Download GATE (Graduate Aptitude Test in Engineering) Last 10 Years 2020, 2019, 2018, 2017, 2016, 2015, 2014, 2013, 2012, 2011 and 2010 XE D Engineering Sciences Question Papers With Solutions And Answer Keys
Q. 1 ? Q. 5 carry one mark each.
Q.1 The chairman requested the aggrieved shareholders to _________________ him.
(A) bare with (B) bore with (C) bear with (D) bare
Q.2 Identify the correct spelling out of the given options:
(A) Managable (B) Manageable (C) Mangaeble (D) Managible
Q.3 Pick the odd one out in the following:
13, 23, 33, 43, 53
(A) 23 (B) 33 (C) 43 (D) 53
Q.4 R2D2 is a robot. R2D2 can repair aeroplanes. No other robot can repair aeroplanes.
Which of the following can be logically inferred from the above statements?
(A) R2D2 is a robot which can only repair aeroplanes.
(B) R2D2 is the only robot which can repair aeroplanes.
(C) R2D2 is a robot which can repair only aeroplanes.
(D) Only R2D2 is a robot.
Q.5 If |9y ?6| =3, then y
2
?4y/3 is .
(A) 0 (B) +1/3 (C) ?1/3 (D) undefined
1/3
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GATE 2016 General Aptitude ? GA Set-8
Q. 1 ? Q. 5 carry one mark each.
Q.1 The chairman requested the aggrieved shareholders to _________________ him.
(A) bare with (B) bore with (C) bear with (D) bare
Q.2 Identify the correct spelling out of the given options:
(A) Managable (B) Manageable (C) Mangaeble (D) Managible
Q.3 Pick the odd one out in the following:
13, 23, 33, 43, 53
(A) 23 (B) 33 (C) 43 (D) 53
Q.4 R2D2 is a robot. R2D2 can repair aeroplanes. No other robot can repair aeroplanes.
Which of the following can be logically inferred from the above statements?
(A) R2D2 is a robot which can only repair aeroplanes.
(B) R2D2 is the only robot which can repair aeroplanes.
(C) R2D2 is a robot which can repair only aeroplanes.
(D) Only R2D2 is a robot.
Q.5 If |9y ?6| =3, then y
2
?4y/3 is .
(A) 0 (B) +1/3 (C) ?1/3 (D) undefined
1/3
GATE 2016 General Aptitude ? GA Set-8
Q. 6 ? Q. 10 carry two marks each.
Q.6 The following graph represents the installed capacity for cement production (in tonnes) and the
actual production (in tonnes) of nine cement plants of a cement company. Capacity utilization of a
plant is defined as ratio of actual production of cement to installed capacity. A plant with installed
capacity of at least 200 tonnes is called a large plant and a plant with lesser capacity is called a
small plant. The difference between total production of large plants and small plants, in tonnes is
____.
Q.7 A poll of students appearing for masters in engineering indicated that 60 % of the students believed
that mechanical engineering is a profession unsuitable for women. A research study on women with
masters or higher degrees in mechanical engineering found that 99 % of such women were
successful in their professions.
Which of the following can be logically inferred from the above paragraph?
(A) Many students have misconceptions regarding various engineering disciplines.
(B) Men with advanced degrees in mechanical engineering believe women are well suited to be
mechanical engineers.
(C) Mechanical engineering is a profession well suited for women with masters or higher degrees
in mechanical engineering.
(D) The number of women pursuing higher degrees in mechanical engineering is small.
2/3
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GATE 2016 General Aptitude ? GA Set-8
Q. 1 ? Q. 5 carry one mark each.
Q.1 The chairman requested the aggrieved shareholders to _________________ him.
(A) bare with (B) bore with (C) bear with (D) bare
Q.2 Identify the correct spelling out of the given options:
(A) Managable (B) Manageable (C) Mangaeble (D) Managible
Q.3 Pick the odd one out in the following:
13, 23, 33, 43, 53
(A) 23 (B) 33 (C) 43 (D) 53
Q.4 R2D2 is a robot. R2D2 can repair aeroplanes. No other robot can repair aeroplanes.
Which of the following can be logically inferred from the above statements?
(A) R2D2 is a robot which can only repair aeroplanes.
(B) R2D2 is the only robot which can repair aeroplanes.
(C) R2D2 is a robot which can repair only aeroplanes.
(D) Only R2D2 is a robot.
Q.5 If |9y ?6| =3, then y
2
?4y/3 is .
(A) 0 (B) +1/3 (C) ?1/3 (D) undefined
1/3
GATE 2016 General Aptitude ? GA Set-8
Q. 6 ? Q. 10 carry two marks each.
Q.6 The following graph represents the installed capacity for cement production (in tonnes) and the
actual production (in tonnes) of nine cement plants of a cement company. Capacity utilization of a
plant is defined as ratio of actual production of cement to installed capacity. A plant with installed
capacity of at least 200 tonnes is called a large plant and a plant with lesser capacity is called a
small plant. The difference between total production of large plants and small plants, in tonnes is
____.
Q.7 A poll of students appearing for masters in engineering indicated that 60 % of the students believed
that mechanical engineering is a profession unsuitable for women. A research study on women with
masters or higher degrees in mechanical engineering found that 99 % of such women were
successful in their professions.
Which of the following can be logically inferred from the above paragraph?
(A) Many students have misconceptions regarding various engineering disciplines.
(B) Men with advanced degrees in mechanical engineering believe women are well suited to be
mechanical engineers.
(C) Mechanical engineering is a profession well suited for women with masters or higher degrees
in mechanical engineering.
(D) The number of women pursuing higher degrees in mechanical engineering is small.
2/3
GATE 2016 General Aptitude ? GA Set-8
3/3
Q.8 Sourya committee had proposed the establishment of Sourya Institutes of Technology (SITs) in line
with Indian Institutes of Technology (IITs) to cater to the technological and industrial needs of a
developing country.
Which of the following can be logically inferred from the above sentence?
Based on the proposal,
(i) In the initial years, SIT students will get degrees from IIT.
(ii) SITs will have a distinct national objective.
(iii) SIT like institutions can only be established in consultation with IIT.
(iv) SITs will serve technological needs of a developing country.
(A) (iii) and (iv) only. (B) (i) and (iv) only.
(C) (ii) and (iv) only. (D) (ii) and (iii) only.
Q.9 Shaquille O? Neal is a 60% career free throw shooter, meaning that he successfully makes 60 free
throws out of 100 attempts on average. What is the probability that he will successfully
make exactly 6 free throws in 10 attempts?
(A) 0.2508
(B) 0.2816 (C) 0.2934 (D) 0.6000
Q.10 The numeral in the units position of 211
870
+ 146
127
? 3
424
is _____.
END OF THE QUESTION PAPER
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GATE 2016 General Aptitude ? GA Set-8
Q. 1 ? Q. 5 carry one mark each.
Q.1 The chairman requested the aggrieved shareholders to _________________ him.
(A) bare with (B) bore with (C) bear with (D) bare
Q.2 Identify the correct spelling out of the given options:
(A) Managable (B) Manageable (C) Mangaeble (D) Managible
Q.3 Pick the odd one out in the following:
13, 23, 33, 43, 53
(A) 23 (B) 33 (C) 43 (D) 53
Q.4 R2D2 is a robot. R2D2 can repair aeroplanes. No other robot can repair aeroplanes.
Which of the following can be logically inferred from the above statements?
(A) R2D2 is a robot which can only repair aeroplanes.
(B) R2D2 is the only robot which can repair aeroplanes.
(C) R2D2 is a robot which can repair only aeroplanes.
(D) Only R2D2 is a robot.
Q.5 If |9y ?6| =3, then y
2
?4y/3 is .
(A) 0 (B) +1/3 (C) ?1/3 (D) undefined
1/3
GATE 2016 General Aptitude ? GA Set-8
Q. 6 ? Q. 10 carry two marks each.
Q.6 The following graph represents the installed capacity for cement production (in tonnes) and the
actual production (in tonnes) of nine cement plants of a cement company. Capacity utilization of a
plant is defined as ratio of actual production of cement to installed capacity. A plant with installed
capacity of at least 200 tonnes is called a large plant and a plant with lesser capacity is called a
small plant. The difference between total production of large plants and small plants, in tonnes is
____.
Q.7 A poll of students appearing for masters in engineering indicated that 60 % of the students believed
that mechanical engineering is a profession unsuitable for women. A research study on women with
masters or higher degrees in mechanical engineering found that 99 % of such women were
successful in their professions.
Which of the following can be logically inferred from the above paragraph?
(A) Many students have misconceptions regarding various engineering disciplines.
(B) Men with advanced degrees in mechanical engineering believe women are well suited to be
mechanical engineers.
(C) Mechanical engineering is a profession well suited for women with masters or higher degrees
in mechanical engineering.
(D) The number of women pursuing higher degrees in mechanical engineering is small.
2/3
GATE 2016 General Aptitude ? GA Set-8
3/3
Q.8 Sourya committee had proposed the establishment of Sourya Institutes of Technology (SITs) in line
with Indian Institutes of Technology (IITs) to cater to the technological and industrial needs of a
developing country.
Which of the following can be logically inferred from the above sentence?
Based on the proposal,
(i) In the initial years, SIT students will get degrees from IIT.
(ii) SITs will have a distinct national objective.
(iii) SIT like institutions can only be established in consultation with IIT.
(iv) SITs will serve technological needs of a developing country.
(A) (iii) and (iv) only. (B) (i) and (iv) only.
(C) (ii) and (iv) only. (D) (ii) and (iii) only.
Q.9 Shaquille O? Neal is a 60% career free throw shooter, meaning that he successfully makes 60 free
throws out of 100 attempts on average. What is the probability that he will successfully
make exactly 6 free throws in 10 attempts?
(A) 0.2508
(B) 0.2816 (C) 0.2934 (D) 0.6000
Q.10 The numeral in the units position of 211
870
+ 146
127
? 3
424
is _____.
END OF THE QUESTION PAPER
GATE 2016 Solid Mechanics
XE-D 1/9
D : SOLID MECHANICS
Q. 1 ? Q. 9 carry one mark each.
Q.1 A single degree of freedom vibrating system has mass of 5 kg, stiffness of 500 N/m and damping
coefficient of 100 N-s/m. To make the system critically damped
(A) only the mass is to be increased by 1.2 times.
(B) only the stiffness is to be reduced to half.
(C) only the damping coefficient is to be doubled.
(D) no change in any of the system parameters is required.
Q.2 A ?L? shaped robotic arm AB is connected to a motor at end A and a magnetic gripper at B as
shown in the figure. If the arm is rotating with an angular velocity of 2 rad/s and an angular
acceleration of 3 rad/s
2
, the magnitude of the acceleration (in m/s
2
) of the end B is
(A) 2.0
(B) 2.5
(C) 5.0 (D) 6.0
Q.3 A block of weight 100 N is in static equilibrium on an inclined plane which makes an angle 15?
with the horizontal. The coefficient of friction between the inclined plane and the block is 0.3. The
magnitude of friction force (in N) acting on the block is __________
0.3 m
0.4 m
A
B
90
0
2 rad/s 3 rad/s
2
15?
100 N
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GATE 2016 General Aptitude ? GA Set-8
Q. 1 ? Q. 5 carry one mark each.
Q.1 The chairman requested the aggrieved shareholders to _________________ him.
(A) bare with (B) bore with (C) bear with (D) bare
Q.2 Identify the correct spelling out of the given options:
(A) Managable (B) Manageable (C) Mangaeble (D) Managible
Q.3 Pick the odd one out in the following:
13, 23, 33, 43, 53
(A) 23 (B) 33 (C) 43 (D) 53
Q.4 R2D2 is a robot. R2D2 can repair aeroplanes. No other robot can repair aeroplanes.
Which of the following can be logically inferred from the above statements?
(A) R2D2 is a robot which can only repair aeroplanes.
(B) R2D2 is the only robot which can repair aeroplanes.
(C) R2D2 is a robot which can repair only aeroplanes.
(D) Only R2D2 is a robot.
Q.5 If |9y ?6| =3, then y
2
?4y/3 is .
(A) 0 (B) +1/3 (C) ?1/3 (D) undefined
1/3
GATE 2016 General Aptitude ? GA Set-8
Q. 6 ? Q. 10 carry two marks each.
Q.6 The following graph represents the installed capacity for cement production (in tonnes) and the
actual production (in tonnes) of nine cement plants of a cement company. Capacity utilization of a
plant is defined as ratio of actual production of cement to installed capacity. A plant with installed
capacity of at least 200 tonnes is called a large plant and a plant with lesser capacity is called a
small plant. The difference between total production of large plants and small plants, in tonnes is
____.
Q.7 A poll of students appearing for masters in engineering indicated that 60 % of the students believed
that mechanical engineering is a profession unsuitable for women. A research study on women with
masters or higher degrees in mechanical engineering found that 99 % of such women were
successful in their professions.
Which of the following can be logically inferred from the above paragraph?
(A) Many students have misconceptions regarding various engineering disciplines.
(B) Men with advanced degrees in mechanical engineering believe women are well suited to be
mechanical engineers.
(C) Mechanical engineering is a profession well suited for women with masters or higher degrees
in mechanical engineering.
(D) The number of women pursuing higher degrees in mechanical engineering is small.
2/3
GATE 2016 General Aptitude ? GA Set-8
3/3
Q.8 Sourya committee had proposed the establishment of Sourya Institutes of Technology (SITs) in line
with Indian Institutes of Technology (IITs) to cater to the technological and industrial needs of a
developing country.
Which of the following can be logically inferred from the above sentence?
Based on the proposal,
(i) In the initial years, SIT students will get degrees from IIT.
(ii) SITs will have a distinct national objective.
(iii) SIT like institutions can only be established in consultation with IIT.
(iv) SITs will serve technological needs of a developing country.
(A) (iii) and (iv) only. (B) (i) and (iv) only.
(C) (ii) and (iv) only. (D) (ii) and (iii) only.
Q.9 Shaquille O? Neal is a 60% career free throw shooter, meaning that he successfully makes 60 free
throws out of 100 attempts on average. What is the probability that he will successfully
make exactly 6 free throws in 10 attempts?
(A) 0.2508
(B) 0.2816 (C) 0.2934 (D) 0.6000
Q.10 The numeral in the units position of 211
870
+ 146
127
? 3
424
is _____.
END OF THE QUESTION PAPER
GATE 2016 Solid Mechanics
XE-D 1/9
D : SOLID MECHANICS
Q. 1 ? Q. 9 carry one mark each.
Q.1 A single degree of freedom vibrating system has mass of 5 kg, stiffness of 500 N/m and damping
coefficient of 100 N-s/m. To make the system critically damped
(A) only the mass is to be increased by 1.2 times.
(B) only the stiffness is to be reduced to half.
(C) only the damping coefficient is to be doubled.
(D) no change in any of the system parameters is required.
Q.2 A ?L? shaped robotic arm AB is connected to a motor at end A and a magnetic gripper at B as
shown in the figure. If the arm is rotating with an angular velocity of 2 rad/s and an angular
acceleration of 3 rad/s
2
, the magnitude of the acceleration (in m/s
2
) of the end B is
(A) 2.0
(B) 2.5
(C) 5.0 (D) 6.0
Q.3 A block of weight 100 N is in static equilibrium on an inclined plane which makes an angle 15?
with the horizontal. The coefficient of friction between the inclined plane and the block is 0.3. The
magnitude of friction force (in N) acting on the block is __________
0.3 m
0.4 m
A
B
90
0
2 rad/s 3 rad/s
2
15?
100 N
GATE 2016 Solid Mechanics
XE-D 2/9
Q.4 The lower end A of the rigid bar AB is moving horizontally on the floor towards right with a
constant velocity of 5 m/s and the point B is sliding down the wall. The magnitude of the velocity
of point B at the instant ? ? 30? is
(A) zero (B) 4.34 m/s (C) 7.25 m/s (D) 8.66 m/s
Q.5 The state of plane stress at a point in a body is shown in the figure. The allowable shear stress of the
material of the body is 200 MPa. According to the maximum shear stress theory of failure the
maximum permissible value of ? (in MPa) is __________
Q.6
For a slender steel column of circular cross-section the critical buckling load is
cr
P . If the diameter
of the column is doubled (keeping other material and geometrical parameters same), then the
critical buckling load of the column is
(A)
cr
P/16 (B) 8
cr
P (C) 2
cr
P (D) 16
cr
P
Q.7 A closed thin cylindrical pressure vessel having an internal diameter of 1000 mm and a thickness of
10 mm is subjected to an internal pressure of 4 MPa. The maximum shear stress (in MPa) induced
in the cylinder is __________ (neglect the radial stress).
Q.8 A solid circular shaft subjected to pure torsion develops a maximum torsional shear stress of
120 MPa. Keeping the torsional moment same, if the diameter of the shaft is doubled then the
maximum shear stress (in MPa) induced in the shaft is __________
A
B
?
Floor
Wall
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GATE 2016 General Aptitude ? GA Set-8
Q. 1 ? Q. 5 carry one mark each.
Q.1 The chairman requested the aggrieved shareholders to _________________ him.
(A) bare with (B) bore with (C) bear with (D) bare
Q.2 Identify the correct spelling out of the given options:
(A) Managable (B) Manageable (C) Mangaeble (D) Managible
Q.3 Pick the odd one out in the following:
13, 23, 33, 43, 53
(A) 23 (B) 33 (C) 43 (D) 53
Q.4 R2D2 is a robot. R2D2 can repair aeroplanes. No other robot can repair aeroplanes.
Which of the following can be logically inferred from the above statements?
(A) R2D2 is a robot which can only repair aeroplanes.
(B) R2D2 is the only robot which can repair aeroplanes.
(C) R2D2 is a robot which can repair only aeroplanes.
(D) Only R2D2 is a robot.
Q.5 If |9y ?6| =3, then y
2
?4y/3 is .
(A) 0 (B) +1/3 (C) ?1/3 (D) undefined
1/3
GATE 2016 General Aptitude ? GA Set-8
Q. 6 ? Q. 10 carry two marks each.
Q.6 The following graph represents the installed capacity for cement production (in tonnes) and the
actual production (in tonnes) of nine cement plants of a cement company. Capacity utilization of a
plant is defined as ratio of actual production of cement to installed capacity. A plant with installed
capacity of at least 200 tonnes is called a large plant and a plant with lesser capacity is called a
small plant. The difference between total production of large plants and small plants, in tonnes is
____.
Q.7 A poll of students appearing for masters in engineering indicated that 60 % of the students believed
that mechanical engineering is a profession unsuitable for women. A research study on women with
masters or higher degrees in mechanical engineering found that 99 % of such women were
successful in their professions.
Which of the following can be logically inferred from the above paragraph?
(A) Many students have misconceptions regarding various engineering disciplines.
(B) Men with advanced degrees in mechanical engineering believe women are well suited to be
mechanical engineers.
(C) Mechanical engineering is a profession well suited for women with masters or higher degrees
in mechanical engineering.
(D) The number of women pursuing higher degrees in mechanical engineering is small.
2/3
GATE 2016 General Aptitude ? GA Set-8
3/3
Q.8 Sourya committee had proposed the establishment of Sourya Institutes of Technology (SITs) in line
with Indian Institutes of Technology (IITs) to cater to the technological and industrial needs of a
developing country.
Which of the following can be logically inferred from the above sentence?
Based on the proposal,
(i) In the initial years, SIT students will get degrees from IIT.
(ii) SITs will have a distinct national objective.
(iii) SIT like institutions can only be established in consultation with IIT.
(iv) SITs will serve technological needs of a developing country.
(A) (iii) and (iv) only. (B) (i) and (iv) only.
(C) (ii) and (iv) only. (D) (ii) and (iii) only.
Q.9 Shaquille O? Neal is a 60% career free throw shooter, meaning that he successfully makes 60 free
throws out of 100 attempts on average. What is the probability that he will successfully
make exactly 6 free throws in 10 attempts?
(A) 0.2508
(B) 0.2816 (C) 0.2934 (D) 0.6000
Q.10 The numeral in the units position of 211
870
+ 146
127
? 3
424
is _____.
END OF THE QUESTION PAPER
GATE 2016 Solid Mechanics
XE-D 1/9
D : SOLID MECHANICS
Q. 1 ? Q. 9 carry one mark each.
Q.1 A single degree of freedom vibrating system has mass of 5 kg, stiffness of 500 N/m and damping
coefficient of 100 N-s/m. To make the system critically damped
(A) only the mass is to be increased by 1.2 times.
(B) only the stiffness is to be reduced to half.
(C) only the damping coefficient is to be doubled.
(D) no change in any of the system parameters is required.
Q.2 A ?L? shaped robotic arm AB is connected to a motor at end A and a magnetic gripper at B as
shown in the figure. If the arm is rotating with an angular velocity of 2 rad/s and an angular
acceleration of 3 rad/s
2
, the magnitude of the acceleration (in m/s
2
) of the end B is
(A) 2.0
(B) 2.5
(C) 5.0 (D) 6.0
Q.3 A block of weight 100 N is in static equilibrium on an inclined plane which makes an angle 15?
with the horizontal. The coefficient of friction between the inclined plane and the block is 0.3. The
magnitude of friction force (in N) acting on the block is __________
0.3 m
0.4 m
A
B
90
0
2 rad/s 3 rad/s
2
15?
100 N
GATE 2016 Solid Mechanics
XE-D 2/9
Q.4 The lower end A of the rigid bar AB is moving horizontally on the floor towards right with a
constant velocity of 5 m/s and the point B is sliding down the wall. The magnitude of the velocity
of point B at the instant ? ? 30? is
(A) zero (B) 4.34 m/s (C) 7.25 m/s (D) 8.66 m/s
Q.5 The state of plane stress at a point in a body is shown in the figure. The allowable shear stress of the
material of the body is 200 MPa. According to the maximum shear stress theory of failure the
maximum permissible value of ? (in MPa) is __________
Q.6
For a slender steel column of circular cross-section the critical buckling load is
cr
P . If the diameter
of the column is doubled (keeping other material and geometrical parameters same), then the
critical buckling load of the column is
(A)
cr
P/16 (B) 8
cr
P (C) 2
cr
P (D) 16
cr
P
Q.7 A closed thin cylindrical pressure vessel having an internal diameter of 1000 mm and a thickness of
10 mm is subjected to an internal pressure of 4 MPa. The maximum shear stress (in MPa) induced
in the cylinder is __________ (neglect the radial stress).
Q.8 A solid circular shaft subjected to pure torsion develops a maximum torsional shear stress of
120 MPa. Keeping the torsional moment same, if the diameter of the shaft is doubled then the
maximum shear stress (in MPa) induced in the shaft is __________
A
B
?
Floor
Wall
GATE 2016 Solid Mechanics
XE-D 3/9
Q.9 On a single straight track, a vehicle of mass 500 kg moving with a velocity of 25 m/s strikes
another vehicle of mass 250 kg moving with a velocity 10 m/s in the same direction. After the
impact, if both the vehicles stick together, the common velocity (in m/s) with which both the
vehicles will move together is __________
Q. 10 ? Q. 22 carry two marks each.
Q.10 A system with three forces and a concentrated moment at A is shown in the figure. The system is
replaced by an equivalent force system with a single force and a single couple at point ?O?. The
magnitude (in N-m) of the equivalent couple at ?O? is __________
Q.11 A block A on a smooth inclined plane is connected to block B as shown in the figure using an
inextensible cord which pass over a mass-less and friction-less pulley. Initially, the block B is
constrained to be at rest. If the constraint on block B is released, the magnitude of velocity (in m/s)
of the block ?B? after 2 seconds from its release is __________ (assume g =10 m/s
2
).
200 N
30
o
O
100 N
50 N-m
2 m 2 m
50 N
4 m
A
1 m
A
B
30?
10 kg
5 kg
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GATE 2016 General Aptitude ? GA Set-8
Q. 1 ? Q. 5 carry one mark each.
Q.1 The chairman requested the aggrieved shareholders to _________________ him.
(A) bare with (B) bore with (C) bear with (D) bare
Q.2 Identify the correct spelling out of the given options:
(A) Managable (B) Manageable (C) Mangaeble (D) Managible
Q.3 Pick the odd one out in the following:
13, 23, 33, 43, 53
(A) 23 (B) 33 (C) 43 (D) 53
Q.4 R2D2 is a robot. R2D2 can repair aeroplanes. No other robot can repair aeroplanes.
Which of the following can be logically inferred from the above statements?
(A) R2D2 is a robot which can only repair aeroplanes.
(B) R2D2 is the only robot which can repair aeroplanes.
(C) R2D2 is a robot which can repair only aeroplanes.
(D) Only R2D2 is a robot.
Q.5 If |9y ?6| =3, then y
2
?4y/3 is .
(A) 0 (B) +1/3 (C) ?1/3 (D) undefined
1/3
GATE 2016 General Aptitude ? GA Set-8
Q. 6 ? Q. 10 carry two marks each.
Q.6 The following graph represents the installed capacity for cement production (in tonnes) and the
actual production (in tonnes) of nine cement plants of a cement company. Capacity utilization of a
plant is defined as ratio of actual production of cement to installed capacity. A plant with installed
capacity of at least 200 tonnes is called a large plant and a plant with lesser capacity is called a
small plant. The difference between total production of large plants and small plants, in tonnes is
____.
Q.7 A poll of students appearing for masters in engineering indicated that 60 % of the students believed
that mechanical engineering is a profession unsuitable for women. A research study on women with
masters or higher degrees in mechanical engineering found that 99 % of such women were
successful in their professions.
Which of the following can be logically inferred from the above paragraph?
(A) Many students have misconceptions regarding various engineering disciplines.
(B) Men with advanced degrees in mechanical engineering believe women are well suited to be
mechanical engineers.
(C) Mechanical engineering is a profession well suited for women with masters or higher degrees
in mechanical engineering.
(D) The number of women pursuing higher degrees in mechanical engineering is small.
2/3
GATE 2016 General Aptitude ? GA Set-8
3/3
Q.8 Sourya committee had proposed the establishment of Sourya Institutes of Technology (SITs) in line
with Indian Institutes of Technology (IITs) to cater to the technological and industrial needs of a
developing country.
Which of the following can be logically inferred from the above sentence?
Based on the proposal,
(i) In the initial years, SIT students will get degrees from IIT.
(ii) SITs will have a distinct national objective.
(iii) SIT like institutions can only be established in consultation with IIT.
(iv) SITs will serve technological needs of a developing country.
(A) (iii) and (iv) only. (B) (i) and (iv) only.
(C) (ii) and (iv) only. (D) (ii) and (iii) only.
Q.9 Shaquille O? Neal is a 60% career free throw shooter, meaning that he successfully makes 60 free
throws out of 100 attempts on average. What is the probability that he will successfully
make exactly 6 free throws in 10 attempts?
(A) 0.2508
(B) 0.2816 (C) 0.2934 (D) 0.6000
Q.10 The numeral in the units position of 211
870
+ 146
127
? 3
424
is _____.
END OF THE QUESTION PAPER
GATE 2016 Solid Mechanics
XE-D 1/9
D : SOLID MECHANICS
Q. 1 ? Q. 9 carry one mark each.
Q.1 A single degree of freedom vibrating system has mass of 5 kg, stiffness of 500 N/m and damping
coefficient of 100 N-s/m. To make the system critically damped
(A) only the mass is to be increased by 1.2 times.
(B) only the stiffness is to be reduced to half.
(C) only the damping coefficient is to be doubled.
(D) no change in any of the system parameters is required.
Q.2 A ?L? shaped robotic arm AB is connected to a motor at end A and a magnetic gripper at B as
shown in the figure. If the arm is rotating with an angular velocity of 2 rad/s and an angular
acceleration of 3 rad/s
2
, the magnitude of the acceleration (in m/s
2
) of the end B is
(A) 2.0
(B) 2.5
(C) 5.0 (D) 6.0
Q.3 A block of weight 100 N is in static equilibrium on an inclined plane which makes an angle 15?
with the horizontal. The coefficient of friction between the inclined plane and the block is 0.3. The
magnitude of friction force (in N) acting on the block is __________
0.3 m
0.4 m
A
B
90
0
2 rad/s 3 rad/s
2
15?
100 N
GATE 2016 Solid Mechanics
XE-D 2/9
Q.4 The lower end A of the rigid bar AB is moving horizontally on the floor towards right with a
constant velocity of 5 m/s and the point B is sliding down the wall. The magnitude of the velocity
of point B at the instant ? ? 30? is
(A) zero (B) 4.34 m/s (C) 7.25 m/s (D) 8.66 m/s
Q.5 The state of plane stress at a point in a body is shown in the figure. The allowable shear stress of the
material of the body is 200 MPa. According to the maximum shear stress theory of failure the
maximum permissible value of ? (in MPa) is __________
Q.6
For a slender steel column of circular cross-section the critical buckling load is
cr
P . If the diameter
of the column is doubled (keeping other material and geometrical parameters same), then the
critical buckling load of the column is
(A)
cr
P/16 (B) 8
cr
P (C) 2
cr
P (D) 16
cr
P
Q.7 A closed thin cylindrical pressure vessel having an internal diameter of 1000 mm and a thickness of
10 mm is subjected to an internal pressure of 4 MPa. The maximum shear stress (in MPa) induced
in the cylinder is __________ (neglect the radial stress).
Q.8 A solid circular shaft subjected to pure torsion develops a maximum torsional shear stress of
120 MPa. Keeping the torsional moment same, if the diameter of the shaft is doubled then the
maximum shear stress (in MPa) induced in the shaft is __________
A
B
?
Floor
Wall
GATE 2016 Solid Mechanics
XE-D 3/9
Q.9 On a single straight track, a vehicle of mass 500 kg moving with a velocity of 25 m/s strikes
another vehicle of mass 250 kg moving with a velocity 10 m/s in the same direction. After the
impact, if both the vehicles stick together, the common velocity (in m/s) with which both the
vehicles will move together is __________
Q. 10 ? Q. 22 carry two marks each.
Q.10 A system with three forces and a concentrated moment at A is shown in the figure. The system is
replaced by an equivalent force system with a single force and a single couple at point ?O?. The
magnitude (in N-m) of the equivalent couple at ?O? is __________
Q.11 A block A on a smooth inclined plane is connected to block B as shown in the figure using an
inextensible cord which pass over a mass-less and friction-less pulley. Initially, the block B is
constrained to be at rest. If the constraint on block B is released, the magnitude of velocity (in m/s)
of the block ?B? after 2 seconds from its release is __________ (assume g =10 m/s
2
).
200 N
30
o
O
100 N
50 N-m
2 m 2 m
50 N
4 m
A
1 m
A
B
30?
10 kg
5 kg
GATE 2016 Solid Mechanics
XE-D 4/9
Q.12 The vibrating system shown in the figure carries a mass of 10 kg at the free end, where the static
deflection is 1 mm. This system is to be replaced by an equivalent vibrating spring mass system
having equivalent mass of 2 kg (assume g =10 m/s
2
). The natural frequency (in rad/s) and the
stiffness (in kN/m) of the equivalent system respectively are
(A) 10 and 20 (B) 20 and 100 (C) 100 and 20 (D) 1000 and 20
Q.13
A beam having flexural rigidity EI and length L is subjected to a concentrated end moment
0
M as
shown in the figure. For
32
410 N-m EI?? , 1m L ? and
0
8kN-m M ? , the strain energy stored
(in kN-m) in the beam and the rotation (in rad) at the free end respectively are
(A) 8.00 and 0.02 (B) 8.00 and 2.00 (C) 8.00 and 0.04 (D) 0.80 and 2.00
2 m 1 m
L
M
0
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude ? GA Set-8
Q. 1 ? Q. 5 carry one mark each.
Q.1 The chairman requested the aggrieved shareholders to _________________ him.
(A) bare with (B) bore with (C) bear with (D) bare
Q.2 Identify the correct spelling out of the given options:
(A) Managable (B) Manageable (C) Mangaeble (D) Managible
Q.3 Pick the odd one out in the following:
13, 23, 33, 43, 53
(A) 23 (B) 33 (C) 43 (D) 53
Q.4 R2D2 is a robot. R2D2 can repair aeroplanes. No other robot can repair aeroplanes.
Which of the following can be logically inferred from the above statements?
(A) R2D2 is a robot which can only repair aeroplanes.
(B) R2D2 is the only robot which can repair aeroplanes.
(C) R2D2 is a robot which can repair only aeroplanes.
(D) Only R2D2 is a robot.
Q.5 If |9y ?6| =3, then y
2
?4y/3 is .
(A) 0 (B) +1/3 (C) ?1/3 (D) undefined
1/3
GATE 2016 General Aptitude ? GA Set-8
Q. 6 ? Q. 10 carry two marks each.
Q.6 The following graph represents the installed capacity for cement production (in tonnes) and the
actual production (in tonnes) of nine cement plants of a cement company. Capacity utilization of a
plant is defined as ratio of actual production of cement to installed capacity. A plant with installed
capacity of at least 200 tonnes is called a large plant and a plant with lesser capacity is called a
small plant. The difference between total production of large plants and small plants, in tonnes is
____.
Q.7 A poll of students appearing for masters in engineering indicated that 60 % of the students believed
that mechanical engineering is a profession unsuitable for women. A research study on women with
masters or higher degrees in mechanical engineering found that 99 % of such women were
successful in their professions.
Which of the following can be logically inferred from the above paragraph?
(A) Many students have misconceptions regarding various engineering disciplines.
(B) Men with advanced degrees in mechanical engineering believe women are well suited to be
mechanical engineers.
(C) Mechanical engineering is a profession well suited for women with masters or higher degrees
in mechanical engineering.
(D) The number of women pursuing higher degrees in mechanical engineering is small.
2/3
GATE 2016 General Aptitude ? GA Set-8
3/3
Q.8 Sourya committee had proposed the establishment of Sourya Institutes of Technology (SITs) in line
with Indian Institutes of Technology (IITs) to cater to the technological and industrial needs of a
developing country.
Which of the following can be logically inferred from the above sentence?
Based on the proposal,
(i) In the initial years, SIT students will get degrees from IIT.
(ii) SITs will have a distinct national objective.
(iii) SIT like institutions can only be established in consultation with IIT.
(iv) SITs will serve technological needs of a developing country.
(A) (iii) and (iv) only. (B) (i) and (iv) only.
(C) (ii) and (iv) only. (D) (ii) and (iii) only.
Q.9 Shaquille O? Neal is a 60% career free throw shooter, meaning that he successfully makes 60 free
throws out of 100 attempts on average. What is the probability that he will successfully
make exactly 6 free throws in 10 attempts?
(A) 0.2508
(B) 0.2816 (C) 0.2934 (D) 0.6000
Q.10 The numeral in the units position of 211
870
+ 146
127
? 3
424
is _____.
END OF THE QUESTION PAPER
GATE 2016 Solid Mechanics
XE-D 1/9
D : SOLID MECHANICS
Q. 1 ? Q. 9 carry one mark each.
Q.1 A single degree of freedom vibrating system has mass of 5 kg, stiffness of 500 N/m and damping
coefficient of 100 N-s/m. To make the system critically damped
(A) only the mass is to be increased by 1.2 times.
(B) only the stiffness is to be reduced to half.
(C) only the damping coefficient is to be doubled.
(D) no change in any of the system parameters is required.
Q.2 A ?L? shaped robotic arm AB is connected to a motor at end A and a magnetic gripper at B as
shown in the figure. If the arm is rotating with an angular velocity of 2 rad/s and an angular
acceleration of 3 rad/s
2
, the magnitude of the acceleration (in m/s
2
) of the end B is
(A) 2.0
(B) 2.5
(C) 5.0 (D) 6.0
Q.3 A block of weight 100 N is in static equilibrium on an inclined plane which makes an angle 15?
with the horizontal. The coefficient of friction between the inclined plane and the block is 0.3. The
magnitude of friction force (in N) acting on the block is __________
0.3 m
0.4 m
A
B
90
0
2 rad/s 3 rad/s
2
15?
100 N
GATE 2016 Solid Mechanics
XE-D 2/9
Q.4 The lower end A of the rigid bar AB is moving horizontally on the floor towards right with a
constant velocity of 5 m/s and the point B is sliding down the wall. The magnitude of the velocity
of point B at the instant ? ? 30? is
(A) zero (B) 4.34 m/s (C) 7.25 m/s (D) 8.66 m/s
Q.5 The state of plane stress at a point in a body is shown in the figure. The allowable shear stress of the
material of the body is 200 MPa. According to the maximum shear stress theory of failure the
maximum permissible value of ? (in MPa) is __________
Q.6
For a slender steel column of circular cross-section the critical buckling load is
cr
P . If the diameter
of the column is doubled (keeping other material and geometrical parameters same), then the
critical buckling load of the column is
(A)
cr
P/16 (B) 8
cr
P (C) 2
cr
P (D) 16
cr
P
Q.7 A closed thin cylindrical pressure vessel having an internal diameter of 1000 mm and a thickness of
10 mm is subjected to an internal pressure of 4 MPa. The maximum shear stress (in MPa) induced
in the cylinder is __________ (neglect the radial stress).
Q.8 A solid circular shaft subjected to pure torsion develops a maximum torsional shear stress of
120 MPa. Keeping the torsional moment same, if the diameter of the shaft is doubled then the
maximum shear stress (in MPa) induced in the shaft is __________
A
B
?
Floor
Wall
GATE 2016 Solid Mechanics
XE-D 3/9
Q.9 On a single straight track, a vehicle of mass 500 kg moving with a velocity of 25 m/s strikes
another vehicle of mass 250 kg moving with a velocity 10 m/s in the same direction. After the
impact, if both the vehicles stick together, the common velocity (in m/s) with which both the
vehicles will move together is __________
Q. 10 ? Q. 22 carry two marks each.
Q.10 A system with three forces and a concentrated moment at A is shown in the figure. The system is
replaced by an equivalent force system with a single force and a single couple at point ?O?. The
magnitude (in N-m) of the equivalent couple at ?O? is __________
Q.11 A block A on a smooth inclined plane is connected to block B as shown in the figure using an
inextensible cord which pass over a mass-less and friction-less pulley. Initially, the block B is
constrained to be at rest. If the constraint on block B is released, the magnitude of velocity (in m/s)
of the block ?B? after 2 seconds from its release is __________ (assume g =10 m/s
2
).
200 N
30
o
O
100 N
50 N-m
2 m 2 m
50 N
4 m
A
1 m
A
B
30?
10 kg
5 kg
GATE 2016 Solid Mechanics
XE-D 4/9
Q.12 The vibrating system shown in the figure carries a mass of 10 kg at the free end, where the static
deflection is 1 mm. This system is to be replaced by an equivalent vibrating spring mass system
having equivalent mass of 2 kg (assume g =10 m/s
2
). The natural frequency (in rad/s) and the
stiffness (in kN/m) of the equivalent system respectively are
(A) 10 and 20 (B) 20 and 100 (C) 100 and 20 (D) 1000 and 20
Q.13
A beam having flexural rigidity EI and length L is subjected to a concentrated end moment
0
M as
shown in the figure. For
32
410 N-m EI?? , 1m L ? and
0
8kN-m M ? , the strain energy stored
(in kN-m) in the beam and the rotation (in rad) at the free end respectively are
(A) 8.00 and 0.02 (B) 8.00 and 2.00 (C) 8.00 and 0.04 (D) 0.80 and 2.00
2 m 1 m
L
M
0
GATE 2016 Solid Mechanics
XE-D 5/9
Q.14 At a point ?O? on a metal sheet a square OABC of a unit side length is drawn. The square
undergoes a small uniform elastic deformation and deforms to OA*B*C* (dashed lines) as shown
in the figure. All dimensions are in mm and the figure is not to scale. The normal strains
x
? ,
y
?
and shear strain
xy
? developed in the square respectively are
(A)
0.0020, 0.0025 and 0.0020 ? (B) 0.0020, 0.0025 and 0.0020 ? ?
(C) 0.0025, 0.0020 and 0.0020 ? (D) 0.0020, 0.0025 and 0.0020 ? ?
Q.15 Mohr?s circle for the state of plane stress at a point is shown in the figure. Unit of stress is MPa and
the circle is drawn not to scale. Which one of the following options (stress values in MPa) is true?
(normal stress)
(shear stress)
A
B
C
O
O ? Origin of ? axis
C ? Center of Mohr?s circle
20
30
40
(
A
,
A
)
( , )
( , 0)
( , 0)
(A)
12
50, 10, 30, 70
AB
? ?? ? ?? ? ? ? ? (B)
12
50, 20, 30, 50
AB
? ?? ? ??? ? ??
(C)
12
30, 30, 30, 10
AB
? ?? ? ?? ? ? ?? (D)
12
20, 10, 50, 30
AB
? ?? ? ??? ? ??
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude ? GA Set-8
Q. 1 ? Q. 5 carry one mark each.
Q.1 The chairman requested the aggrieved shareholders to _________________ him.
(A) bare with (B) bore with (C) bear with (D) bare
Q.2 Identify the correct spelling out of the given options:
(A) Managable (B) Manageable (C) Mangaeble (D) Managible
Q.3 Pick the odd one out in the following:
13, 23, 33, 43, 53
(A) 23 (B) 33 (C) 43 (D) 53
Q.4 R2D2 is a robot. R2D2 can repair aeroplanes. No other robot can repair aeroplanes.
Which of the following can be logically inferred from the above statements?
(A) R2D2 is a robot which can only repair aeroplanes.
(B) R2D2 is the only robot which can repair aeroplanes.
(C) R2D2 is a robot which can repair only aeroplanes.
(D) Only R2D2 is a robot.
Q.5 If |9y ?6| =3, then y
2
?4y/3 is .
(A) 0 (B) +1/3 (C) ?1/3 (D) undefined
1/3
GATE 2016 General Aptitude ? GA Set-8
Q. 6 ? Q. 10 carry two marks each.
Q.6 The following graph represents the installed capacity for cement production (in tonnes) and the
actual production (in tonnes) of nine cement plants of a cement company. Capacity utilization of a
plant is defined as ratio of actual production of cement to installed capacity. A plant with installed
capacity of at least 200 tonnes is called a large plant and a plant with lesser capacity is called a
small plant. The difference between total production of large plants and small plants, in tonnes is
____.
Q.7 A poll of students appearing for masters in engineering indicated that 60 % of the students believed
that mechanical engineering is a profession unsuitable for women. A research study on women with
masters or higher degrees in mechanical engineering found that 99 % of such women were
successful in their professions.
Which of the following can be logically inferred from the above paragraph?
(A) Many students have misconceptions regarding various engineering disciplines.
(B) Men with advanced degrees in mechanical engineering believe women are well suited to be
mechanical engineers.
(C) Mechanical engineering is a profession well suited for women with masters or higher degrees
in mechanical engineering.
(D) The number of women pursuing higher degrees in mechanical engineering is small.
2/3
GATE 2016 General Aptitude ? GA Set-8
3/3
Q.8 Sourya committee had proposed the establishment of Sourya Institutes of Technology (SITs) in line
with Indian Institutes of Technology (IITs) to cater to the technological and industrial needs of a
developing country.
Which of the following can be logically inferred from the above sentence?
Based on the proposal,
(i) In the initial years, SIT students will get degrees from IIT.
(ii) SITs will have a distinct national objective.
(iii) SIT like institutions can only be established in consultation with IIT.
(iv) SITs will serve technological needs of a developing country.
(A) (iii) and (iv) only. (B) (i) and (iv) only.
(C) (ii) and (iv) only. (D) (ii) and (iii) only.
Q.9 Shaquille O? Neal is a 60% career free throw shooter, meaning that he successfully makes 60 free
throws out of 100 attempts on average. What is the probability that he will successfully
make exactly 6 free throws in 10 attempts?
(A) 0.2508
(B) 0.2816 (C) 0.2934 (D) 0.6000
Q.10 The numeral in the units position of 211
870
+ 146
127
? 3
424
is _____.
END OF THE QUESTION PAPER
GATE 2016 Solid Mechanics
XE-D 1/9
D : SOLID MECHANICS
Q. 1 ? Q. 9 carry one mark each.
Q.1 A single degree of freedom vibrating system has mass of 5 kg, stiffness of 500 N/m and damping
coefficient of 100 N-s/m. To make the system critically damped
(A) only the mass is to be increased by 1.2 times.
(B) only the stiffness is to be reduced to half.
(C) only the damping coefficient is to be doubled.
(D) no change in any of the system parameters is required.
Q.2 A ?L? shaped robotic arm AB is connected to a motor at end A and a magnetic gripper at B as
shown in the figure. If the arm is rotating with an angular velocity of 2 rad/s and an angular
acceleration of 3 rad/s
2
, the magnitude of the acceleration (in m/s
2
) of the end B is
(A) 2.0
(B) 2.5
(C) 5.0 (D) 6.0
Q.3 A block of weight 100 N is in static equilibrium on an inclined plane which makes an angle 15?
with the horizontal. The coefficient of friction between the inclined plane and the block is 0.3. The
magnitude of friction force (in N) acting on the block is __________
0.3 m
0.4 m
A
B
90
0
2 rad/s 3 rad/s
2
15?
100 N
GATE 2016 Solid Mechanics
XE-D 2/9
Q.4 The lower end A of the rigid bar AB is moving horizontally on the floor towards right with a
constant velocity of 5 m/s and the point B is sliding down the wall. The magnitude of the velocity
of point B at the instant ? ? 30? is
(A) zero (B) 4.34 m/s (C) 7.25 m/s (D) 8.66 m/s
Q.5 The state of plane stress at a point in a body is shown in the figure. The allowable shear stress of the
material of the body is 200 MPa. According to the maximum shear stress theory of failure the
maximum permissible value of ? (in MPa) is __________
Q.6
For a slender steel column of circular cross-section the critical buckling load is
cr
P . If the diameter
of the column is doubled (keeping other material and geometrical parameters same), then the
critical buckling load of the column is
(A)
cr
P/16 (B) 8
cr
P (C) 2
cr
P (D) 16
cr
P
Q.7 A closed thin cylindrical pressure vessel having an internal diameter of 1000 mm and a thickness of
10 mm is subjected to an internal pressure of 4 MPa. The maximum shear stress (in MPa) induced
in the cylinder is __________ (neglect the radial stress).
Q.8 A solid circular shaft subjected to pure torsion develops a maximum torsional shear stress of
120 MPa. Keeping the torsional moment same, if the diameter of the shaft is doubled then the
maximum shear stress (in MPa) induced in the shaft is __________
A
B
?
Floor
Wall
GATE 2016 Solid Mechanics
XE-D 3/9
Q.9 On a single straight track, a vehicle of mass 500 kg moving with a velocity of 25 m/s strikes
another vehicle of mass 250 kg moving with a velocity 10 m/s in the same direction. After the
impact, if both the vehicles stick together, the common velocity (in m/s) with which both the
vehicles will move together is __________
Q. 10 ? Q. 22 carry two marks each.
Q.10 A system with three forces and a concentrated moment at A is shown in the figure. The system is
replaced by an equivalent force system with a single force and a single couple at point ?O?. The
magnitude (in N-m) of the equivalent couple at ?O? is __________
Q.11 A block A on a smooth inclined plane is connected to block B as shown in the figure using an
inextensible cord which pass over a mass-less and friction-less pulley. Initially, the block B is
constrained to be at rest. If the constraint on block B is released, the magnitude of velocity (in m/s)
of the block ?B? after 2 seconds from its release is __________ (assume g =10 m/s
2
).
200 N
30
o
O
100 N
50 N-m
2 m 2 m
50 N
4 m
A
1 m
A
B
30?
10 kg
5 kg
GATE 2016 Solid Mechanics
XE-D 4/9
Q.12 The vibrating system shown in the figure carries a mass of 10 kg at the free end, where the static
deflection is 1 mm. This system is to be replaced by an equivalent vibrating spring mass system
having equivalent mass of 2 kg (assume g =10 m/s
2
). The natural frequency (in rad/s) and the
stiffness (in kN/m) of the equivalent system respectively are
(A) 10 and 20 (B) 20 and 100 (C) 100 and 20 (D) 1000 and 20
Q.13
A beam having flexural rigidity EI and length L is subjected to a concentrated end moment
0
M as
shown in the figure. For
32
410 N-m EI?? , 1m L ? and
0
8kN-m M ? , the strain energy stored
(in kN-m) in the beam and the rotation (in rad) at the free end respectively are
(A) 8.00 and 0.02 (B) 8.00 and 2.00 (C) 8.00 and 0.04 (D) 0.80 and 2.00
2 m 1 m
L
M
0
GATE 2016 Solid Mechanics
XE-D 5/9
Q.14 At a point ?O? on a metal sheet a square OABC of a unit side length is drawn. The square
undergoes a small uniform elastic deformation and deforms to OA*B*C* (dashed lines) as shown
in the figure. All dimensions are in mm and the figure is not to scale. The normal strains
x
? ,
y
?
and shear strain
xy
? developed in the square respectively are
(A)
0.0020, 0.0025 and 0.0020 ? (B) 0.0020, 0.0025 and 0.0020 ? ?
(C) 0.0025, 0.0020 and 0.0020 ? (D) 0.0020, 0.0025 and 0.0020 ? ?
Q.15 Mohr?s circle for the state of plane stress at a point is shown in the figure. Unit of stress is MPa and
the circle is drawn not to scale. Which one of the following options (stress values in MPa) is true?
(normal stress)
(shear stress)
A
B
C
O
O ? Origin of ? axis
C ? Center of Mohr?s circle
20
30
40
(
A
,
A
)
( , )
( , 0)
( , 0)
(A)
12
50, 10, 30, 70
AB
? ?? ? ?? ? ? ? ? (B)
12
50, 20, 30, 50
AB
? ?? ? ??? ? ??
(C)
12
30, 30, 30, 10
AB
? ?? ? ?? ? ? ?? (D)
12
20, 10, 50, 30
AB
? ?? ? ??? ? ??
GATE 2016 Solid Mechanics
XE-D 6/9
Q.16 As shown in the figure, links AB and CD support the rigid member BD. Links AB and CD are
made of aluminum alloy?? 100GPa E ? and each has a cross-sectional area of
2
100 mm .
All the
members are pin connected and all the dimensions are in mm. Neglecting the weights of the
members, the elongation (in mm) of the link AB is __________
A
B
C
D
6 kN
400 400
100 200
Q.17 Figure shows an elastic beam of constant flexural rigidity EI and length . L The transverse
deflection () vx for the beam is represented by the equation
? ?
32
0
() (4 ), vx M x xL EIL ??
where
0
M is the applied couple. If 100mm L ? and
0
100 N-mm M ? , then the magnitude of the
shear force (in N) at the middle of the beam (at /2) xL ? is __________
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude ? GA Set-8
Q. 1 ? Q. 5 carry one mark each.
Q.1 The chairman requested the aggrieved shareholders to _________________ him.
(A) bare with (B) bore with (C) bear with (D) bare
Q.2 Identify the correct spelling out of the given options:
(A) Managable (B) Manageable (C) Mangaeble (D) Managible
Q.3 Pick the odd one out in the following:
13, 23, 33, 43, 53
(A) 23 (B) 33 (C) 43 (D) 53
Q.4 R2D2 is a robot. R2D2 can repair aeroplanes. No other robot can repair aeroplanes.
Which of the following can be logically inferred from the above statements?
(A) R2D2 is a robot which can only repair aeroplanes.
(B) R2D2 is the only robot which can repair aeroplanes.
(C) R2D2 is a robot which can repair only aeroplanes.
(D) Only R2D2 is a robot.
Q.5 If |9y ?6| =3, then y
2
?4y/3 is .
(A) 0 (B) +1/3 (C) ?1/3 (D) undefined
1/3
GATE 2016 General Aptitude ? GA Set-8
Q. 6 ? Q. 10 carry two marks each.
Q.6 The following graph represents the installed capacity for cement production (in tonnes) and the
actual production (in tonnes) of nine cement plants of a cement company. Capacity utilization of a
plant is defined as ratio of actual production of cement to installed capacity. A plant with installed
capacity of at least 200 tonnes is called a large plant and a plant with lesser capacity is called a
small plant. The difference between total production of large plants and small plants, in tonnes is
____.
Q.7 A poll of students appearing for masters in engineering indicated that 60 % of the students believed
that mechanical engineering is a profession unsuitable for women. A research study on women with
masters or higher degrees in mechanical engineering found that 99 % of such women were
successful in their professions.
Which of the following can be logically inferred from the above paragraph?
(A) Many students have misconceptions regarding various engineering disciplines.
(B) Men with advanced degrees in mechanical engineering believe women are well suited to be
mechanical engineers.
(C) Mechanical engineering is a profession well suited for women with masters or higher degrees
in mechanical engineering.
(D) The number of women pursuing higher degrees in mechanical engineering is small.
2/3
GATE 2016 General Aptitude ? GA Set-8
3/3
Q.8 Sourya committee had proposed the establishment of Sourya Institutes of Technology (SITs) in line
with Indian Institutes of Technology (IITs) to cater to the technological and industrial needs of a
developing country.
Which of the following can be logically inferred from the above sentence?
Based on the proposal,
(i) In the initial years, SIT students will get degrees from IIT.
(ii) SITs will have a distinct national objective.
(iii) SIT like institutions can only be established in consultation with IIT.
(iv) SITs will serve technological needs of a developing country.
(A) (iii) and (iv) only. (B) (i) and (iv) only.
(C) (ii) and (iv) only. (D) (ii) and (iii) only.
Q.9 Shaquille O? Neal is a 60% career free throw shooter, meaning that he successfully makes 60 free
throws out of 100 attempts on average. What is the probability that he will successfully
make exactly 6 free throws in 10 attempts?
(A) 0.2508
(B) 0.2816 (C) 0.2934 (D) 0.6000
Q.10 The numeral in the units position of 211
870
+ 146
127
? 3
424
is _____.
END OF THE QUESTION PAPER
GATE 2016 Solid Mechanics
XE-D 1/9
D : SOLID MECHANICS
Q. 1 ? Q. 9 carry one mark each.
Q.1 A single degree of freedom vibrating system has mass of 5 kg, stiffness of 500 N/m and damping
coefficient of 100 N-s/m. To make the system critically damped
(A) only the mass is to be increased by 1.2 times.
(B) only the stiffness is to be reduced to half.
(C) only the damping coefficient is to be doubled.
(D) no change in any of the system parameters is required.
Q.2 A ?L? shaped robotic arm AB is connected to a motor at end A and a magnetic gripper at B as
shown in the figure. If the arm is rotating with an angular velocity of 2 rad/s and an angular
acceleration of 3 rad/s
2
, the magnitude of the acceleration (in m/s
2
) of the end B is
(A) 2.0
(B) 2.5
(C) 5.0 (D) 6.0
Q.3 A block of weight 100 N is in static equilibrium on an inclined plane which makes an angle 15?
with the horizontal. The coefficient of friction between the inclined plane and the block is 0.3. The
magnitude of friction force (in N) acting on the block is __________
0.3 m
0.4 m
A
B
90
0
2 rad/s 3 rad/s
2
15?
100 N
GATE 2016 Solid Mechanics
XE-D 2/9
Q.4 The lower end A of the rigid bar AB is moving horizontally on the floor towards right with a
constant velocity of 5 m/s and the point B is sliding down the wall. The magnitude of the velocity
of point B at the instant ? ? 30? is
(A) zero (B) 4.34 m/s (C) 7.25 m/s (D) 8.66 m/s
Q.5 The state of plane stress at a point in a body is shown in the figure. The allowable shear stress of the
material of the body is 200 MPa. According to the maximum shear stress theory of failure the
maximum permissible value of ? (in MPa) is __________
Q.6
For a slender steel column of circular cross-section the critical buckling load is
cr
P . If the diameter
of the column is doubled (keeping other material and geometrical parameters same), then the
critical buckling load of the column is
(A)
cr
P/16 (B) 8
cr
P (C) 2
cr
P (D) 16
cr
P
Q.7 A closed thin cylindrical pressure vessel having an internal diameter of 1000 mm and a thickness of
10 mm is subjected to an internal pressure of 4 MPa. The maximum shear stress (in MPa) induced
in the cylinder is __________ (neglect the radial stress).
Q.8 A solid circular shaft subjected to pure torsion develops a maximum torsional shear stress of
120 MPa. Keeping the torsional moment same, if the diameter of the shaft is doubled then the
maximum shear stress (in MPa) induced in the shaft is __________
A
B
?
Floor
Wall
GATE 2016 Solid Mechanics
XE-D 3/9
Q.9 On a single straight track, a vehicle of mass 500 kg moving with a velocity of 25 m/s strikes
another vehicle of mass 250 kg moving with a velocity 10 m/s in the same direction. After the
impact, if both the vehicles stick together, the common velocity (in m/s) with which both the
vehicles will move together is __________
Q. 10 ? Q. 22 carry two marks each.
Q.10 A system with three forces and a concentrated moment at A is shown in the figure. The system is
replaced by an equivalent force system with a single force and a single couple at point ?O?. The
magnitude (in N-m) of the equivalent couple at ?O? is __________
Q.11 A block A on a smooth inclined plane is connected to block B as shown in the figure using an
inextensible cord which pass over a mass-less and friction-less pulley. Initially, the block B is
constrained to be at rest. If the constraint on block B is released, the magnitude of velocity (in m/s)
of the block ?B? after 2 seconds from its release is __________ (assume g =10 m/s
2
).
200 N
30
o
O
100 N
50 N-m
2 m 2 m
50 N
4 m
A
1 m
A
B
30?
10 kg
5 kg
GATE 2016 Solid Mechanics
XE-D 4/9
Q.12 The vibrating system shown in the figure carries a mass of 10 kg at the free end, where the static
deflection is 1 mm. This system is to be replaced by an equivalent vibrating spring mass system
having equivalent mass of 2 kg (assume g =10 m/s
2
). The natural frequency (in rad/s) and the
stiffness (in kN/m) of the equivalent system respectively are
(A) 10 and 20 (B) 20 and 100 (C) 100 and 20 (D) 1000 and 20
Q.13
A beam having flexural rigidity EI and length L is subjected to a concentrated end moment
0
M as
shown in the figure. For
32
410 N-m EI?? , 1m L ? and
0
8kN-m M ? , the strain energy stored
(in kN-m) in the beam and the rotation (in rad) at the free end respectively are
(A) 8.00 and 0.02 (B) 8.00 and 2.00 (C) 8.00 and 0.04 (D) 0.80 and 2.00
2 m 1 m
L
M
0
GATE 2016 Solid Mechanics
XE-D 5/9
Q.14 At a point ?O? on a metal sheet a square OABC of a unit side length is drawn. The square
undergoes a small uniform elastic deformation and deforms to OA*B*C* (dashed lines) as shown
in the figure. All dimensions are in mm and the figure is not to scale. The normal strains
x
? ,
y
?
and shear strain
xy
? developed in the square respectively are
(A)
0.0020, 0.0025 and 0.0020 ? (B) 0.0020, 0.0025 and 0.0020 ? ?
(C) 0.0025, 0.0020 and 0.0020 ? (D) 0.0020, 0.0025 and 0.0020 ? ?
Q.15 Mohr?s circle for the state of plane stress at a point is shown in the figure. Unit of stress is MPa and
the circle is drawn not to scale. Which one of the following options (stress values in MPa) is true?
(normal stress)
(shear stress)
A
B
C
O
O ? Origin of ? axis
C ? Center of Mohr?s circle
20
30
40
(
A
,
A
)
( , )
( , 0)
( , 0)
(A)
12
50, 10, 30, 70
AB
? ?? ? ?? ? ? ? ? (B)
12
50, 20, 30, 50
AB
? ?? ? ??? ? ??
(C)
12
30, 30, 30, 10
AB
? ?? ? ?? ? ? ?? (D)
12
20, 10, 50, 30
AB
? ?? ? ??? ? ??
GATE 2016 Solid Mechanics
XE-D 6/9
Q.16 As shown in the figure, links AB and CD support the rigid member BD. Links AB and CD are
made of aluminum alloy?? 100GPa E ? and each has a cross-sectional area of
2
100 mm .
All the
members are pin connected and all the dimensions are in mm. Neglecting the weights of the
members, the elongation (in mm) of the link AB is __________
A
B
C
D
6 kN
400 400
100 200
Q.17 Figure shows an elastic beam of constant flexural rigidity EI and length . L The transverse
deflection () vx for the beam is represented by the equation
? ?
32
0
() (4 ), vx M x xL EIL ??
where
0
M is the applied couple. If 100mm L ? and
0
100 N-mm M ? , then the magnitude of the
shear force (in N) at the middle of the beam (at /2) xL ? is __________
GATE 2016 Solid Mechanics
XE-D 7/9
Q.18 Which one of the following represents the correct bending moment diagram of the beam PQR
loaded as shown in the figure?
(A)
(B)
(C)
(D)
Q.19
A point in a body is subjected to plane state of stress in XY plane. If 140MPa,
x
? ?
60 MPa
y
? ? and the major principal stress is 150 MPa, the magnitude of the in-plane shear stress
xy
? (in MPa) is
(A) 75 (B) 30 (C) 40 (D) 70
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude ? GA Set-8
Q. 1 ? Q. 5 carry one mark each.
Q.1 The chairman requested the aggrieved shareholders to _________________ him.
(A) bare with (B) bore with (C) bear with (D) bare
Q.2 Identify the correct spelling out of the given options:
(A) Managable (B) Manageable (C) Mangaeble (D) Managible
Q.3 Pick the odd one out in the following:
13, 23, 33, 43, 53
(A) 23 (B) 33 (C) 43 (D) 53
Q.4 R2D2 is a robot. R2D2 can repair aeroplanes. No other robot can repair aeroplanes.
Which of the following can be logically inferred from the above statements?
(A) R2D2 is a robot which can only repair aeroplanes.
(B) R2D2 is the only robot which can repair aeroplanes.
(C) R2D2 is a robot which can repair only aeroplanes.
(D) Only R2D2 is a robot.
Q.5 If |9y ?6| =3, then y
2
?4y/3 is .
(A) 0 (B) +1/3 (C) ?1/3 (D) undefined
1/3
GATE 2016 General Aptitude ? GA Set-8
Q. 6 ? Q. 10 carry two marks each.
Q.6 The following graph represents the installed capacity for cement production (in tonnes) and the
actual production (in tonnes) of nine cement plants of a cement company. Capacity utilization of a
plant is defined as ratio of actual production of cement to installed capacity. A plant with installed
capacity of at least 200 tonnes is called a large plant and a plant with lesser capacity is called a
small plant. The difference between total production of large plants and small plants, in tonnes is
____.
Q.7 A poll of students appearing for masters in engineering indicated that 60 % of the students believed
that mechanical engineering is a profession unsuitable for women. A research study on women with
masters or higher degrees in mechanical engineering found that 99 % of such women were
successful in their professions.
Which of the following can be logically inferred from the above paragraph?
(A) Many students have misconceptions regarding various engineering disciplines.
(B) Men with advanced degrees in mechanical engineering believe women are well suited to be
mechanical engineers.
(C) Mechanical engineering is a profession well suited for women with masters or higher degrees
in mechanical engineering.
(D) The number of women pursuing higher degrees in mechanical engineering is small.
2/3
GATE 2016 General Aptitude ? GA Set-8
3/3
Q.8 Sourya committee had proposed the establishment of Sourya Institutes of Technology (SITs) in line
with Indian Institutes of Technology (IITs) to cater to the technological and industrial needs of a
developing country.
Which of the following can be logically inferred from the above sentence?
Based on the proposal,
(i) In the initial years, SIT students will get degrees from IIT.
(ii) SITs will have a distinct national objective.
(iii) SIT like institutions can only be established in consultation with IIT.
(iv) SITs will serve technological needs of a developing country.
(A) (iii) and (iv) only. (B) (i) and (iv) only.
(C) (ii) and (iv) only. (D) (ii) and (iii) only.
Q.9 Shaquille O? Neal is a 60% career free throw shooter, meaning that he successfully makes 60 free
throws out of 100 attempts on average. What is the probability that he will successfully
make exactly 6 free throws in 10 attempts?
(A) 0.2508
(B) 0.2816 (C) 0.2934 (D) 0.6000
Q.10 The numeral in the units position of 211
870
+ 146
127
? 3
424
is _____.
END OF THE QUESTION PAPER
GATE 2016 Solid Mechanics
XE-D 1/9
D : SOLID MECHANICS
Q. 1 ? Q. 9 carry one mark each.
Q.1 A single degree of freedom vibrating system has mass of 5 kg, stiffness of 500 N/m and damping
coefficient of 100 N-s/m. To make the system critically damped
(A) only the mass is to be increased by 1.2 times.
(B) only the stiffness is to be reduced to half.
(C) only the damping coefficient is to be doubled.
(D) no change in any of the system parameters is required.
Q.2 A ?L? shaped robotic arm AB is connected to a motor at end A and a magnetic gripper at B as
shown in the figure. If the arm is rotating with an angular velocity of 2 rad/s and an angular
acceleration of 3 rad/s
2
, the magnitude of the acceleration (in m/s
2
) of the end B is
(A) 2.0
(B) 2.5
(C) 5.0 (D) 6.0
Q.3 A block of weight 100 N is in static equilibrium on an inclined plane which makes an angle 15?
with the horizontal. The coefficient of friction between the inclined plane and the block is 0.3. The
magnitude of friction force (in N) acting on the block is __________
0.3 m
0.4 m
A
B
90
0
2 rad/s 3 rad/s
2
15?
100 N
GATE 2016 Solid Mechanics
XE-D 2/9
Q.4 The lower end A of the rigid bar AB is moving horizontally on the floor towards right with a
constant velocity of 5 m/s and the point B is sliding down the wall. The magnitude of the velocity
of point B at the instant ? ? 30? is
(A) zero (B) 4.34 m/s (C) 7.25 m/s (D) 8.66 m/s
Q.5 The state of plane stress at a point in a body is shown in the figure. The allowable shear stress of the
material of the body is 200 MPa. According to the maximum shear stress theory of failure the
maximum permissible value of ? (in MPa) is __________
Q.6
For a slender steel column of circular cross-section the critical buckling load is
cr
P . If the diameter
of the column is doubled (keeping other material and geometrical parameters same), then the
critical buckling load of the column is
(A)
cr
P/16 (B) 8
cr
P (C) 2
cr
P (D) 16
cr
P
Q.7 A closed thin cylindrical pressure vessel having an internal diameter of 1000 mm and a thickness of
10 mm is subjected to an internal pressure of 4 MPa. The maximum shear stress (in MPa) induced
in the cylinder is __________ (neglect the radial stress).
Q.8 A solid circular shaft subjected to pure torsion develops a maximum torsional shear stress of
120 MPa. Keeping the torsional moment same, if the diameter of the shaft is doubled then the
maximum shear stress (in MPa) induced in the shaft is __________
A
B
?
Floor
Wall
GATE 2016 Solid Mechanics
XE-D 3/9
Q.9 On a single straight track, a vehicle of mass 500 kg moving with a velocity of 25 m/s strikes
another vehicle of mass 250 kg moving with a velocity 10 m/s in the same direction. After the
impact, if both the vehicles stick together, the common velocity (in m/s) with which both the
vehicles will move together is __________
Q. 10 ? Q. 22 carry two marks each.
Q.10 A system with three forces and a concentrated moment at A is shown in the figure. The system is
replaced by an equivalent force system with a single force and a single couple at point ?O?. The
magnitude (in N-m) of the equivalent couple at ?O? is __________
Q.11 A block A on a smooth inclined plane is connected to block B as shown in the figure using an
inextensible cord which pass over a mass-less and friction-less pulley. Initially, the block B is
constrained to be at rest. If the constraint on block B is released, the magnitude of velocity (in m/s)
of the block ?B? after 2 seconds from its release is __________ (assume g =10 m/s
2
).
200 N
30
o
O
100 N
50 N-m
2 m 2 m
50 N
4 m
A
1 m
A
B
30?
10 kg
5 kg
GATE 2016 Solid Mechanics
XE-D 4/9
Q.12 The vibrating system shown in the figure carries a mass of 10 kg at the free end, where the static
deflection is 1 mm. This system is to be replaced by an equivalent vibrating spring mass system
having equivalent mass of 2 kg (assume g =10 m/s
2
). The natural frequency (in rad/s) and the
stiffness (in kN/m) of the equivalent system respectively are
(A) 10 and 20 (B) 20 and 100 (C) 100 and 20 (D) 1000 and 20
Q.13
A beam having flexural rigidity EI and length L is subjected to a concentrated end moment
0
M as
shown in the figure. For
32
410 N-m EI?? , 1m L ? and
0
8kN-m M ? , the strain energy stored
(in kN-m) in the beam and the rotation (in rad) at the free end respectively are
(A) 8.00 and 0.02 (B) 8.00 and 2.00 (C) 8.00 and 0.04 (D) 0.80 and 2.00
2 m 1 m
L
M
0
GATE 2016 Solid Mechanics
XE-D 5/9
Q.14 At a point ?O? on a metal sheet a square OABC of a unit side length is drawn. The square
undergoes a small uniform elastic deformation and deforms to OA*B*C* (dashed lines) as shown
in the figure. All dimensions are in mm and the figure is not to scale. The normal strains
x
? ,
y
?
and shear strain
xy
? developed in the square respectively are
(A)
0.0020, 0.0025 and 0.0020 ? (B) 0.0020, 0.0025 and 0.0020 ? ?
(C) 0.0025, 0.0020 and 0.0020 ? (D) 0.0020, 0.0025 and 0.0020 ? ?
Q.15 Mohr?s circle for the state of plane stress at a point is shown in the figure. Unit of stress is MPa and
the circle is drawn not to scale. Which one of the following options (stress values in MPa) is true?
(normal stress)
(shear stress)
A
B
C
O
O ? Origin of ? axis
C ? Center of Mohr?s circle
20
30
40
(
A
,
A
)
( , )
( , 0)
( , 0)
(A)
12
50, 10, 30, 70
AB
? ?? ? ?? ? ? ? ? (B)
12
50, 20, 30, 50
AB
? ?? ? ??? ? ??
(C)
12
30, 30, 30, 10
AB
? ?? ? ?? ? ? ?? (D)
12
20, 10, 50, 30
AB
? ?? ? ??? ? ??
GATE 2016 Solid Mechanics
XE-D 6/9
Q.16 As shown in the figure, links AB and CD support the rigid member BD. Links AB and CD are
made of aluminum alloy?? 100GPa E ? and each has a cross-sectional area of
2
100 mm .
All the
members are pin connected and all the dimensions are in mm. Neglecting the weights of the
members, the elongation (in mm) of the link AB is __________
A
B
C
D
6 kN
400 400
100 200
Q.17 Figure shows an elastic beam of constant flexural rigidity EI and length . L The transverse
deflection () vx for the beam is represented by the equation
? ?
32
0
() (4 ), vx M x xL EIL ??
where
0
M is the applied couple. If 100mm L ? and
0
100 N-mm M ? , then the magnitude of the
shear force (in N) at the middle of the beam (at /2) xL ? is __________
GATE 2016 Solid Mechanics
XE-D 7/9
Q.18 Which one of the following represents the correct bending moment diagram of the beam PQR
loaded as shown in the figure?
(A)
(B)
(C)
(D)
Q.19
A point in a body is subjected to plane state of stress in XY plane. If 140MPa,
x
? ?
60 MPa
y
? ? and the major principal stress is 150 MPa, the magnitude of the in-plane shear stress
xy
? (in MPa) is
(A) 75 (B) 30 (C) 40 (D) 70
GATE 2016 Solid Mechanics
XE-D 8/9
Q.20 A 40 mm diameter rotor shaft of a helicopter transmits a torque T = 0.16 ? kN-m and a tensile force
P = 24 ? kN. The maximum tensile stress (in MPa) induced in the shaft is __________. Use the
value of ? = 3.1416.
T
T
P
P
Q.21 A wooden block of length 400 mm, width 50 mm and depth 100 mm is subjected to uniaxial load as
shown in the figure. An inclined plane ABCD is shown which makes an angle ? with the XZ
plane and the line CD is parallel to the Z-axis. The normal stress on the plane ABCD is
1 n
? when
o
? 30 ? and the normal stress on the plane ABCD is
2 n
? when
o
120 ? ? . The value of
2
1
n
n
?
?
is __________
10 kN
X
10 kN
?
?
A
C
D
B
Y
Z
400 mm
FirstRanker.com - FirstRanker's Choice
GATE 2016 General Aptitude ? GA Set-8
Q. 1 ? Q. 5 carry one mark each.
Q.1 The chairman requested the aggrieved shareholders to _________________ him.
(A) bare with (B) bore with (C) bear with (D) bare
Q.2 Identify the correct spelling out of the given options:
(A) Managable (B) Manageable (C) Mangaeble (D) Managible
Q.3 Pick the odd one out in the following:
13, 23, 33, 43, 53
(A) 23 (B) 33 (C) 43 (D) 53
Q.4 R2D2 is a robot. R2D2 can repair aeroplanes. No other robot can repair aeroplanes.
Which of the following can be logically inferred from the above statements?
(A) R2D2 is a robot which can only repair aeroplanes.
(B) R2D2 is the only robot which can repair aeroplanes.
(C) R2D2 is a robot which can repair only aeroplanes.
(D) Only R2D2 is a robot.
Q.5 If |9y ?6| =3, then y
2
?4y/3 is .
(A) 0 (B) +1/3 (C) ?1/3 (D) undefined
1/3
GATE 2016 General Aptitude ? GA Set-8
Q. 6 ? Q. 10 carry two marks each.
Q.6 The following graph represents the installed capacity for cement production (in tonnes) and the
actual production (in tonnes) of nine cement plants of a cement company. Capacity utilization of a
plant is defined as ratio of actual production of cement to installed capacity. A plant with installed
capacity of at least 200 tonnes is called a large plant and a plant with lesser capacity is called a
small plant. The difference between total production of large plants and small plants, in tonnes is
____.
Q.7 A poll of students appearing for masters in engineering indicated that 60 % of the students believed
that mechanical engineering is a profession unsuitable for women. A research study on women with
masters or higher degrees in mechanical engineering found that 99 % of such women were
successful in their professions.
Which of the following can be logically inferred from the above paragraph?
(A) Many students have misconceptions regarding various engineering disciplines.
(B) Men with advanced degrees in mechanical engineering believe women are well suited to be
mechanical engineers.
(C) Mechanical engineering is a profession well suited for women with masters or higher degrees
in mechanical engineering.
(D) The number of women pursuing higher degrees in mechanical engineering is small.
2/3
GATE 2016 General Aptitude ? GA Set-8
3/3
Q.8 Sourya committee had proposed the establishment of Sourya Institutes of Technology (SITs) in line
with Indian Institutes of Technology (IITs) to cater to the technological and industrial needs of a
developing country.
Which of the following can be logically inferred from the above sentence?
Based on the proposal,
(i) In the initial years, SIT students will get degrees from IIT.
(ii) SITs will have a distinct national objective.
(iii) SIT like institutions can only be established in consultation with IIT.
(iv) SITs will serve technological needs of a developing country.
(A) (iii) and (iv) only. (B) (i) and (iv) only.
(C) (ii) and (iv) only. (D) (ii) and (iii) only.
Q.9 Shaquille O? Neal is a 60% career free throw shooter, meaning that he successfully makes 60 free
throws out of 100 attempts on average. What is the probability that he will successfully
make exactly 6 free throws in 10 attempts?
(A) 0.2508
(B) 0.2816 (C) 0.2934 (D) 0.6000
Q.10 The numeral in the units position of 211
870
+ 146
127
? 3
424
is _____.
END OF THE QUESTION PAPER
GATE 2016 Solid Mechanics
XE-D 1/9
D : SOLID MECHANICS
Q. 1 ? Q. 9 carry one mark each.
Q.1 A single degree of freedom vibrating system has mass of 5 kg, stiffness of 500 N/m and damping
coefficient of 100 N-s/m. To make the system critically damped
(A) only the mass is to be increased by 1.2 times.
(B) only the stiffness is to be reduced to half.
(C) only the damping coefficient is to be doubled.
(D) no change in any of the system parameters is required.
Q.2 A ?L? shaped robotic arm AB is connected to a motor at end A and a magnetic gripper at B as
shown in the figure. If the arm is rotating with an angular velocity of 2 rad/s and an angular
acceleration of 3 rad/s
2
, the magnitude of the acceleration (in m/s
2
) of the end B is
(A) 2.0
(B) 2.5
(C) 5.0 (D) 6.0
Q.3 A block of weight 100 N is in static equilibrium on an inclined plane which makes an angle 15?
with the horizontal. The coefficient of friction between the inclined plane and the block is 0.3. The
magnitude of friction force (in N) acting on the block is __________
0.3 m
0.4 m
A
B
90
0
2 rad/s 3 rad/s
2
15?
100 N
GATE 2016 Solid Mechanics
XE-D 2/9
Q.4 The lower end A of the rigid bar AB is moving horizontally on the floor towards right with a
constant velocity of 5 m/s and the point B is sliding down the wall. The magnitude of the velocity
of point B at the instant ? ? 30? is
(A) zero (B) 4.34 m/s (C) 7.25 m/s (D) 8.66 m/s
Q.5 The state of plane stress at a point in a body is shown in the figure. The allowable shear stress of the
material of the body is 200 MPa. According to the maximum shear stress theory of failure the
maximum permissible value of ? (in MPa) is __________
Q.6
For a slender steel column of circular cross-section the critical buckling load is
cr
P . If the diameter
of the column is doubled (keeping other material and geometrical parameters same), then the
critical buckling load of the column is
(A)
cr
P/16 (B) 8
cr
P (C) 2
cr
P (D) 16
cr
P
Q.7 A closed thin cylindrical pressure vessel having an internal diameter of 1000 mm and a thickness of
10 mm is subjected to an internal pressure of 4 MPa. The maximum shear stress (in MPa) induced
in the cylinder is __________ (neglect the radial stress).
Q.8 A solid circular shaft subjected to pure torsion develops a maximum torsional shear stress of
120 MPa. Keeping the torsional moment same, if the diameter of the shaft is doubled then the
maximum shear stress (in MPa) induced in the shaft is __________
A
B
?
Floor
Wall
GATE 2016 Solid Mechanics
XE-D 3/9
Q.9 On a single straight track, a vehicle of mass 500 kg moving with a velocity of 25 m/s strikes
another vehicle of mass 250 kg moving with a velocity 10 m/s in the same direction. After the
impact, if both the vehicles stick together, the common velocity (in m/s) with which both the
vehicles will move together is __________
Q. 10 ? Q. 22 carry two marks each.
Q.10 A system with three forces and a concentrated moment at A is shown in the figure. The system is
replaced by an equivalent force system with a single force and a single couple at point ?O?. The
magnitude (in N-m) of the equivalent couple at ?O? is __________
Q.11 A block A on a smooth inclined plane is connected to block B as shown in the figure using an
inextensible cord which pass over a mass-less and friction-less pulley. Initially, the block B is
constrained to be at rest. If the constraint on block B is released, the magnitude of velocity (in m/s)
of the block ?B? after 2 seconds from its release is __________ (assume g =10 m/s
2
).
200 N
30
o
O
100 N
50 N-m
2 m 2 m
50 N
4 m
A
1 m
A
B
30?
10 kg
5 kg
GATE 2016 Solid Mechanics
XE-D 4/9
Q.12 The vibrating system shown in the figure carries a mass of 10 kg at the free end, where the static
deflection is 1 mm. This system is to be replaced by an equivalent vibrating spring mass system
having equivalent mass of 2 kg (assume g =10 m/s
2
). The natural frequency (in rad/s) and the
stiffness (in kN/m) of the equivalent system respectively are
(A) 10 and 20 (B) 20 and 100 (C) 100 and 20 (D) 1000 and 20
Q.13
A beam having flexural rigidity EI and length L is subjected to a concentrated end moment
0
M as
shown in the figure. For
32
410 N-m EI?? , 1m L ? and
0
8kN-m M ? , the strain energy stored
(in kN-m) in the beam and the rotation (in rad) at the free end respectively are
(A) 8.00 and 0.02 (B) 8.00 and 2.00 (C) 8.00 and 0.04 (D) 0.80 and 2.00
2 m 1 m
L
M
0
GATE 2016 Solid Mechanics
XE-D 5/9
Q.14 At a point ?O? on a metal sheet a square OABC of a unit side length is drawn. The square
undergoes a small uniform elastic deformation and deforms to OA*B*C* (dashed lines) as shown
in the figure. All dimensions are in mm and the figure is not to scale. The normal strains
x
? ,
y
?
and shear strain
xy
? developed in the square respectively are
(A)
0.0020, 0.0025 and 0.0020 ? (B) 0.0020, 0.0025 and 0.0020 ? ?
(C) 0.0025, 0.0020 and 0.0020 ? (D) 0.0020, 0.0025 and 0.0020 ? ?
Q.15 Mohr?s circle for the state of plane stress at a point is shown in the figure. Unit of stress is MPa and
the circle is drawn not to scale. Which one of the following options (stress values in MPa) is true?
(normal stress)
(shear stress)
A
B
C
O
O ? Origin of ? axis
C ? Center of Mohr?s circle
20
30
40
(
A
,
A
)
( , )
( , 0)
( , 0)
(A)
12
50, 10, 30, 70
AB
? ?? ? ?? ? ? ? ? (B)
12
50, 20, 30, 50
AB
? ?? ? ??? ? ??
(C)
12
30, 30, 30, 10
AB
? ?? ? ?? ? ? ?? (D)
12
20, 10, 50, 30
AB
? ?? ? ??? ? ??
GATE 2016 Solid Mechanics
XE-D 6/9
Q.16 As shown in the figure, links AB and CD support the rigid member BD. Links AB and CD are
made of aluminum alloy?? 100GPa E ? and each has a cross-sectional area of
2
100 mm .
All the
members are pin connected and all the dimensions are in mm. Neglecting the weights of the
members, the elongation (in mm) of the link AB is __________
A
B
C
D
6 kN
400 400
100 200
Q.17 Figure shows an elastic beam of constant flexural rigidity EI and length . L The transverse
deflection () vx for the beam is represented by the equation
? ?
32
0
() (4 ), vx M x xL EIL ??
where
0
M is the applied couple. If 100mm L ? and
0
100 N-mm M ? , then the magnitude of the
shear force (in N) at the middle of the beam (at /2) xL ? is __________
GATE 2016 Solid Mechanics
XE-D 7/9
Q.18 Which one of the following represents the correct bending moment diagram of the beam PQR
loaded as shown in the figure?
(A)
(B)
(C)
(D)
Q.19
A point in a body is subjected to plane state of stress in XY plane. If 140MPa,
x
? ?
60 MPa
y
? ? and the major principal stress is 150 MPa, the magnitude of the in-plane shear stress
xy
? (in MPa) is
(A) 75 (B) 30 (C) 40 (D) 70
GATE 2016 Solid Mechanics
XE-D 8/9
Q.20 A 40 mm diameter rotor shaft of a helicopter transmits a torque T = 0.16 ? kN-m and a tensile force
P = 24 ? kN. The maximum tensile stress (in MPa) induced in the shaft is __________. Use the
value of ? = 3.1416.
T
T
P
P
Q.21 A wooden block of length 400 mm, width 50 mm and depth 100 mm is subjected to uniaxial load as
shown in the figure. An inclined plane ABCD is shown which makes an angle ? with the XZ
plane and the line CD is parallel to the Z-axis. The normal stress on the plane ABCD is
1 n
? when
o
? 30 ? and the normal stress on the plane ABCD is
2 n
? when
o
120 ? ? . The value of
2
1
n
n
?
?
is __________
10 kN
X
10 kN
?
?
A
C
D
B
Y
Z
400 mm
GATE 2016 Solid Mechanics
XE-D 9/9
Q.22 For the truss shown in the figure, which one of the following statements is true?
(A) AG is the only zero force member.
(B) AG and BH are the only two zero force members.
(C) AG, BH and HF are zero force members.
(D) AG, BH, HF and GC are zero force members.
END OF THE QUESTION PAPER
9 k N
12 k N
D F
E
3 m
4 m
4 m 4 m
A
B
C
G H
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This post was last modified on 18 December 2019