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

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

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)
‘Lesser than’ 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)
‘hanged’ means death by hanging ‘hung’ 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)
‘lying prone’ means lie down flat. ‘Prone to’ means 
vulnerable to.
Q4 Fact: If it rains, then the field is wet.
Read the following statements:
(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)
‘Lesser than’ 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)
‘hanged’ means death by hanging ‘hung’ 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)
‘lying prone’ means lie down flat. ‘Prone to’ means 
vulnerable to.
Q4 Fact: If it rains, then the field is wet.
Read the following statements:
(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)
‘Lesser than’ 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)
‘hanged’ means death by hanging ‘hung’ 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)
‘lying prone’ means lie down flat. ‘Prone to’ means 
vulnerable to.
Q4 Fact: If it rains, then the field is wet.
Read the following statements:
(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)
‘Lesser than’ 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)
‘hanged’ means death by hanging ‘hung’ 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)
‘lying prone’ means lie down flat. ‘Prone to’ means 
vulnerable to.
Q4 Fact: If it rains, then the field is wet.
Read the following statements:
(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 ______
s1 Correct answer is 2.248
 
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 
to and axial load P, transverse load F, and a twisting 
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)
‘Lesser than’ 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)
‘hanged’ means death by hanging ‘hung’ 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)
‘lying prone’ means lie down flat. ‘Prone to’ means 
vulnerable to.
Q4 Fact: If it rains, then the field is wet.
Read the following statements:
(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 ______
s1 Correct answer is 2.248
 
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 
to and axial load P, transverse load F, and a twisting 
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
(C) quadratic
(D) cubic
s1 Correct option is (A)
Q25 A hollow cylinder has length L, inner radius r
1
, 
outer radius r
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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