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# GATE SOLVED PAPER-ME GATE-2016-SET-2 Mechanical Engineering Notes | EduRev

## Mechanical Engineering : GATE SOLVED PAPER-ME GATE-2016-SET-2 Mechanical Engineering Notes | EduRev

``` Page 1

Mechanical Paper Set-2 2016  Page 1
2016 paper set-II
Q.1-Q.5 carry one mark each
Q1 The volume of a sphere of diameter 1 unit is
______ than the volume of a cube of side 1 unit.
(A) least
(B) less
(C) lesser
(D) low
s1 Correct option is (C)
â€˜Lesser thanâ€™ is apt because the sentence should be in
comparative degree.
Q2 The unruly crowd demanded that the accused be
______ without trial.
(A) hanged
(B) hanging
(C) hankering
(D) hung
s1 Correct option is (A)
â€˜hangedâ€™ means death by hanging â€˜hungâ€™ is used only with
things and not with people.
Q3 Choose the statement(s) where the underlined word
is used correctly.
(i) A prone is a dried plum.
(ii) He was lying prone on the floor.
(iii) People who eat a lot of fat are prone to heart disease.
(A) (i) and (iii) only
(B) (iii) only
(C) (i) and (ii) only
(D) (ii) and (iii) only
s1 Correct option is (D)
â€˜lying proneâ€™ means lie down flat. â€˜Prone toâ€™ means
vulnerable to.
Q4 Fact: If it rains, then the field is wet.
(i) It rains
(ii) The field is not wet
(iii) The field is wet
(iv) It did not rain
Which one of the options given below in NOT logically
possible, based on the given fact?
(A) If (iii), then (iv)
(B) If (i), then (iii)
(C) If (i), then (ii)
(D) If (ii), then (iv)
s1 Correct option is (C)
Statements (i) and (ii) are not logically possible based on
the given fact.
Q5 A window is made up of a square portion and an
equilateral triangle portion above it. The base of the
triangular portion coincides with the upper side of the
square. If the perimeter of the window is 6 m, the area of
the window in m
2
is ______
(A) 1.43
(B) 2.06
(C) 2.68
(D) 2.88
s1 Correct option is (B)
From the given data, the following window is possible
The perimeter of the window
x 5 =
6 = m
x
5
6
=
. 120 = m
Area of the window = Area of square+Area of e
l
T
.. . 12 12
4
3
12
2
##
=+ ^h
.. 1440 623 =+
.m 206
2
=
Q.6-Q.10 carry two marks each
Q6 Students taking an exam are divided into two groups,
P and Q such that each group has the same number
of students. The performance of each of the students in
a test was evaluated out of 200 marks. It was observed
that the mean of group P was 105, while that of group
Q was 85. The standard deviation of group P was 25,
while that of group, Q was 5. Assuming that the marks
were distributed on a normal distribution which of the
following statements will have the highest probability of
being TRUE?
(A) No students in group Q scored less marks than any
student in group P.
(B) No student in group P scored less marks than any
student in group Q.
Page 2

Mechanical Paper Set-2 2016  Page 1
2016 paper set-II
Q.1-Q.5 carry one mark each
Q1 The volume of a sphere of diameter 1 unit is
______ than the volume of a cube of side 1 unit.
(A) least
(B) less
(C) lesser
(D) low
s1 Correct option is (C)
â€˜Lesser thanâ€™ is apt because the sentence should be in
comparative degree.
Q2 The unruly crowd demanded that the accused be
______ without trial.
(A) hanged
(B) hanging
(C) hankering
(D) hung
s1 Correct option is (A)
â€˜hangedâ€™ means death by hanging â€˜hungâ€™ is used only with
things and not with people.
Q3 Choose the statement(s) where the underlined word
is used correctly.
(i) A prone is a dried plum.
(ii) He was lying prone on the floor.
(iii) People who eat a lot of fat are prone to heart disease.
(A) (i) and (iii) only
(B) (iii) only
(C) (i) and (ii) only
(D) (ii) and (iii) only
s1 Correct option is (D)
â€˜lying proneâ€™ means lie down flat. â€˜Prone toâ€™ means
vulnerable to.
Q4 Fact: If it rains, then the field is wet.
(i) It rains
(ii) The field is not wet
(iii) The field is wet
(iv) It did not rain
Which one of the options given below in NOT logically
possible, based on the given fact?
(A) If (iii), then (iv)
(B) If (i), then (iii)
(C) If (i), then (ii)
(D) If (ii), then (iv)
s1 Correct option is (C)
Statements (i) and (ii) are not logically possible based on
the given fact.
Q5 A window is made up of a square portion and an
equilateral triangle portion above it. The base of the
triangular portion coincides with the upper side of the
square. If the perimeter of the window is 6 m, the area of
the window in m
2
is ______
(A) 1.43
(B) 2.06
(C) 2.68
(D) 2.88
s1 Correct option is (B)
From the given data, the following window is possible
The perimeter of the window
x 5 =
6 = m
x
5
6
=
. 120 = m
Area of the window = Area of square+Area of e
l
T
.. . 12 12
4
3
12
2
##
=+ ^h
.. 1440 623 =+
.m 206
2
=
Q.6-Q.10 carry two marks each
Q6 Students taking an exam are divided into two groups,
P and Q such that each group has the same number
of students. The performance of each of the students in
a test was evaluated out of 200 marks. It was observed
that the mean of group P was 105, while that of group
Q was 85. The standard deviation of group P was 25,
while that of group, Q was 5. Assuming that the marks
were distributed on a normal distribution which of the
following statements will have the highest probability of
being TRUE?
(A) No students in group Q scored less marks than any
student in group P.
(B) No student in group P scored less marks than any
student in group Q.
Page 2  Mechanical Paper Set-2 2016
(C) Most students of group Q scored marks in a narrow-
er range than students in group P.
(D) The median of the marks of group P is 100.
s1 Correct option is (C)
Mean µ ^h 105 =
Standard deviation,
1
s ^h 25 =
` 68% within one standard deviation

1
µ
1
s =
105 25 =-
80 =

11
µs + 105 25 =+
130 =
Distribution of P
Group Q
Mean
2
µ ^h 85 =
Standard deviation, 2
s
^h 5 =
Pr x << µs µs -+ ^h . 0 6827 -
` 68% within one standard deviation

22
µs - 85 5 =-
80 =

22
µs + 85 5 =+
90 =
` range of Q in one standard deviation is 80 to 90
68% within one standard deviation of Q is narrower
` 68% within one standard deviation of Q means most
students of group Q.
` Most students of group Q [\ scored marks in a narrower
range than students in group P [\.
Q7 A smart city integrates all modes of transport, uses
clean energy and promotes sustainable use of resources.
It also uses technology to ensure safety and security of
the city, something which critics argue, will lead to a
surveillance state.
Which of the following can be logically inferred from the
above paragraph?
(i) All smart cities encourage the formation of surveillances
states.
(ii) Surveillances is an integral part of a smart city.
(iii) Sustainability and surveillance go hand in hand in a
smart city.
(iv) There is a perception that smart cities promote
surveillance.
(A) (i) and (iv) only
(B) (ii) and (iii) only
(C) (iv) only
(D) (i) only
s1 Correct option is (B)
Q8 Find the missing sequence in the letter series.
B, FH, LNP, ______
(A) SUWY
(B) TUVW
(C) TVXZ
(D) TWXZ
s1 Correct option is (C)
The following letter series is in the order of even letters
series.
Q9 The binary operation 4 is defined as ab ab
ab
4 =+
+ ^h
, where a and b are any two real number. The value of the
identity element of this operation, defined as the number
x such that ax a 4 = , for any a, is.
(A) 0
(B) 1
(C) 2
(D) 10
s1 Correct option is (A)
The binary operation 4 is defined
& ab 4 ab ab =+ + ^h
ax 4 a =
` From the equation b [\ is the variable
Option A: x 0 =
ao 4 a
a
0
0
#
=+
+ ^h
aa 0 =+ =
Option B: x 1 =
a 1 4 aa 11
#
=+ + ^h
aa 1 =+ +
a 21 =+
Option C: x 2 =
a 2 4 aa 22 &
#
++ ^h
aa 22 =+ +
a 32 =+
Option D: x 10 =
a 10 4 aa 10 10 &
#
++ ^h
Page 3

Mechanical Paper Set-2 2016  Page 1
2016 paper set-II
Q.1-Q.5 carry one mark each
Q1 The volume of a sphere of diameter 1 unit is
______ than the volume of a cube of side 1 unit.
(A) least
(B) less
(C) lesser
(D) low
s1 Correct option is (C)
â€˜Lesser thanâ€™ is apt because the sentence should be in
comparative degree.
Q2 The unruly crowd demanded that the accused be
______ without trial.
(A) hanged
(B) hanging
(C) hankering
(D) hung
s1 Correct option is (A)
â€˜hangedâ€™ means death by hanging â€˜hungâ€™ is used only with
things and not with people.
Q3 Choose the statement(s) where the underlined word
is used correctly.
(i) A prone is a dried plum.
(ii) He was lying prone on the floor.
(iii) People who eat a lot of fat are prone to heart disease.
(A) (i) and (iii) only
(B) (iii) only
(C) (i) and (ii) only
(D) (ii) and (iii) only
s1 Correct option is (D)
â€˜lying proneâ€™ means lie down flat. â€˜Prone toâ€™ means
vulnerable to.
Q4 Fact: If it rains, then the field is wet.
(i) It rains
(ii) The field is not wet
(iii) The field is wet
(iv) It did not rain
Which one of the options given below in NOT logically
possible, based on the given fact?
(A) If (iii), then (iv)
(B) If (i), then (iii)
(C) If (i), then (ii)
(D) If (ii), then (iv)
s1 Correct option is (C)
Statements (i) and (ii) are not logically possible based on
the given fact.
Q5 A window is made up of a square portion and an
equilateral triangle portion above it. The base of the
triangular portion coincides with the upper side of the
square. If the perimeter of the window is 6 m, the area of
the window in m
2
is ______
(A) 1.43
(B) 2.06
(C) 2.68
(D) 2.88
s1 Correct option is (B)
From the given data, the following window is possible
The perimeter of the window
x 5 =
6 = m
x
5
6
=
. 120 = m
Area of the window = Area of square+Area of e
l
T
.. . 12 12
4
3
12
2
##
=+ ^h
.. 1440 623 =+
.m 206
2
=
Q.6-Q.10 carry two marks each
Q6 Students taking an exam are divided into two groups,
P and Q such that each group has the same number
of students. The performance of each of the students in
a test was evaluated out of 200 marks. It was observed
that the mean of group P was 105, while that of group
Q was 85. The standard deviation of group P was 25,
while that of group, Q was 5. Assuming that the marks
were distributed on a normal distribution which of the
following statements will have the highest probability of
being TRUE?
(A) No students in group Q scored less marks than any
student in group P.
(B) No student in group P scored less marks than any
student in group Q.
Page 2  Mechanical Paper Set-2 2016
(C) Most students of group Q scored marks in a narrow-
er range than students in group P.
(D) The median of the marks of group P is 100.
s1 Correct option is (C)
Mean µ ^h 105 =
Standard deviation,
1
s ^h 25 =
` 68% within one standard deviation

1
µ
1
s =
105 25 =-
80 =

11
µs + 105 25 =+
130 =
Distribution of P
Group Q
Mean
2
µ ^h 85 =
Standard deviation, 2
s
^h 5 =
Pr x << µs µs -+ ^h . 0 6827 -
` 68% within one standard deviation

22
µs - 85 5 =-
80 =

22
µs + 85 5 =+
90 =
` range of Q in one standard deviation is 80 to 90
68% within one standard deviation of Q is narrower
` 68% within one standard deviation of Q means most
students of group Q.
` Most students of group Q [\ scored marks in a narrower
range than students in group P [\.
Q7 A smart city integrates all modes of transport, uses
clean energy and promotes sustainable use of resources.
It also uses technology to ensure safety and security of
the city, something which critics argue, will lead to a
surveillance state.
Which of the following can be logically inferred from the
above paragraph?
(i) All smart cities encourage the formation of surveillances
states.
(ii) Surveillances is an integral part of a smart city.
(iii) Sustainability and surveillance go hand in hand in a
smart city.
(iv) There is a perception that smart cities promote
surveillance.
(A) (i) and (iv) only
(B) (ii) and (iii) only
(C) (iv) only
(D) (i) only
s1 Correct option is (B)
Q8 Find the missing sequence in the letter series.
B, FH, LNP, ______
(A) SUWY
(B) TUVW
(C) TVXZ
(D) TWXZ
s1 Correct option is (C)
The following letter series is in the order of even letters
series.
Q9 The binary operation 4 is defined as ab ab
ab
4 =+
+ ^h
, where a and b are any two real number. The value of the
identity element of this operation, defined as the number
x such that ax a 4 = , for any a, is.
(A) 0
(B) 1
(C) 2
(D) 10
s1 Correct option is (A)
The binary operation 4 is defined
& ab 4 ab ab =+ + ^h
ax 4 a =
` From the equation b [\ is the variable
Option A: x 0 =
ao 4 a
a
0
0
#
=+
+ ^h
aa 0 =+ =
Option B: x 1 =
a 1 4 aa 11
#
=+ + ^h
aa 1 =+ +
a 21 =+
Option C: x 2 =
a 2 4 aa 22 &
#
++ ^h
aa 22 =+ +
a 32 =+
Option D: x 10 =
a 10 4 aa 10 10 &
#
++ ^h
Mechanical Paper Set-2 2016  Page 3
aa 10 10 =+ +
a 11 10 =+
` Option A only True.
Q10 Which of the following curves represents the function
ln ye
sin x
=
_
` ^
i
j h
for x 2 < p ? Here, x represents the
abscissa and y represents the ordinate.
s1 Correct option is (C)
Q.11-Q.35 carry one mark each.
Q11 The condition for which the eigen values of the
matrix A
k
2
1
1
= >H are positive, is
(A) / k 12 >
(B) k 2 >-
(C) k 0 >
(D) / k 12 <-
s1 Correct option is (A)
A
k
2
1
1
= >H
If ,
12
ll are eigen values of A
x 22
then
A
12
ll =
A k 21 =-
,
12
ll 0 >
k 21 - 0 >
` k
2
1
>
Q12 The values of x for which the function fx
xx
xx
34
34
2
2
=
+-
--
^h  is NOT continuous are
(A) 4 and 1 -
(B) 4 and 1
(C) 4 - and 1
(D) 4 - and -1
s1 Correct option is (C) 4 - and 1
The function, fx ^h
xx
xx
34
34
2
2
=
+-
--
is not defined at
x 1 = and x 4 =-
` The function fx ^h is not continuous at , x 41 =- .
Q13 Laplace transform of cos t ? ^h is
(A)
s
s
22
? +
(B)
s
22
w
w
+
(C)
s
s
22
? -
(D)
s
22
w
w
-
s1 Correct option is (A)
cos Lt ? ^h #-
s
s
22
?
=
+
cos Lat
sa
s
22
` =
+
^
b
h
l
#-
Q14 A function f of the complex variable zx iy =+ , is
given as ,, , fx yu xy xy =+ ^^ ^ hh h where , ux ykxy 2 = ^h and
, vx yx y
22
=- ^h . The value of k, for which the function is
analytic, is _____
s1 Correct answer is 1 -
Given, u kxy 2 = & vx y
22
=-
u
x
v
y
=
& ky 2 y 2 =-
` k 1 =-
Q15 Numerical integration using trapezoidal rule gives
the best result for a single variable function, which is
(A) linear
(B) parabolic
(C) logarithmic
(D) hyperbolic
s1 Correct option is (A)
fx ^h is a linear function.
Q16 A point mass having mass M is moving with a
velocity V at an angle ?  to the wall as shown in the
figure. The mass undergoes a perfectly elastic collision
with the smooth walls and rebounds. The total change
(final minus initial) in the momentum of the mass is
Page 4

Mechanical Paper Set-2 2016  Page 1
2016 paper set-II
Q.1-Q.5 carry one mark each
Q1 The volume of a sphere of diameter 1 unit is
______ than the volume of a cube of side 1 unit.
(A) least
(B) less
(C) lesser
(D) low
s1 Correct option is (C)
â€˜Lesser thanâ€™ is apt because the sentence should be in
comparative degree.
Q2 The unruly crowd demanded that the accused be
______ without trial.
(A) hanged
(B) hanging
(C) hankering
(D) hung
s1 Correct option is (A)
â€˜hangedâ€™ means death by hanging â€˜hungâ€™ is used only with
things and not with people.
Q3 Choose the statement(s) where the underlined word
is used correctly.
(i) A prone is a dried plum.
(ii) He was lying prone on the floor.
(iii) People who eat a lot of fat are prone to heart disease.
(A) (i) and (iii) only
(B) (iii) only
(C) (i) and (ii) only
(D) (ii) and (iii) only
s1 Correct option is (D)
â€˜lying proneâ€™ means lie down flat. â€˜Prone toâ€™ means
vulnerable to.
Q4 Fact: If it rains, then the field is wet.
(i) It rains
(ii) The field is not wet
(iii) The field is wet
(iv) It did not rain
Which one of the options given below in NOT logically
possible, based on the given fact?
(A) If (iii), then (iv)
(B) If (i), then (iii)
(C) If (i), then (ii)
(D) If (ii), then (iv)
s1 Correct option is (C)
Statements (i) and (ii) are not logically possible based on
the given fact.
Q5 A window is made up of a square portion and an
equilateral triangle portion above it. The base of the
triangular portion coincides with the upper side of the
square. If the perimeter of the window is 6 m, the area of
the window in m
2
is ______
(A) 1.43
(B) 2.06
(C) 2.68
(D) 2.88
s1 Correct option is (B)
From the given data, the following window is possible
The perimeter of the window
x 5 =
6 = m
x
5
6
=
. 120 = m
Area of the window = Area of square+Area of e
l
T
.. . 12 12
4
3
12
2
##
=+ ^h
.. 1440 623 =+
.m 206
2
=
Q.6-Q.10 carry two marks each
Q6 Students taking an exam are divided into two groups,
P and Q such that each group has the same number
of students. The performance of each of the students in
a test was evaluated out of 200 marks. It was observed
that the mean of group P was 105, while that of group
Q was 85. The standard deviation of group P was 25,
while that of group, Q was 5. Assuming that the marks
were distributed on a normal distribution which of the
following statements will have the highest probability of
being TRUE?
(A) No students in group Q scored less marks than any
student in group P.
(B) No student in group P scored less marks than any
student in group Q.
Page 2  Mechanical Paper Set-2 2016
(C) Most students of group Q scored marks in a narrow-
er range than students in group P.
(D) The median of the marks of group P is 100.
s1 Correct option is (C)
Mean µ ^h 105 =
Standard deviation,
1
s ^h 25 =
` 68% within one standard deviation

1
µ
1
s =
105 25 =-
80 =

11
µs + 105 25 =+
130 =
Distribution of P
Group Q
Mean
2
µ ^h 85 =
Standard deviation, 2
s
^h 5 =
Pr x << µs µs -+ ^h . 0 6827 -
` 68% within one standard deviation

22
µs - 85 5 =-
80 =

22
µs + 85 5 =+
90 =
` range of Q in one standard deviation is 80 to 90
68% within one standard deviation of Q is narrower
` 68% within one standard deviation of Q means most
students of group Q.
` Most students of group Q [\ scored marks in a narrower
range than students in group P [\.
Q7 A smart city integrates all modes of transport, uses
clean energy and promotes sustainable use of resources.
It also uses technology to ensure safety and security of
the city, something which critics argue, will lead to a
surveillance state.
Which of the following can be logically inferred from the
above paragraph?
(i) All smart cities encourage the formation of surveillances
states.
(ii) Surveillances is an integral part of a smart city.
(iii) Sustainability and surveillance go hand in hand in a
smart city.
(iv) There is a perception that smart cities promote
surveillance.
(A) (i) and (iv) only
(B) (ii) and (iii) only
(C) (iv) only
(D) (i) only
s1 Correct option is (B)
Q8 Find the missing sequence in the letter series.
B, FH, LNP, ______
(A) SUWY
(B) TUVW
(C) TVXZ
(D) TWXZ
s1 Correct option is (C)
The following letter series is in the order of even letters
series.
Q9 The binary operation 4 is defined as ab ab
ab
4 =+
+ ^h
, where a and b are any two real number. The value of the
identity element of this operation, defined as the number
x such that ax a 4 = , for any a, is.
(A) 0
(B) 1
(C) 2
(D) 10
s1 Correct option is (A)
The binary operation 4 is defined
& ab 4 ab ab =+ + ^h
ax 4 a =
` From the equation b [\ is the variable
Option A: x 0 =
ao 4 a
a
0
0
#
=+
+ ^h
aa 0 =+ =
Option B: x 1 =
a 1 4 aa 11
#
=+ + ^h
aa 1 =+ +
a 21 =+
Option C: x 2 =
a 2 4 aa 22 &
#
++ ^h
aa 22 =+ +
a 32 =+
Option D: x 10 =
a 10 4 aa 10 10 &
#
++ ^h
Mechanical Paper Set-2 2016  Page 3
aa 10 10 =+ +
a 11 10 =+
` Option A only True.
Q10 Which of the following curves represents the function
ln ye
sin x
=
_
` ^
i
j h
for x 2 < p ? Here, x represents the
abscissa and y represents the ordinate.
s1 Correct option is (C)
Q.11-Q.35 carry one mark each.
Q11 The condition for which the eigen values of the
matrix A
k
2
1
1
= >H are positive, is
(A) / k 12 >
(B) k 2 >-
(C) k 0 >
(D) / k 12 <-
s1 Correct option is (A)
A
k
2
1
1
= >H
If ,
12
ll are eigen values of A
x 22
then
A
12
ll =
A k 21 =-
,
12
ll 0 >
k 21 - 0 >
` k
2
1
>
Q12 The values of x for which the function fx
xx
xx
34
34
2
2
=
+-
--
^h  is NOT continuous are
(A) 4 and 1 -
(B) 4 and 1
(C) 4 - and 1
(D) 4 - and -1
s1 Correct option is (C) 4 - and 1
The function, fx ^h
xx
xx
34
34
2
2
=
+-
--
is not defined at
x 1 = and x 4 =-
` The function fx ^h is not continuous at , x 41 =- .
Q13 Laplace transform of cos t ? ^h is
(A)
s
s
22
? +
(B)
s
22
w
w
+
(C)
s
s
22
? -
(D)
s
22
w
w
-
s1 Correct option is (A)
cos Lt ? ^h #-
s
s
22
?
=
+
cos Lat
sa
s
22
` =
+
^
b
h
l
#-
Q14 A function f of the complex variable zx iy =+ , is
given as ,, , fx yu xy xy =+ ^^ ^ hh h where , ux ykxy 2 = ^h and
, vx yx y
22
=- ^h . The value of k, for which the function is
analytic, is _____
s1 Correct answer is 1 -
Given, u kxy 2 = & vx y
22
=-
u
x
v
y
=
& ky 2 y 2 =-
` k 1 =-
Q15 Numerical integration using trapezoidal rule gives
the best result for a single variable function, which is
(A) linear
(B) parabolic
(C) logarithmic
(D) hyperbolic
s1 Correct option is (A)
fx ^h is a linear function.
Q16 A point mass having mass M is moving with a
velocity V at an angle ?  to the wall as shown in the
figure. The mass undergoes a perfectly elastic collision
with the smooth walls and rebounds. The total change
(final minus initial) in the momentum of the mass is
Page 4  Mechanical Paper Set-2 2016
(A) cos MV j 2 ? -
t
(B) sin MV j 2 ?
t
(C) cos MV j 2 ?
t
(D) sin MV j 2 ? -
t
s1 Correct option is (D)
U
v
cossin Vi Vj qq =+
V
v
cossin Vi Vj qq =-
mv T mV U =- ^h
sin mV j 2 ? =-
Q17 A shaft with a circular cross-section is subjected to
pure twisting moment. The ratio of the maximum shear
stress to the largest principal stress is
(A) 2.0
(B) 1.0
(C) 0.5
(D) 0
s1 Correct option is (B)

max
1
s
t
1 =
Q18 A thin cylindrical pressure vessel with closed-ends is
subjected to internal pressure. The ratio of circumferential
(hoop) stress to the longitudinal stress is
(A) 0.25
(B) 0.50
(C) 1.0
(D) 2.0
s1 Correct option is (D)

l
h
s
s

t
pd
t
pd
4
2
=
_
^
i
h
2 =
Q19 The forces F
1
and F
2
in a brake band and the
direction of rotation of the drum are as shown in the
figure. The coefficient of friction is 0.25. The angle of
wrap is
2
3p
radians. It is given that R 1 = m and F21 =
N. The torque (in N-m) exerted on the drum is ______

F
F
2
1
e =
µ?
e
./ 0253 2
=
# p
. 3 248 =
` F
1
. 3 248 = N
Torque, T FF r
12 #
=- ^h

. 3 248 1
1
#
=
- ^h
. 2 248 = N-m
Q20 A single degree of freedom mass-spring-viscous
damper system with mass m, spring constant k and
viscous damping coefficient q is critically damped. The
correct relation among , mk and q is
(A) qkm 2 =
(B) qkm 2 =
(C) q
m
k 2
=
(D) q
m
k
2 =
s1 Correct option is (B)
Critical damping constant km 2 =
q km 2 =
Q21 A machine element XY , fixed at end X , is subjected
moment T at its free and Y . The most critical point from
the strength point of view is
(A) a point on the circumference at location Y
(B) a point at the center at location Y
(C) a point on the circumference at location X
Page 5

Mechanical Paper Set-2 2016  Page 1
2016 paper set-II
Q.1-Q.5 carry one mark each
Q1 The volume of a sphere of diameter 1 unit is
______ than the volume of a cube of side 1 unit.
(A) least
(B) less
(C) lesser
(D) low
s1 Correct option is (C)
â€˜Lesser thanâ€™ is apt because the sentence should be in
comparative degree.
Q2 The unruly crowd demanded that the accused be
______ without trial.
(A) hanged
(B) hanging
(C) hankering
(D) hung
s1 Correct option is (A)
â€˜hangedâ€™ means death by hanging â€˜hungâ€™ is used only with
things and not with people.
Q3 Choose the statement(s) where the underlined word
is used correctly.
(i) A prone is a dried plum.
(ii) He was lying prone on the floor.
(iii) People who eat a lot of fat are prone to heart disease.
(A) (i) and (iii) only
(B) (iii) only
(C) (i) and (ii) only
(D) (ii) and (iii) only
s1 Correct option is (D)
â€˜lying proneâ€™ means lie down flat. â€˜Prone toâ€™ means
vulnerable to.
Q4 Fact: If it rains, then the field is wet.
(i) It rains
(ii) The field is not wet
(iii) The field is wet
(iv) It did not rain
Which one of the options given below in NOT logically
possible, based on the given fact?
(A) If (iii), then (iv)
(B) If (i), then (iii)
(C) If (i), then (ii)
(D) If (ii), then (iv)
s1 Correct option is (C)
Statements (i) and (ii) are not logically possible based on
the given fact.
Q5 A window is made up of a square portion and an
equilateral triangle portion above it. The base of the
triangular portion coincides with the upper side of the
square. If the perimeter of the window is 6 m, the area of
the window in m
2
is ______
(A) 1.43
(B) 2.06
(C) 2.68
(D) 2.88
s1 Correct option is (B)
From the given data, the following window is possible
The perimeter of the window
x 5 =
6 = m
x
5
6
=
. 120 = m
Area of the window = Area of square+Area of e
l
T
.. . 12 12
4
3
12
2
##
=+ ^h
.. 1440 623 =+
.m 206
2
=
Q.6-Q.10 carry two marks each
Q6 Students taking an exam are divided into two groups,
P and Q such that each group has the same number
of students. The performance of each of the students in
a test was evaluated out of 200 marks. It was observed
that the mean of group P was 105, while that of group
Q was 85. The standard deviation of group P was 25,
while that of group, Q was 5. Assuming that the marks
were distributed on a normal distribution which of the
following statements will have the highest probability of
being TRUE?
(A) No students in group Q scored less marks than any
student in group P.
(B) No student in group P scored less marks than any
student in group Q.
Page 2  Mechanical Paper Set-2 2016
(C) Most students of group Q scored marks in a narrow-
er range than students in group P.
(D) The median of the marks of group P is 100.
s1 Correct option is (C)
Mean µ ^h 105 =
Standard deviation,
1
s ^h 25 =
` 68% within one standard deviation

1
µ
1
s =
105 25 =-
80 =

11
µs + 105 25 =+
130 =
Distribution of P
Group Q
Mean
2
µ ^h 85 =
Standard deviation, 2
s
^h 5 =
Pr x << µs µs -+ ^h . 0 6827 -
` 68% within one standard deviation

22
µs - 85 5 =-
80 =

22
µs + 85 5 =+
90 =
` range of Q in one standard deviation is 80 to 90
68% within one standard deviation of Q is narrower
` 68% within one standard deviation of Q means most
students of group Q.
` Most students of group Q [\ scored marks in a narrower
range than students in group P [\.
Q7 A smart city integrates all modes of transport, uses
clean energy and promotes sustainable use of resources.
It also uses technology to ensure safety and security of
the city, something which critics argue, will lead to a
surveillance state.
Which of the following can be logically inferred from the
above paragraph?
(i) All smart cities encourage the formation of surveillances
states.
(ii) Surveillances is an integral part of a smart city.
(iii) Sustainability and surveillance go hand in hand in a
smart city.
(iv) There is a perception that smart cities promote
surveillance.
(A) (i) and (iv) only
(B) (ii) and (iii) only
(C) (iv) only
(D) (i) only
s1 Correct option is (B)
Q8 Find the missing sequence in the letter series.
B, FH, LNP, ______
(A) SUWY
(B) TUVW
(C) TVXZ
(D) TWXZ
s1 Correct option is (C)
The following letter series is in the order of even letters
series.
Q9 The binary operation 4 is defined as ab ab
ab
4 =+
+ ^h
, where a and b are any two real number. The value of the
identity element of this operation, defined as the number
x such that ax a 4 = , for any a, is.
(A) 0
(B) 1
(C) 2
(D) 10
s1 Correct option is (A)
The binary operation 4 is defined
& ab 4 ab ab =+ + ^h
ax 4 a =
` From the equation b [\ is the variable
Option A: x 0 =
ao 4 a
a
0
0
#
=+
+ ^h
aa 0 =+ =
Option B: x 1 =
a 1 4 aa 11
#
=+ + ^h
aa 1 =+ +
a 21 =+
Option C: x 2 =
a 2 4 aa 22 &
#
++ ^h
aa 22 =+ +
a 32 =+
Option D: x 10 =
a 10 4 aa 10 10 &
#
++ ^h
Mechanical Paper Set-2 2016  Page 3
aa 10 10 =+ +
a 11 10 =+
` Option A only True.
Q10 Which of the following curves represents the function
ln ye
sin x
=
_
` ^
i
j h
for x 2 < p ? Here, x represents the
abscissa and y represents the ordinate.
s1 Correct option is (C)
Q.11-Q.35 carry one mark each.
Q11 The condition for which the eigen values of the
matrix A
k
2
1
1
= >H are positive, is
(A) / k 12 >
(B) k 2 >-
(C) k 0 >
(D) / k 12 <-
s1 Correct option is (A)
A
k
2
1
1
= >H
If ,
12
ll are eigen values of A
x 22
then
A
12
ll =
A k 21 =-
,
12
ll 0 >
k 21 - 0 >
` k
2
1
>
Q12 The values of x for which the function fx
xx
xx
34
34
2
2
=
+-
--
^h  is NOT continuous are
(A) 4 and 1 -
(B) 4 and 1
(C) 4 - and 1
(D) 4 - and -1
s1 Correct option is (C) 4 - and 1
The function, fx ^h
xx
xx
34
34
2
2
=
+-
--
is not defined at
x 1 = and x 4 =-
` The function fx ^h is not continuous at , x 41 =- .
Q13 Laplace transform of cos t ? ^h is
(A)
s
s
22
? +
(B)
s
22
w
w
+
(C)
s
s
22
? -
(D)
s
22
w
w
-
s1 Correct option is (A)
cos Lt ? ^h #-
s
s
22
?
=
+
cos Lat
sa
s
22
` =
+
^
b
h
l
#-
Q14 A function f of the complex variable zx iy =+ , is
given as ,, , fx yu xy xy =+ ^^ ^ hh h where , ux ykxy 2 = ^h and
, vx yx y
22
=- ^h . The value of k, for which the function is
analytic, is _____
s1 Correct answer is 1 -
Given, u kxy 2 = & vx y
22
=-
u
x
v
y
=
& ky 2 y 2 =-
` k 1 =-
Q15 Numerical integration using trapezoidal rule gives
the best result for a single variable function, which is
(A) linear
(B) parabolic
(C) logarithmic
(D) hyperbolic
s1 Correct option is (A)
fx ^h is a linear function.
Q16 A point mass having mass M is moving with a
velocity V at an angle ?  to the wall as shown in the
figure. The mass undergoes a perfectly elastic collision
with the smooth walls and rebounds. The total change
(final minus initial) in the momentum of the mass is
Page 4  Mechanical Paper Set-2 2016
(A) cos MV j 2 ? -
t
(B) sin MV j 2 ?
t
(C) cos MV j 2 ?
t
(D) sin MV j 2 ? -
t
s1 Correct option is (D)
U
v
cossin Vi Vj qq =+
V
v
cossin Vi Vj qq =-
mv T mV U =- ^h
sin mV j 2 ? =-
Q17 A shaft with a circular cross-section is subjected to
pure twisting moment. The ratio of the maximum shear
stress to the largest principal stress is
(A) 2.0
(B) 1.0
(C) 0.5
(D) 0
s1 Correct option is (B)

max
1
s
t
1 =
Q18 A thin cylindrical pressure vessel with closed-ends is
subjected to internal pressure. The ratio of circumferential
(hoop) stress to the longitudinal stress is
(A) 0.25
(B) 0.50
(C) 1.0
(D) 2.0
s1 Correct option is (D)

l
h
s
s

t
pd
t
pd
4
2
=
_
^
i
h
2 =
Q19 The forces F
1
and F
2
in a brake band and the
direction of rotation of the drum are as shown in the
figure. The coefficient of friction is 0.25. The angle of
wrap is
2
3p
radians. It is given that R 1 = m and F21 =
N. The torque (in N-m) exerted on the drum is ______

F
F
2
1
e =
µ?
e
./ 0253 2
=
# p
. 3 248 =
` F
1
. 3 248 = N
Torque, T FF r
12 #
=- ^h

. 3 248 1
1
#
=
- ^h
. 2 248 = N-m
Q20 A single degree of freedom mass-spring-viscous
damper system with mass m, spring constant k and
viscous damping coefficient q is critically damped. The
correct relation among , mk and q is
(A) qkm 2 =
(B) qkm 2 =
(C) q
m
k 2
=
(D) q
m
k
2 =
s1 Correct option is (B)
Critical damping constant km 2 =
q km 2 =
Q21 A machine element XY , fixed at end X , is subjected
moment T at its free and Y . The most critical point from
the strength point of view is
(A) a point on the circumference at location Y
(B) a point at the center at location Y
(C) a point on the circumference at location X
Mechanical Paper Set-2 2016  Page 5
(D) a point at the center at location X
s1 Correct option is (C)
At centre
b
s  0 = and torsional shear stress are zero.
Q22 For the brake shown in the figure, which one of the
following is TRUE?
(A) Self energizing for clockwise rotation of the drum
(B) Self energizing for anti-clockwise rotation of the
drum
(C) Self energizing for rotation in either direction of the
drum
(D) Not of the self energizing type
s1 Correct option is (A)
For clockwise rotation
M
pivot
/ 0 =
Fl Rx Ra
NN ## #
µ +- + 0 =
When applied moment and frictional moment are in same
direction is called self energizing brake.
Q23 The volumetric flow rate (per unit depth) between
two streamlines having stream functions
1
?  and
2
?  is
(A)
12
yy
(B)
12
yy
(C)
2
1
y
y
(D)
12
yy -
s1 Correct option is (D)
Q24 Assuming constant temperature condition and air
to be an ideal gas, the variation in atmospheric pressure
with height calculated from fluid statics is
(A) linear
(B) exponential
(D) cubic
s1 Correct option is (A)
Q25 A hollow cylinder has length L, inner radius r
1
,
2
, and thermal conductivity k. The thermal
resistance of the cylinder for radial conduction is
(A)
ln
kL 2
r
r
1
2
p
^h
(B)
ln
kL 2
r
r
2
1
p
^h
(C)
ln
kL 2
r
r
1
2
p
^h
(D)
ln
kL 2
r
r
2
1
p
^h
s1 Correct option is (A)
Q26 Consider the radiation heat exchange inside a
annulus between two very long concentric cylinders. The
radius of the outer cylinder is R
o
and that of the inner
cylinder is R
i
. The radiation view factor of the outer
cylinder onto itself is
(A)
R
R
1
o
i
-
(B)
R
R
1
o
i
-
(C)
R
R
1
/
o
i
13
-cm
(D)
R
R
1
o
i
-
s1 Correct option is (D)
F
11
0 =
F
12
1 =
F
21

A
A
F
2
1
12 #
=

RL
RL
2
2
1
o
i
#
p
p
=

R
R
o
i
=
```
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