GATE SOLVED PAPER-ME GATE 2016 SET-III GATE Notes | EduRev

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GATE : GATE SOLVED PAPER-ME GATE 2016 SET-III GATE Notes | EduRev

 Page 1


Mechanical Paper Set-3 2016  Page 1
2016 paper set-III
Q.1-Q.5 carry one mark each.
Q1 Based on the given statements, select the appropriate 
option with respect to grammar and usage.
Statements:
(i) The height of Mr. X is 6 feet.
(ii) The height of Mr. Y is 5 feet.
(A) Mr. X is longer than Mr. Y.
(B) Mr. X is more elongated than Mr. Y.
(C) Mr. X is taller than Mr. Y.
(D) Mr. X is lengthier than Mr. Y.
s1 Correct option is (C)
In degrees of comparison Mr. X is taller than Mr. Y is apt.
Positive degree – tall
Comparative degree – taller
Superlative degree – tallest
Q2 The students ______ the teacher on teacher’s 
day for twenty years of dedicated teaching.
(A) facilitated
(B) felicitated
(C) fantasized
(D) facillitated
s1 Correct option is (B)
Felicitate means honour.
Q3 After india’s cricket world cup victory in 1985, 
Shrotria who was playing both tennis and cricket till then, 
decided to concentrate only on cricket. And the rest is 
history.
What does the underlined phrase mean in this context?
(A) history will rest in peace
(B) rest is recorded in history books
(C) rest is well known
(D) rest in archaic
s1 Correct option is (C)
‘rest in history’ is an idiomatic expression which means 
‘rest is well known.’
Q4 Given 
inches 9
/ 12
^h .yards 025
/ 12
= ^h
Which one of the following statements is TRUE?
(A) 3 inches=0.5 yards
(B) 9 inches=1.5 yards
(C) 9 inches=0.25 yards
(D) 81 inches =0.0625 yards
s1 Correct option is (C)
Q5 S, M, E and F are working in shifts in a team to finish 
a project. M works with twice the efficiency of others but 
for half as many days as E worked. S and M have 6 hour 
shifts in a day, whereas E and F have  12 hours shifts. 
What is the ratio of contribution of M to contribution of 
E in the project?
(A) 1:1
(B) 1:2
(C) 1:4
(D) 2:1
s1 Correct option is (B)
 M efficiency 2 = [efficiency of S, E and F]
Contribution of M in the project
  x = days 
#
 6 hrs 
#
 2
Contribution of E in the project
  x 2 = days 
#
 12 hrs 
#
 1
Contribution of M : Contribution of E
 x 62
##
 : x 2121
##
 1 : 2
Q.6-Q.10 Carry two marks each
Q6 The Venn diagram shows the preference of the 
student population for leisure activities.
From the data given, the number of students who like to 
read books or play sports is ______
(A) 44
(B) 51
(C) 79
(D) 108
s1 Correct option is (D)
 Read books n
R
= ^h
  12 44 713 =+ ++
  76 =
 Play sports n
s
= ^h
  4471715 =+ ++
  83 =
 nR S k ^h 44 7 =+
  51 =
 nR S j ^h nR nS nR S k =+ - ^^ ^ hh h
Page 2


Mechanical Paper Set-3 2016  Page 1
2016 paper set-III
Q.1-Q.5 carry one mark each.
Q1 Based on the given statements, select the appropriate 
option with respect to grammar and usage.
Statements:
(i) The height of Mr. X is 6 feet.
(ii) The height of Mr. Y is 5 feet.
(A) Mr. X is longer than Mr. Y.
(B) Mr. X is more elongated than Mr. Y.
(C) Mr. X is taller than Mr. Y.
(D) Mr. X is lengthier than Mr. Y.
s1 Correct option is (C)
In degrees of comparison Mr. X is taller than Mr. Y is apt.
Positive degree – tall
Comparative degree – taller
Superlative degree – tallest
Q2 The students ______ the teacher on teacher’s 
day for twenty years of dedicated teaching.
(A) facilitated
(B) felicitated
(C) fantasized
(D) facillitated
s1 Correct option is (B)
Felicitate means honour.
Q3 After india’s cricket world cup victory in 1985, 
Shrotria who was playing both tennis and cricket till then, 
decided to concentrate only on cricket. And the rest is 
history.
What does the underlined phrase mean in this context?
(A) history will rest in peace
(B) rest is recorded in history books
(C) rest is well known
(D) rest in archaic
s1 Correct option is (C)
‘rest in history’ is an idiomatic expression which means 
‘rest is well known.’
Q4 Given 
inches 9
/ 12
^h .yards 025
/ 12
= ^h
Which one of the following statements is TRUE?
(A) 3 inches=0.5 yards
(B) 9 inches=1.5 yards
(C) 9 inches=0.25 yards
(D) 81 inches =0.0625 yards
s1 Correct option is (C)
Q5 S, M, E and F are working in shifts in a team to finish 
a project. M works with twice the efficiency of others but 
for half as many days as E worked. S and M have 6 hour 
shifts in a day, whereas E and F have  12 hours shifts. 
What is the ratio of contribution of M to contribution of 
E in the project?
(A) 1:1
(B) 1:2
(C) 1:4
(D) 2:1
s1 Correct option is (B)
 M efficiency 2 = [efficiency of S, E and F]
Contribution of M in the project
  x = days 
#
 6 hrs 
#
 2
Contribution of E in the project
  x 2 = days 
#
 12 hrs 
#
 1
Contribution of M : Contribution of E
 x 62
##
 : x 2121
##
 1 : 2
Q.6-Q.10 Carry two marks each
Q6 The Venn diagram shows the preference of the 
student population for leisure activities.
From the data given, the number of students who like to 
read books or play sports is ______
(A) 44
(B) 51
(C) 79
(D) 108
s1 Correct option is (D)
 Read books n
R
= ^h
  12 44 713 =+ ++
  76 =
 Play sports n
s
= ^h
  4471715 =+ ++
  83 =
 nR S k ^h 44 7 =+
  51 =
 nR S j ^h nR nS nR S k =+ - ^^ ^ hh h
Page 2  Mechanical Paper Set-3 2016
  76 83 51 =+ -
  108 =
Q7 Social science disciplines were in existence in an 
amorphous form until the colonial period when they were 
institutionalized. In varying degrees, they were intended 
to further the colonial interest In the time of globalization 
and the economic rise postcolonial countries like India. 
Conventional ways of knowledge production have become 
obsolete.
Which of the following can be logically inferred from the 
above statements?
(i) Social science disciplines have become obsolete
(ii) Social science disciplines had a pre colonial origin
(iii) Social science disciplines always promote colonialism.
(iv) Social science must maintain disciplinary boundaries.
(A) (ii) only
(B) (i) and (iii) only
(C) (ii) and (iv) only
(D) (iii) and (iv) only
s1 Correct option is (A)
Until the colonial period means pre-colonial origin. Other 
options can’t be inferred.
Q8 Two and a quarter hours back, when seen in a mirror, 
the reflection of a wall clock without number markings 
seemed to shown 1:30. What is the actual current time 
shown by the clock?
(A) 8:15
(B) 11:15
(C) 12:15
(D) 12:45
s1 Correct option is (D)
 Time back 2
4
1
=
  2 = hrs 15 min
 Clock time (C.T.)+Mirror time (M.T.) 12 =
1.30 60
`  C.T. . 12 00 =
  
.
.
130
10 30
` The actual time shown by the clock .. 10 30 215 =+
  . 12 45 =
Q9 M and N start from the same location. M travels 
10 km East and then 10 km. North-East. N travels 5 
km south-East. What is the shortest distance (in km) 
between M and N at the end of their travel?
(A) 18.60
(B) 22.50
(C) 20.61
(D) 25.00
s1 Correct option is (C)
From the given data, the following diagram is possible
 cos45c 
DE
4
=
 DE cos454
#
c =
  . 2 828 = km
 sin45c 
EN
4
=
 EN sin454
#
c =
  . 2 828 = km
 sin45c 
EN
4
=
 EN sin454
#
c =
  . 2 828 = km
 CN NE CE =+
  . 2 828 5 =+
  . 7 828 = km
 CB AB AC =-
  . 10 2 828 =-
  . 7 171 = km
 NB
2
^h NC BC
22
=+ ^^ hh
  .. 7 828 7 171
22
=+ ^^ hh
` NB .. 7 828 7 171
22
=+ ^^ hh
  . 10 616 = l,
` NM NB BM =+
  . 10 616 10 =+
  . 20 61 = km
Q10 A wire of length 340 mm is to be cut into two parts. 
One of the parts is to be made into a square and the 
other into a rectangular where sides are in the ratio of 1:2. 
What is the length of the side of the square (in mm) such 
that the combined area of the square and the rectangular 
is a MINIMUM?
(A) 30
(B) 40
(C) 120
(D) 180
s1 Correct option is (B)
 Length of the wire 340 = m
Page 3


Mechanical Paper Set-3 2016  Page 1
2016 paper set-III
Q.1-Q.5 carry one mark each.
Q1 Based on the given statements, select the appropriate 
option with respect to grammar and usage.
Statements:
(i) The height of Mr. X is 6 feet.
(ii) The height of Mr. Y is 5 feet.
(A) Mr. X is longer than Mr. Y.
(B) Mr. X is more elongated than Mr. Y.
(C) Mr. X is taller than Mr. Y.
(D) Mr. X is lengthier than Mr. Y.
s1 Correct option is (C)
In degrees of comparison Mr. X is taller than Mr. Y is apt.
Positive degree – tall
Comparative degree – taller
Superlative degree – tallest
Q2 The students ______ the teacher on teacher’s 
day for twenty years of dedicated teaching.
(A) facilitated
(B) felicitated
(C) fantasized
(D) facillitated
s1 Correct option is (B)
Felicitate means honour.
Q3 After india’s cricket world cup victory in 1985, 
Shrotria who was playing both tennis and cricket till then, 
decided to concentrate only on cricket. And the rest is 
history.
What does the underlined phrase mean in this context?
(A) history will rest in peace
(B) rest is recorded in history books
(C) rest is well known
(D) rest in archaic
s1 Correct option is (C)
‘rest in history’ is an idiomatic expression which means 
‘rest is well known.’
Q4 Given 
inches 9
/ 12
^h .yards 025
/ 12
= ^h
Which one of the following statements is TRUE?
(A) 3 inches=0.5 yards
(B) 9 inches=1.5 yards
(C) 9 inches=0.25 yards
(D) 81 inches =0.0625 yards
s1 Correct option is (C)
Q5 S, M, E and F are working in shifts in a team to finish 
a project. M works with twice the efficiency of others but 
for half as many days as E worked. S and M have 6 hour 
shifts in a day, whereas E and F have  12 hours shifts. 
What is the ratio of contribution of M to contribution of 
E in the project?
(A) 1:1
(B) 1:2
(C) 1:4
(D) 2:1
s1 Correct option is (B)
 M efficiency 2 = [efficiency of S, E and F]
Contribution of M in the project
  x = days 
#
 6 hrs 
#
 2
Contribution of E in the project
  x 2 = days 
#
 12 hrs 
#
 1
Contribution of M : Contribution of E
 x 62
##
 : x 2121
##
 1 : 2
Q.6-Q.10 Carry two marks each
Q6 The Venn diagram shows the preference of the 
student population for leisure activities.
From the data given, the number of students who like to 
read books or play sports is ______
(A) 44
(B) 51
(C) 79
(D) 108
s1 Correct option is (D)
 Read books n
R
= ^h
  12 44 713 =+ ++
  76 =
 Play sports n
s
= ^h
  4471715 =+ ++
  83 =
 nR S k ^h 44 7 =+
  51 =
 nR S j ^h nR nS nR S k =+ - ^^ ^ hh h
Page 2  Mechanical Paper Set-3 2016
  76 83 51 =+ -
  108 =
Q7 Social science disciplines were in existence in an 
amorphous form until the colonial period when they were 
institutionalized. In varying degrees, they were intended 
to further the colonial interest In the time of globalization 
and the economic rise postcolonial countries like India. 
Conventional ways of knowledge production have become 
obsolete.
Which of the following can be logically inferred from the 
above statements?
(i) Social science disciplines have become obsolete
(ii) Social science disciplines had a pre colonial origin
(iii) Social science disciplines always promote colonialism.
(iv) Social science must maintain disciplinary boundaries.
(A) (ii) only
(B) (i) and (iii) only
(C) (ii) and (iv) only
(D) (iii) and (iv) only
s1 Correct option is (A)
Until the colonial period means pre-colonial origin. Other 
options can’t be inferred.
Q8 Two and a quarter hours back, when seen in a mirror, 
the reflection of a wall clock without number markings 
seemed to shown 1:30. What is the actual current time 
shown by the clock?
(A) 8:15
(B) 11:15
(C) 12:15
(D) 12:45
s1 Correct option is (D)
 Time back 2
4
1
=
  2 = hrs 15 min
 Clock time (C.T.)+Mirror time (M.T.) 12 =
1.30 60
`  C.T. . 12 00 =
  
.
.
130
10 30
` The actual time shown by the clock .. 10 30 215 =+
  . 12 45 =
Q9 M and N start from the same location. M travels 
10 km East and then 10 km. North-East. N travels 5 
km south-East. What is the shortest distance (in km) 
between M and N at the end of their travel?
(A) 18.60
(B) 22.50
(C) 20.61
(D) 25.00
s1 Correct option is (C)
From the given data, the following diagram is possible
 cos45c 
DE
4
=
 DE cos454
#
c =
  . 2 828 = km
 sin45c 
EN
4
=
 EN sin454
#
c =
  . 2 828 = km
 sin45c 
EN
4
=
 EN sin454
#
c =
  . 2 828 = km
 CN NE CE =+
  . 2 828 5 =+
  . 7 828 = km
 CB AB AC =-
  . 10 2 828 =-
  . 7 171 = km
 NB
2
^h NC BC
22
=+ ^^ hh
  .. 7 828 7 171
22
=+ ^^ hh
` NB .. 7 828 7 171
22
=+ ^^ hh
  . 10 616 = l,
` NM NB BM =+
  . 10 616 10 =+
  . 20 61 = km
Q10 A wire of length 340 mm is to be cut into two parts. 
One of the parts is to be made into a square and the 
other into a rectangular where sides are in the ratio of 1:2. 
What is the length of the side of the square (in mm) such 
that the combined area of the square and the rectangular 
is a MINIMUM?
(A) 30
(B) 40
(C) 120
(D) 180
s1 Correct option is (B)
 Length of the wire 340 = m
Mechanical Paper Set-3 2016  Page 3
Perimeter of rectangle
  
xx
2
33
2
=+
:D
  x 2 =
Perimeter of square
  x 340 2 =-
 Side of square 
x
4
340 2
=
-
 Total area = Area of square+Area of rectangle
  
xx x
4
340 2
33
2
2
#
=
-
+ :D
  
xx
4
340 2
3
2
2 2
=
-
+ :D
 Combined area of square+rectangle = minimum
 fx ^h 0 =
 fx ^h 
x
x
4
340 2
9
2
2
2
=
-
+ :D
 fx l^h x
x
9
4
4
340 2
=-
-
  0 =
 x
9
4
 x
4
1
340 2 =- 6@ x 90 & =
 side of square 
x
4
340 2
=
-
  40 = mm
Q.11-Q.35 carry one mark each.
Q11 A real square matrix A is called skew-symmetric if
(A) AA
T
=
(B) AA
T 1
=
-
(C) AA
T
=-
(D) AA A
T 1
=+
-
s1 Correct option is (C)
By using definition
A real square matrix A is said to be skew-symmetric 
matrix if
 A
T
 A =- (or) a
ij
a
ji ij
6 =-
Q12 
log
Lt
e
x
1
14
x
x
e
0
3
-
+
"
^h
 is equal to
(A) 0
(B) 
12
1
(C) 
3
4
(D) 1
s1 Correct option is (C)
 
log
Lt
e
x
1
14
x
x
0
3
-
+
"
^h
 lim
e 3
4
x
x
x
0
3
14
1
=
"
+
^h
  
3
4
=
Q13 Solution of Laplace’s equation having continuous 
second order partial derivatives are called 
(A) biharmonic functions
(B) harmonic functions
(C) conjugate harmonic functions
(D) error functions
s1 Correct option is (B)
The solution of Laplace’s equation having continuous 2nd 
order partial derivatives is called a harmonic function.
Q14 The area (in percentage under standard normal 
distribution curve of random variable Z within limits 
from 3 - to 3 + is ______
s1 Correct answer is 99.73
In the standard normal curve the area between 3 - & 3 
is 0.9973
` Percentage of area is 99.73
Q15 The root of the function fx xx 1
3
=+ - ^h obtained 
after first iteration on application of Newton-Raphson 
scheme using an initial guess of x 1
0
= is
(A) 0.682
(B) 0.686
(C) 0.750
(D) 1.000
s1  Correct option is (C)
Let fx ^h xx 1
3
=+ - & x 1
0
=
Then fx l_i x 31
2
=+
 x
1
 x
fx
fx
0
0
0
=-
l^
^
h
h
  1
31
111
=-
+
+-
^
^
h
h
  . 075 =
Q16 A force F is acting on a bent bar which is clamped 
at one end as shown in the figure.
The CORRECT free body diagram is 
Page 4


Mechanical Paper Set-3 2016  Page 1
2016 paper set-III
Q.1-Q.5 carry one mark each.
Q1 Based on the given statements, select the appropriate 
option with respect to grammar and usage.
Statements:
(i) The height of Mr. X is 6 feet.
(ii) The height of Mr. Y is 5 feet.
(A) Mr. X is longer than Mr. Y.
(B) Mr. X is more elongated than Mr. Y.
(C) Mr. X is taller than Mr. Y.
(D) Mr. X is lengthier than Mr. Y.
s1 Correct option is (C)
In degrees of comparison Mr. X is taller than Mr. Y is apt.
Positive degree – tall
Comparative degree – taller
Superlative degree – tallest
Q2 The students ______ the teacher on teacher’s 
day for twenty years of dedicated teaching.
(A) facilitated
(B) felicitated
(C) fantasized
(D) facillitated
s1 Correct option is (B)
Felicitate means honour.
Q3 After india’s cricket world cup victory in 1985, 
Shrotria who was playing both tennis and cricket till then, 
decided to concentrate only on cricket. And the rest is 
history.
What does the underlined phrase mean in this context?
(A) history will rest in peace
(B) rest is recorded in history books
(C) rest is well known
(D) rest in archaic
s1 Correct option is (C)
‘rest in history’ is an idiomatic expression which means 
‘rest is well known.’
Q4 Given 
inches 9
/ 12
^h .yards 025
/ 12
= ^h
Which one of the following statements is TRUE?
(A) 3 inches=0.5 yards
(B) 9 inches=1.5 yards
(C) 9 inches=0.25 yards
(D) 81 inches =0.0625 yards
s1 Correct option is (C)
Q5 S, M, E and F are working in shifts in a team to finish 
a project. M works with twice the efficiency of others but 
for half as many days as E worked. S and M have 6 hour 
shifts in a day, whereas E and F have  12 hours shifts. 
What is the ratio of contribution of M to contribution of 
E in the project?
(A) 1:1
(B) 1:2
(C) 1:4
(D) 2:1
s1 Correct option is (B)
 M efficiency 2 = [efficiency of S, E and F]
Contribution of M in the project
  x = days 
#
 6 hrs 
#
 2
Contribution of E in the project
  x 2 = days 
#
 12 hrs 
#
 1
Contribution of M : Contribution of E
 x 62
##
 : x 2121
##
 1 : 2
Q.6-Q.10 Carry two marks each
Q6 The Venn diagram shows the preference of the 
student population for leisure activities.
From the data given, the number of students who like to 
read books or play sports is ______
(A) 44
(B) 51
(C) 79
(D) 108
s1 Correct option is (D)
 Read books n
R
= ^h
  12 44 713 =+ ++
  76 =
 Play sports n
s
= ^h
  4471715 =+ ++
  83 =
 nR S k ^h 44 7 =+
  51 =
 nR S j ^h nR nS nR S k =+ - ^^ ^ hh h
Page 2  Mechanical Paper Set-3 2016
  76 83 51 =+ -
  108 =
Q7 Social science disciplines were in existence in an 
amorphous form until the colonial period when they were 
institutionalized. In varying degrees, they were intended 
to further the colonial interest In the time of globalization 
and the economic rise postcolonial countries like India. 
Conventional ways of knowledge production have become 
obsolete.
Which of the following can be logically inferred from the 
above statements?
(i) Social science disciplines have become obsolete
(ii) Social science disciplines had a pre colonial origin
(iii) Social science disciplines always promote colonialism.
(iv) Social science must maintain disciplinary boundaries.
(A) (ii) only
(B) (i) and (iii) only
(C) (ii) and (iv) only
(D) (iii) and (iv) only
s1 Correct option is (A)
Until the colonial period means pre-colonial origin. Other 
options can’t be inferred.
Q8 Two and a quarter hours back, when seen in a mirror, 
the reflection of a wall clock without number markings 
seemed to shown 1:30. What is the actual current time 
shown by the clock?
(A) 8:15
(B) 11:15
(C) 12:15
(D) 12:45
s1 Correct option is (D)
 Time back 2
4
1
=
  2 = hrs 15 min
 Clock time (C.T.)+Mirror time (M.T.) 12 =
1.30 60
`  C.T. . 12 00 =
  
.
.
130
10 30
` The actual time shown by the clock .. 10 30 215 =+
  . 12 45 =
Q9 M and N start from the same location. M travels 
10 km East and then 10 km. North-East. N travels 5 
km south-East. What is the shortest distance (in km) 
between M and N at the end of their travel?
(A) 18.60
(B) 22.50
(C) 20.61
(D) 25.00
s1 Correct option is (C)
From the given data, the following diagram is possible
 cos45c 
DE
4
=
 DE cos454
#
c =
  . 2 828 = km
 sin45c 
EN
4
=
 EN sin454
#
c =
  . 2 828 = km
 sin45c 
EN
4
=
 EN sin454
#
c =
  . 2 828 = km
 CN NE CE =+
  . 2 828 5 =+
  . 7 828 = km
 CB AB AC =-
  . 10 2 828 =-
  . 7 171 = km
 NB
2
^h NC BC
22
=+ ^^ hh
  .. 7 828 7 171
22
=+ ^^ hh
` NB .. 7 828 7 171
22
=+ ^^ hh
  . 10 616 = l,
` NM NB BM =+
  . 10 616 10 =+
  . 20 61 = km
Q10 A wire of length 340 mm is to be cut into two parts. 
One of the parts is to be made into a square and the 
other into a rectangular where sides are in the ratio of 1:2. 
What is the length of the side of the square (in mm) such 
that the combined area of the square and the rectangular 
is a MINIMUM?
(A) 30
(B) 40
(C) 120
(D) 180
s1 Correct option is (B)
 Length of the wire 340 = m
Mechanical Paper Set-3 2016  Page 3
Perimeter of rectangle
  
xx
2
33
2
=+
:D
  x 2 =
Perimeter of square
  x 340 2 =-
 Side of square 
x
4
340 2
=
-
 Total area = Area of square+Area of rectangle
  
xx x
4
340 2
33
2
2
#
=
-
+ :D
  
xx
4
340 2
3
2
2 2
=
-
+ :D
 Combined area of square+rectangle = minimum
 fx ^h 0 =
 fx ^h 
x
x
4
340 2
9
2
2
2
=
-
+ :D
 fx l^h x
x
9
4
4
340 2
=-
-
  0 =
 x
9
4
 x
4
1
340 2 =- 6@ x 90 & =
 side of square 
x
4
340 2
=
-
  40 = mm
Q.11-Q.35 carry one mark each.
Q11 A real square matrix A is called skew-symmetric if
(A) AA
T
=
(B) AA
T 1
=
-
(C) AA
T
=-
(D) AA A
T 1
=+
-
s1 Correct option is (C)
By using definition
A real square matrix A is said to be skew-symmetric 
matrix if
 A
T
 A =- (or) a
ij
a
ji ij
6 =-
Q12 
log
Lt
e
x
1
14
x
x
e
0
3
-
+
"
^h
 is equal to
(A) 0
(B) 
12
1
(C) 
3
4
(D) 1
s1 Correct option is (C)
 
log
Lt
e
x
1
14
x
x
0
3
-
+
"
^h
 lim
e 3
4
x
x
x
0
3
14
1
=
"
+
^h
  
3
4
=
Q13 Solution of Laplace’s equation having continuous 
second order partial derivatives are called 
(A) biharmonic functions
(B) harmonic functions
(C) conjugate harmonic functions
(D) error functions
s1 Correct option is (B)
The solution of Laplace’s equation having continuous 2nd 
order partial derivatives is called a harmonic function.
Q14 The area (in percentage under standard normal 
distribution curve of random variable Z within limits 
from 3 - to 3 + is ______
s1 Correct answer is 99.73
In the standard normal curve the area between 3 - & 3 
is 0.9973
` Percentage of area is 99.73
Q15 The root of the function fx xx 1
3
=+ - ^h obtained 
after first iteration on application of Newton-Raphson 
scheme using an initial guess of x 1
0
= is
(A) 0.682
(B) 0.686
(C) 0.750
(D) 1.000
s1  Correct option is (C)
Let fx ^h xx 1
3
=+ - & x 1
0
=
Then fx l_i x 31
2
=+
 x
1
 x
fx
fx
0
0
0
=-
l^
^
h
h
  1
31
111
=-
+
+-
^
^
h
h
  . 075 =
Q16 A force F is acting on a bent bar which is clamped 
at one end as shown in the figure.
The CORRECT free body diagram is 
Page 4  Mechanical Paper Set-3 2016
s1 Correct option is (A)
Q17 The cross-section of two solid bars made of the same 
material are shown in the figure. The square cross-section 
has flexural (bending) rigidity I
1
, while the circular cross-
section has flexural rigidity I
2
. Both sections have the 
same cross-sectional area. The ratio 
I
I
2
1
 is
(A) 
1
p 
(B) 
2
p 
(C) 
3
p 
(D) 
6
p 
s1 Correct option is (C)
 a
2
 r
2
p =
 
I
I
2
1
 
d
a
64
12
4
4
=
p 
  
3
p 
=
Q18 The state of stress at a point on a element is shown 
in figure (a). The same state of stress is shown in another 
coordinate system in figure (b).
            
The components ,,
xx yy xy
tt t
^h
 are given by
(A) /, /, pp 22 0 -
_i
(B) ,,p 00 ^h
(C) ,, / pp 2 -- ^h
(D) ,, / p 00 2 ^h
s1 Correct option is (B)
 At the plane ?  45c = (in Mohr circle 90c ? = )
 
1
s  
2
s =
  0 =
 
xx
t  
yy
t =
  0 =
 
xy
t  p =
Q19 A rigid link PQ is undergoing plane motion as shown 
in the figure (V
P
 and V
Q
 are non-zero). 
V
QP
 is the relative velocity of point Q with respect to 
point P.
Which one of the following is TRUE?
(A) V
QP
 has components along and perpendicular to PQ
(B) V
QP
 has only one component directed from P to Q
(C) V
QP
 has only one component directed from Q to P
(D) V
QP
 has only one component perpendicular to PQ
s1 Correct option is (D)
 V
Q
 VV
PPQ
=+
Page 5


Mechanical Paper Set-3 2016  Page 1
2016 paper set-III
Q.1-Q.5 carry one mark each.
Q1 Based on the given statements, select the appropriate 
option with respect to grammar and usage.
Statements:
(i) The height of Mr. X is 6 feet.
(ii) The height of Mr. Y is 5 feet.
(A) Mr. X is longer than Mr. Y.
(B) Mr. X is more elongated than Mr. Y.
(C) Mr. X is taller than Mr. Y.
(D) Mr. X is lengthier than Mr. Y.
s1 Correct option is (C)
In degrees of comparison Mr. X is taller than Mr. Y is apt.
Positive degree – tall
Comparative degree – taller
Superlative degree – tallest
Q2 The students ______ the teacher on teacher’s 
day for twenty years of dedicated teaching.
(A) facilitated
(B) felicitated
(C) fantasized
(D) facillitated
s1 Correct option is (B)
Felicitate means honour.
Q3 After india’s cricket world cup victory in 1985, 
Shrotria who was playing both tennis and cricket till then, 
decided to concentrate only on cricket. And the rest is 
history.
What does the underlined phrase mean in this context?
(A) history will rest in peace
(B) rest is recorded in history books
(C) rest is well known
(D) rest in archaic
s1 Correct option is (C)
‘rest in history’ is an idiomatic expression which means 
‘rest is well known.’
Q4 Given 
inches 9
/ 12
^h .yards 025
/ 12
= ^h
Which one of the following statements is TRUE?
(A) 3 inches=0.5 yards
(B) 9 inches=1.5 yards
(C) 9 inches=0.25 yards
(D) 81 inches =0.0625 yards
s1 Correct option is (C)
Q5 S, M, E and F are working in shifts in a team to finish 
a project. M works with twice the efficiency of others but 
for half as many days as E worked. S and M have 6 hour 
shifts in a day, whereas E and F have  12 hours shifts. 
What is the ratio of contribution of M to contribution of 
E in the project?
(A) 1:1
(B) 1:2
(C) 1:4
(D) 2:1
s1 Correct option is (B)
 M efficiency 2 = [efficiency of S, E and F]
Contribution of M in the project
  x = days 
#
 6 hrs 
#
 2
Contribution of E in the project
  x 2 = days 
#
 12 hrs 
#
 1
Contribution of M : Contribution of E
 x 62
##
 : x 2121
##
 1 : 2
Q.6-Q.10 Carry two marks each
Q6 The Venn diagram shows the preference of the 
student population for leisure activities.
From the data given, the number of students who like to 
read books or play sports is ______
(A) 44
(B) 51
(C) 79
(D) 108
s1 Correct option is (D)
 Read books n
R
= ^h
  12 44 713 =+ ++
  76 =
 Play sports n
s
= ^h
  4471715 =+ ++
  83 =
 nR S k ^h 44 7 =+
  51 =
 nR S j ^h nR nS nR S k =+ - ^^ ^ hh h
Page 2  Mechanical Paper Set-3 2016
  76 83 51 =+ -
  108 =
Q7 Social science disciplines were in existence in an 
amorphous form until the colonial period when they were 
institutionalized. In varying degrees, they were intended 
to further the colonial interest In the time of globalization 
and the economic rise postcolonial countries like India. 
Conventional ways of knowledge production have become 
obsolete.
Which of the following can be logically inferred from the 
above statements?
(i) Social science disciplines have become obsolete
(ii) Social science disciplines had a pre colonial origin
(iii) Social science disciplines always promote colonialism.
(iv) Social science must maintain disciplinary boundaries.
(A) (ii) only
(B) (i) and (iii) only
(C) (ii) and (iv) only
(D) (iii) and (iv) only
s1 Correct option is (A)
Until the colonial period means pre-colonial origin. Other 
options can’t be inferred.
Q8 Two and a quarter hours back, when seen in a mirror, 
the reflection of a wall clock without number markings 
seemed to shown 1:30. What is the actual current time 
shown by the clock?
(A) 8:15
(B) 11:15
(C) 12:15
(D) 12:45
s1 Correct option is (D)
 Time back 2
4
1
=
  2 = hrs 15 min
 Clock time (C.T.)+Mirror time (M.T.) 12 =
1.30 60
`  C.T. . 12 00 =
  
.
.
130
10 30
` The actual time shown by the clock .. 10 30 215 =+
  . 12 45 =
Q9 M and N start from the same location. M travels 
10 km East and then 10 km. North-East. N travels 5 
km south-East. What is the shortest distance (in km) 
between M and N at the end of their travel?
(A) 18.60
(B) 22.50
(C) 20.61
(D) 25.00
s1 Correct option is (C)
From the given data, the following diagram is possible
 cos45c 
DE
4
=
 DE cos454
#
c =
  . 2 828 = km
 sin45c 
EN
4
=
 EN sin454
#
c =
  . 2 828 = km
 sin45c 
EN
4
=
 EN sin454
#
c =
  . 2 828 = km
 CN NE CE =+
  . 2 828 5 =+
  . 7 828 = km
 CB AB AC =-
  . 10 2 828 =-
  . 7 171 = km
 NB
2
^h NC BC
22
=+ ^^ hh
  .. 7 828 7 171
22
=+ ^^ hh
` NB .. 7 828 7 171
22
=+ ^^ hh
  . 10 616 = l,
` NM NB BM =+
  . 10 616 10 =+
  . 20 61 = km
Q10 A wire of length 340 mm is to be cut into two parts. 
One of the parts is to be made into a square and the 
other into a rectangular where sides are in the ratio of 1:2. 
What is the length of the side of the square (in mm) such 
that the combined area of the square and the rectangular 
is a MINIMUM?
(A) 30
(B) 40
(C) 120
(D) 180
s1 Correct option is (B)
 Length of the wire 340 = m
Mechanical Paper Set-3 2016  Page 3
Perimeter of rectangle
  
xx
2
33
2
=+
:D
  x 2 =
Perimeter of square
  x 340 2 =-
 Side of square 
x
4
340 2
=
-
 Total area = Area of square+Area of rectangle
  
xx x
4
340 2
33
2
2
#
=
-
+ :D
  
xx
4
340 2
3
2
2 2
=
-
+ :D
 Combined area of square+rectangle = minimum
 fx ^h 0 =
 fx ^h 
x
x
4
340 2
9
2
2
2
=
-
+ :D
 fx l^h x
x
9
4
4
340 2
=-
-
  0 =
 x
9
4
 x
4
1
340 2 =- 6@ x 90 & =
 side of square 
x
4
340 2
=
-
  40 = mm
Q.11-Q.35 carry one mark each.
Q11 A real square matrix A is called skew-symmetric if
(A) AA
T
=
(B) AA
T 1
=
-
(C) AA
T
=-
(D) AA A
T 1
=+
-
s1 Correct option is (C)
By using definition
A real square matrix A is said to be skew-symmetric 
matrix if
 A
T
 A =- (or) a
ij
a
ji ij
6 =-
Q12 
log
Lt
e
x
1
14
x
x
e
0
3
-
+
"
^h
 is equal to
(A) 0
(B) 
12
1
(C) 
3
4
(D) 1
s1 Correct option is (C)
 
log
Lt
e
x
1
14
x
x
0
3
-
+
"
^h
 lim
e 3
4
x
x
x
0
3
14
1
=
"
+
^h
  
3
4
=
Q13 Solution of Laplace’s equation having continuous 
second order partial derivatives are called 
(A) biharmonic functions
(B) harmonic functions
(C) conjugate harmonic functions
(D) error functions
s1 Correct option is (B)
The solution of Laplace’s equation having continuous 2nd 
order partial derivatives is called a harmonic function.
Q14 The area (in percentage under standard normal 
distribution curve of random variable Z within limits 
from 3 - to 3 + is ______
s1 Correct answer is 99.73
In the standard normal curve the area between 3 - & 3 
is 0.9973
` Percentage of area is 99.73
Q15 The root of the function fx xx 1
3
=+ - ^h obtained 
after first iteration on application of Newton-Raphson 
scheme using an initial guess of x 1
0
= is
(A) 0.682
(B) 0.686
(C) 0.750
(D) 1.000
s1  Correct option is (C)
Let fx ^h xx 1
3
=+ - & x 1
0
=
Then fx l_i x 31
2
=+
 x
1
 x
fx
fx
0
0
0
=-
l^
^
h
h
  1
31
111
=-
+
+-
^
^
h
h
  . 075 =
Q16 A force F is acting on a bent bar which is clamped 
at one end as shown in the figure.
The CORRECT free body diagram is 
Page 4  Mechanical Paper Set-3 2016
s1 Correct option is (A)
Q17 The cross-section of two solid bars made of the same 
material are shown in the figure. The square cross-section 
has flexural (bending) rigidity I
1
, while the circular cross-
section has flexural rigidity I
2
. Both sections have the 
same cross-sectional area. The ratio 
I
I
2
1
 is
(A) 
1
p 
(B) 
2
p 
(C) 
3
p 
(D) 
6
p 
s1 Correct option is (C)
 a
2
 r
2
p =
 
I
I
2
1
 
d
a
64
12
4
4
=
p 
  
3
p 
=
Q18 The state of stress at a point on a element is shown 
in figure (a). The same state of stress is shown in another 
coordinate system in figure (b).
            
The components ,,
xx yy xy
tt t
^h
 are given by
(A) /, /, pp 22 0 -
_i
(B) ,,p 00 ^h
(C) ,, / pp 2 -- ^h
(D) ,, / p 00 2 ^h
s1 Correct option is (B)
 At the plane ?  45c = (in Mohr circle 90c ? = )
 
1
s  
2
s =
  0 =
 
xx
t  
yy
t =
  0 =
 
xy
t  p =
Q19 A rigid link PQ is undergoing plane motion as shown 
in the figure (V
P
 and V
Q
 are non-zero). 
V
QP
 is the relative velocity of point Q with respect to 
point P.
Which one of the following is TRUE?
(A) V
QP
 has components along and perpendicular to PQ
(B) V
QP
 has only one component directed from P to Q
(C) V
QP
 has only one component directed from Q to P
(D) V
QP
 has only one component perpendicular to PQ
s1 Correct option is (D)
 V
Q
 VV
PPQ
=+
Mechanical Paper Set-3 2016  Page 5
Q20 The number of degrees of freedom in a planar 
mechanism having n links and j simple hinge joints is
(A) nj 33 2 -- ^h
(B) j 31 2 -- ^h
(C) nj 32 -
(D) jn 23 4 -+
s1 Correct option is (B)
“Grubler”s equation.
Q21 The static deflection of a spring under gravity, 
when a mass of 1 kg is suspended from it, is 1 mm. 
Assume the acceleration due to gravity / gm s 10
2
= . The 
natural frequency of this spring mass system (in rad/s) is 
______.
s1 Correct answer is 100
 
n
?  
g
d 
=
  
110
10
3
#
=
-
  100 = rad/sec
Q22 Which of the bearings given below SHOULD NOT 
be subjected to a thrust load?
(A) Deep groove ball bearing
(B) Angular contact ball bearing
(C) Cylindrical (Straight) roller bearing
(D) Single row tapered roller bearing
s1 Correct option is (C)
Q23 A channel of width 450 mm branches into two sub-
channels having width 300 mm and 200 mm as shown 
in figure. If the volumetric flow rate (taking unit depth) 
of an incompressible flow through the main channel is 
./ ms 09
3
 and the velocity in the sub-channel of width 200 
mm is 3 m/s, the velocity in the sub-channel of width 300 
mm is ______
Assume both inlet and outlet to be at the same elevation.
s1 Correct answer is 1
 AV
11
 AV AV
22 33
=+
 Q
1
 QQ
23
=+
 0.9 .. V 30 21 03 1
## ##
=+
 V 1 = m/sec
Q24 For a certain two-dimensional incompressible flow, 
velocity field is given by xyiy j 2
2
-
tt
.
The streamlines for this flow are given by the family of 
curves
(A) xy
22
= constant
(B) xy
2
= constant
(C) xy y 2
2
-= constant
(D) xy = constant
s1 Correct option is (B)
 
u
dx
 
v
dy
=
 
xy
dx
2
 
y
dy
2
=
-
 ln x lnyc =- +
 ln xy
#
 c =
 xy c =
Squaring on both sides
 xy
2
 c =
Q25 Steady one-dimensional heat conduction takes place 
across the faces 1 and 3 of a composite slab consisting of 
slabs A and B in perfect contact as shown in the figure. 
where , kk
AB
 denote the respective thermal conductivities. 
Using the data as given in the figure, the interface 
temperature T
2
 (in C c ) is ______
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