
J
J
1
2
 
rr
rr
2
4
1
4
2
4
4
3
4
=
-
-
p 
7
7
A
A
  
rr rr
rr rr
2
2
1
2
2
2
1
2
4
2
3
2
4
2
3
2
=
+-
+-
^^
^^
hh
hh
  
rr
rr
2
2
1
2
4
2
3
2
=
+
+
 rr rr
4
2
3
2
2
2
1
2
` -=- 7A
 
J
J
1
2
 1 > & rr rr >>
42 31
` 6@
Q19 A cantilever beam having square cross-section of 
side a is subjected to an end load. If a is increased by 
19%, the tip deflection decrease approximately by
(A) 19%
(B) 29%
(C) 41%
(D) 50%
s1 Correct option is (D)
 
1
d  
EI
W
3
1
3
=
 
1
2
d
d
 
. a
a
12
119
12
4
4
=
_
^
^
i
h
h
  
. 119
1
4
=
^h
  . 05 =
 
2
d  . 05
1
d = ^h
  
2
d  reduced by 50%
Q20 A car is moving on a curved horizontal road of radius 
100 m with a speed of 20 m/s. The rotating masses of the 
engine have an angular speed of 100 rad/s in clockwise 
direction when viewed from the front of the car. The 
combined moment of inertia of the rotating masses is 
10 kg-m
2
. The magnitude of the gyroscopic moment (in 
N-m) is ______
s1 Correct answer is 200
 R 100 = m,
 v 20 = m/sec
 
p
?  
R
v
=
  .
sec
rad
02 =
 
s
?  100 = rad/sec
 I Kg m 10
2
-
=
Mechanical Paper Set-1 2016  Page 5
 Gyroscopic moment I
sp
ww
  . 10 02 100
##
= N-m
  200 = N-m
Q21 A single degree of freedom spring mass system with 
viscous damping has a spring constant of 10 kN/m. The 
system is excited by a sinusoidal force of amplitude 100 
N. If the damping factor (ratio) is 0.25, the amplitude of 
steady state oscillation at resonance is ______ mm.
s1 Correct answer is 20
 k 10 = kN/m
 F
0
 100 = N
 ?  . 025 =
 X 
12
k
F
2
2 2
nn
0
? 
=
-+
?
?
?
?
^ _
^
^
h i
h
h
 
n
w
w
 1 = at resonance
 X 
k
F
2
0
? 
=
  
. 2100 25 10
100
3
## #
=
  20 = mm
Q22 The spring constant of a helical compression spring 
DOES NOT depend on
(A) coil diameter
(B) material strength
(C) number of active turns
(D) wire diameter
s1 Correct option is (B)
Q23 The instantaneous stream-wise velocity of a turbulent 
flow is given as follows:
 ,, ,, , ux yz tu xy z ^^ hh ,, , ux yz t l^h
The time-average of the fluctuating velocity ,, , ux yz t l^h is
(A) 
u
2
l
(B) 
u
2
-
(C) zero
(D) 
u
2
s1 Correct option is (C)
Time average of fluctuating velocity is zero.
Q24 For a floating body, buoyant force acts at the
(A) centroid of the floating body
(B) center of gravity of the body
(C) centroid of the fluid vertically below the body
(D) centroid of the displaced fluid.
s1 Correct option is (D)
For floating body Buoyancy force acts through the centre 
of buoyancy which is C.G. for displaced volume.
Q25 A plastic sleeve of outer radius r 1
0
= mm covers 
a wire (radius . r 05 = mm) carrying electric current. 
Thermal conductivity of the plastic is 0.15 W/m-K. The 
heat transfer coefficient on the outer surface of the sleeve 
exposed to air is / Wm 25
2
-K. Due to the addition of 
the plastic cover, the heat transfer from the wire to the 
ambient will
(A) increase
(B) remain the same
(C) decrease
(D) be zero
s1 Correct option is (A)
 r
0
 1 = mm,
 k . 015 = W/m-K
 h / Wm 25
2
= -K
 r
c
 
h
k
0
= for cylindrical shape
  
.
25
015
1000
#
=
  . 01540
#
=
  6 = mm
` rr >
c 0
 & The heat transfer from the wire to the 
ambient will increase.
Q26 Which of the following statements are TRUE with 
respect to heat and work?
(i) They are boundary phenomena
(ii) They are exact differentials
(iii) They are path functions
(A) both (i) and (ii)
(B) both (i) and (iii)
(C) both (ii) and (iii)
(D) only (iii)
s1 Correct option is (B)
Q27 Propane CH
38 ^h is burned in an oxygen atmosphere 
with 10% deficit oxygen with respect to the stoichiometric 
requirement. Assuming no hydrocarbons in the products, 
the volume percentage of CO in the products is ______
s1 Correct answer is 14.29%
 CH O x
38 2
+ CO HO ab
22
" +
Carbon balance
 a 3 =
Hydrogen balance:
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