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

## 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 ______
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 ______
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 ______
R 100 = m,
v 20 = m/sec

p
?
R
v
=
.
sec
02 =

s
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 ______
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 ______
R 100 = m,
v 20 = m/sec

p
?
R
v
=
.
sec
02 =

s
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.
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 ______
CH O x
38 2
+ CO HO ab
22
" +
Carbon balance
a 3 =
Hydrogen balance:
```
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