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# Mechanical Engineering (ME) 2013 GATE Paper (Set A) with solution Mechanical Engineering Notes | EduRev

## GATE : Mechanical Engineering (ME) 2013 GATE Paper (Set A) with solution Mechanical Engineering Notes | EduRev

``` Page 1

|ME-GATE-2013 PAPER|
1
Q. No. 1 – 25 Carry One Mark Each
1. The partial differential equation
2
2
u u u
u
t x x
? ? ?
+ =
? ? ?
is a
(A) Linear equation of order 2 (B) Non-linear equation of order 1
(C) Linear equation of order 1 (D) Non-linear equation of order 2
2. The eigen values of symmetric matrix are all
(A) Complex with non-zero positive imaginary part
(B) Complex with non-zero negative imaginary part
(C) Real
(D) Pure imaginary
3. Match the CORRECT pairs:
Numerical Integration Scheme Order of Fitting Polynomial
P. Simpson’s 3/8 Rule 1. First
Q. Trapezoidal Rule 2. Second
R. Simpson’s 1/3 Rule 3. Third
(A) P-2; Q-1; R-3 (B) P-3; Q-2; R-1 (C) P-1; Q-2; R-3 (D) P-3; Q-1; R-2
4. A rod of length L having uniform cross-sectional area A is subjected to a tensile
force P as shown in the figure below. If the Young’s modulus of the material
varies linearly from
1
E to
2
E along the length of the rod, the normal stress
developed at the section-SS is
(A)
P
A
(B)
( )
( )
1 2
1 2
P E E
A E E
-
+
(C)
2
1
PE
AE
(D)
1
2
PE
AE
Stress depends on area.
5. The threaded bolts A and B of same material and length are subjected to identical
tensile load. If the elastic strain energy stored in bolt A is 4 times that of the bolt B
and the mean diameter of bolt A is 12mm, the mean diameter of bolt B in mm is
(A) 16 (B) 24 (C) 36 (D) 48
1
E
2
E
S
S
L /2
L
P P
Page 2

|ME-GATE-2013 PAPER|
1
Q. No. 1 – 25 Carry One Mark Each
1. The partial differential equation
2
2
u u u
u
t x x
? ? ?
+ =
? ? ?
is a
(A) Linear equation of order 2 (B) Non-linear equation of order 1
(C) Linear equation of order 1 (D) Non-linear equation of order 2
2. The eigen values of symmetric matrix are all
(A) Complex with non-zero positive imaginary part
(B) Complex with non-zero negative imaginary part
(C) Real
(D) Pure imaginary
3. Match the CORRECT pairs:
Numerical Integration Scheme Order of Fitting Polynomial
P. Simpson’s 3/8 Rule 1. First
Q. Trapezoidal Rule 2. Second
R. Simpson’s 1/3 Rule 3. Third
(A) P-2; Q-1; R-3 (B) P-3; Q-2; R-1 (C) P-1; Q-2; R-3 (D) P-3; Q-1; R-2
4. A rod of length L having uniform cross-sectional area A is subjected to a tensile
force P as shown in the figure below. If the Young’s modulus of the material
varies linearly from
1
E to
2
E along the length of the rod, the normal stress
developed at the section-SS is
(A)
P
A
(B)
( )
( )
1 2
1 2
P E E
A E E
-
+
(C)
2
1
PE
AE
(D)
1
2
PE
AE
Stress depends on area.
5. The threaded bolts A and B of same material and length are subjected to identical
tensile load. If the elastic strain energy stored in bolt A is 4 times that of the bolt B
and the mean diameter of bolt A is 12mm, the mean diameter of bolt B in mm is
(A) 16 (B) 24 (C) 36 (D) 48
1
E
2
E
S
S
L /2
L
P P
|ME-GATE-2013 PAPER|
2
Explanation:
2
1 1 2
2
2 1
2
P l
2AE
E A
E A
P l
2AE
? ?
? ?
? ?
? ?
= =
? ?
? ?
? ?
? ?
2
2
2
1
2 1
d
4
d
d 12 d 24
=
= × =
6. A link OB is rotating with a constant angular velocity of 2 rad/s in counter
clockwise direction and a block is sliding radially outward on it with an uniform
velocity of 0.75 m/s with respect to the rod, as shown in the figure below. If
OA = 1m, the magnitude of the absolute acceleration of the block at location A in
2
m / s is
(A) 3 (B) 4 (C) 5 (D) 6
Explanation:
t
2
r
2 2
2v 2 0.75 2 3
v
4
r
Resultant 3 4 5
a = ? = × × =
a = =
? a = + =
7. For steady, fully developed flow inside a straight pipe of diameter D, neglecting
gravity effects, the pressure drop p ? over a length L and the wall shear stress
w
t
are related by
(A)
w
pD
4L
?
t = (B)
2
w 2
pD
4L
?
t = (C)
w
pD
2L
?
t = (D)
w
4 pL
D
?
t =
Explanation:
( )
2
pD
DL D p
4 4L
? ?
p ?
t p = ·? ?t =
A
B
O
Page 3

|ME-GATE-2013 PAPER|
1
Q. No. 1 – 25 Carry One Mark Each
1. The partial differential equation
2
2
u u u
u
t x x
? ? ?
+ =
? ? ?
is a
(A) Linear equation of order 2 (B) Non-linear equation of order 1
(C) Linear equation of order 1 (D) Non-linear equation of order 2
2. The eigen values of symmetric matrix are all
(A) Complex with non-zero positive imaginary part
(B) Complex with non-zero negative imaginary part
(C) Real
(D) Pure imaginary
3. Match the CORRECT pairs:
Numerical Integration Scheme Order of Fitting Polynomial
P. Simpson’s 3/8 Rule 1. First
Q. Trapezoidal Rule 2. Second
R. Simpson’s 1/3 Rule 3. Third
(A) P-2; Q-1; R-3 (B) P-3; Q-2; R-1 (C) P-1; Q-2; R-3 (D) P-3; Q-1; R-2
4. A rod of length L having uniform cross-sectional area A is subjected to a tensile
force P as shown in the figure below. If the Young’s modulus of the material
varies linearly from
1
E to
2
E along the length of the rod, the normal stress
developed at the section-SS is
(A)
P
A
(B)
( )
( )
1 2
1 2
P E E
A E E
-
+
(C)
2
1
PE
AE
(D)
1
2
PE
AE
Stress depends on area.
5. The threaded bolts A and B of same material and length are subjected to identical
tensile load. If the elastic strain energy stored in bolt A is 4 times that of the bolt B
and the mean diameter of bolt A is 12mm, the mean diameter of bolt B in mm is
(A) 16 (B) 24 (C) 36 (D) 48
1
E
2
E
S
S
L /2
L
P P
|ME-GATE-2013 PAPER|
2
Explanation:
2
1 1 2
2
2 1
2
P l
2AE
E A
E A
P l
2AE
? ?
? ?
? ?
? ?
= =
? ?
? ?
? ?
? ?
2
2
2
1
2 1
d
4
d
d 12 d 24
=
= × =
6. A link OB is rotating with a constant angular velocity of 2 rad/s in counter
clockwise direction and a block is sliding radially outward on it with an uniform
velocity of 0.75 m/s with respect to the rod, as shown in the figure below. If
OA = 1m, the magnitude of the absolute acceleration of the block at location A in
2
m / s is
(A) 3 (B) 4 (C) 5 (D) 6
Explanation:
t
2
r
2 2
2v 2 0.75 2 3
v
4
r
Resultant 3 4 5
a = ? = × × =
a = =
? a = + =
7. For steady, fully developed flow inside a straight pipe of diameter D, neglecting
gravity effects, the pressure drop p ? over a length L and the wall shear stress
w
t
are related by
(A)
w
pD
4L
?
t = (B)
2
w 2
pD
4L
?
t = (C)
w
pD
2L
?
t = (D)
w
4 pL
D
?
t =
Explanation:
( )
2
pD
DL D p
4 4L
? ?
p ?
t p = ·? ?t =
A
B
O
|ME-GATE-2013 PAPER|
3
8. The pressure, dry bulb temperature, and relative humidity of air in a room are
1bar, 30ºC and 70% respectively. If the saturated steam pressure at 30ºC is
4.25kPa, the specific humidity of the room air in kg water vapour / kg dry air is
(A) 0.0083 (B) 0.0101 (C) 0.0191 (D) 0.0232
Explanation:
5
P 1 bar 10 Pa 100 KPa = = =
sat
P 4.25KPa =
( )
× ×
= =
-
p
0.622 0.7 4.25
S .humidity 0.019
100 4.25

9. Consider one-dimensional steady state heat conduction, without heat generation,
in a plane wall; with boundary conditions as shown in the figure below. The
conductivity of the wall is given by
0
k k bT = + ; where
0
k and b are positive
constants and T is temperature.
As x increases, the temperature gradient ( ) dT / dx will
(A) Remain constant (B) Be zero (C) Increase (D) Decrease
10. In a rolling process, the state of stress of the material undergoing deformation is
(A) Pure compression   (B) Pure shear
(C) Compression and shear (D) Tension and shear
11. Match the CORRECT pairs.
Processes Characteristics / Application
P. Friction Welding 1. Non-consumable electrode
Q. Gas Metal Arc Welding 2. Joining of thick plates
R. Tungsten Inert Gas Welding 3. Consumable electrode wire
S. Electroslag Welding 4. Joining of cylindrical dissimilar materials
(A) P-4;Q-3;R-1;S-2 (B) P-4;Q-2;R-3;S-1
(C) P-2;Q-3;R-4;S-1 (D) P-2;Q-4;R-1;S-3
1
T
2 2 1
T where T T >
x
Page 4

|ME-GATE-2013 PAPER|
1
Q. No. 1 – 25 Carry One Mark Each
1. The partial differential equation
2
2
u u u
u
t x x
? ? ?
+ =
? ? ?
is a
(A) Linear equation of order 2 (B) Non-linear equation of order 1
(C) Linear equation of order 1 (D) Non-linear equation of order 2
2. The eigen values of symmetric matrix are all
(A) Complex with non-zero positive imaginary part
(B) Complex with non-zero negative imaginary part
(C) Real
(D) Pure imaginary
3. Match the CORRECT pairs:
Numerical Integration Scheme Order of Fitting Polynomial
P. Simpson’s 3/8 Rule 1. First
Q. Trapezoidal Rule 2. Second
R. Simpson’s 1/3 Rule 3. Third
(A) P-2; Q-1; R-3 (B) P-3; Q-2; R-1 (C) P-1; Q-2; R-3 (D) P-3; Q-1; R-2
4. A rod of length L having uniform cross-sectional area A is subjected to a tensile
force P as shown in the figure below. If the Young’s modulus of the material
varies linearly from
1
E to
2
E along the length of the rod, the normal stress
developed at the section-SS is
(A)
P
A
(B)
( )
( )
1 2
1 2
P E E
A E E
-
+
(C)
2
1
PE
AE
(D)
1
2
PE
AE
Stress depends on area.
5. The threaded bolts A and B of same material and length are subjected to identical
tensile load. If the elastic strain energy stored in bolt A is 4 times that of the bolt B
and the mean diameter of bolt A is 12mm, the mean diameter of bolt B in mm is
(A) 16 (B) 24 (C) 36 (D) 48
1
E
2
E
S
S
L /2
L
P P
|ME-GATE-2013 PAPER|
2
Explanation:
2
1 1 2
2
2 1
2
P l
2AE
E A
E A
P l
2AE
? ?
? ?
? ?
? ?
= =
? ?
? ?
? ?
? ?
2
2
2
1
2 1
d
4
d
d 12 d 24
=
= × =
6. A link OB is rotating with a constant angular velocity of 2 rad/s in counter
clockwise direction and a block is sliding radially outward on it with an uniform
velocity of 0.75 m/s with respect to the rod, as shown in the figure below. If
OA = 1m, the magnitude of the absolute acceleration of the block at location A in
2
m / s is
(A) 3 (B) 4 (C) 5 (D) 6
Explanation:
t
2
r
2 2
2v 2 0.75 2 3
v
4
r
Resultant 3 4 5
a = ? = × × =
a = =
? a = + =
7. For steady, fully developed flow inside a straight pipe of diameter D, neglecting
gravity effects, the pressure drop p ? over a length L and the wall shear stress
w
t
are related by
(A)
w
pD
4L
?
t = (B)
2
w 2
pD
4L
?
t = (C)
w
pD
2L
?
t = (D)
w
4 pL
D
?
t =
Explanation:
( )
2
pD
DL D p
4 4L
? ?
p ?
t p = ·? ?t =
A
B
O
|ME-GATE-2013 PAPER|
3
8. The pressure, dry bulb temperature, and relative humidity of air in a room are
1bar, 30ºC and 70% respectively. If the saturated steam pressure at 30ºC is
4.25kPa, the specific humidity of the room air in kg water vapour / kg dry air is
(A) 0.0083 (B) 0.0101 (C) 0.0191 (D) 0.0232
Explanation:
5
P 1 bar 10 Pa 100 KPa = = =
sat
P 4.25KPa =
( )
× ×
= =
-
p
0.622 0.7 4.25
S .humidity 0.019
100 4.25

9. Consider one-dimensional steady state heat conduction, without heat generation,
in a plane wall; with boundary conditions as shown in the figure below. The
conductivity of the wall is given by
0
k k bT = + ; where
0
k and b are positive
constants and T is temperature.
As x increases, the temperature gradient ( ) dT / dx will
(A) Remain constant (B) Be zero (C) Increase (D) Decrease
10. In a rolling process, the state of stress of the material undergoing deformation is
(A) Pure compression   (B) Pure shear
(C) Compression and shear (D) Tension and shear
11. Match the CORRECT pairs.
Processes Characteristics / Application
P. Friction Welding 1. Non-consumable electrode
Q. Gas Metal Arc Welding 2. Joining of thick plates
R. Tungsten Inert Gas Welding 3. Consumable electrode wire
S. Electroslag Welding 4. Joining of cylindrical dissimilar materials
(A) P-4;Q-3;R-1;S-2 (B) P-4;Q-2;R-3;S-1
(C) P-2;Q-3;R-4;S-1 (D) P-2;Q-4;R-1;S-3
1
T
2 2 1
T where T T >
x
|ME-GATE-2013 PAPER|
4
12. A metric thread of pitch 2mm and thread angle 60º is inspected for its pitch
diameter using 3-wire method. The diameter of the best size wire in mm is
(A) 0.866 (B) 1.000 (C) 1.154 (D) 2.000
Explanations:- For 60
o
thread angle, best wire size =0.57135xP=1.154
13. Customers arrive at a ticket counter at a rate of 50 per hour and tickets are
issued in the order of their arrival. The average time taken for issuing a ticket is
1min. Assuming that customer arrivals form a Poisson process and service times
are exponentially distributed, the average waiting time in queue in minutes is:
(A) 3 (B) 4 (C) 5 (D) 6
Explanation:
( )
50 / hr 60 / hr W.T 0.083hr 5min
?
? = µ = = = =
µ µ - ?

14. In simple exponential smoothing forecasting, to give higher weightage to recent
demand information, the smoothing constant must be close to
(A) -1 (B) zero (C) 0.5 (D) 1
Explanations:- Value of a close to one have less of a smoothing effect and give greater
weight to recent changes in the data.
15. A steel bar 200 mm in diameter is turned at a feed of 0.25 mm/rev with a depth
of cut of 4 mm. The rotational speed of the workpiece is 160 rpm. The material
removal rate in
3
mm / s is
(A) 160 (B) 167.6 (C) 1600 (D) 1675.5
Explanations:- f d v × ×
( )( )
200 160
0.25 4
60
p× ×
= × 1675.5 =
16. A cube shaped casting solidifies in 5 minutes. The solidification time in minutes
for a cube of the same material, which is 8 times heavier than the original casting
will be
(A) 10 (B) 20 (C) 24 (D) 40

Explanations:-
2
2
1
1
1
V V
t C ; t 5 C
A A
? ?
? ?
= = =
? ?
? ?
? ?
? ?
2 1
Now V 8V =
Which implies each ride is getting doubled.  So
2 1
A 4A =
2 2
2 1
2 1
2 2
V V
t c c 4 t 4 5 20min
A 4A
? ? ? ?
= = = × = × =
? ? ? ?
? ? ? ?

Page 5

|ME-GATE-2013 PAPER|
1
Q. No. 1 – 25 Carry One Mark Each
1. The partial differential equation
2
2
u u u
u
t x x
? ? ?
+ =
? ? ?
is a
(A) Linear equation of order 2 (B) Non-linear equation of order 1
(C) Linear equation of order 1 (D) Non-linear equation of order 2
2. The eigen values of symmetric matrix are all
(A) Complex with non-zero positive imaginary part
(B) Complex with non-zero negative imaginary part
(C) Real
(D) Pure imaginary
3. Match the CORRECT pairs:
Numerical Integration Scheme Order of Fitting Polynomial
P. Simpson’s 3/8 Rule 1. First
Q. Trapezoidal Rule 2. Second
R. Simpson’s 1/3 Rule 3. Third
(A) P-2; Q-1; R-3 (B) P-3; Q-2; R-1 (C) P-1; Q-2; R-3 (D) P-3; Q-1; R-2
4. A rod of length L having uniform cross-sectional area A is subjected to a tensile
force P as shown in the figure below. If the Young’s modulus of the material
varies linearly from
1
E to
2
E along the length of the rod, the normal stress
developed at the section-SS is
(A)
P
A
(B)
( )
( )
1 2
1 2
P E E
A E E
-
+
(C)
2
1
PE
AE
(D)
1
2
PE
AE
Stress depends on area.
5. The threaded bolts A and B of same material and length are subjected to identical
tensile load. If the elastic strain energy stored in bolt A is 4 times that of the bolt B
and the mean diameter of bolt A is 12mm, the mean diameter of bolt B in mm is
(A) 16 (B) 24 (C) 36 (D) 48
1
E
2
E
S
S
L /2
L
P P
|ME-GATE-2013 PAPER|
2
Explanation:
2
1 1 2
2
2 1
2
P l
2AE
E A
E A
P l
2AE
? ?
? ?
? ?
? ?
= =
? ?
? ?
? ?
? ?
2
2
2
1
2 1
d
4
d
d 12 d 24
=
= × =
6. A link OB is rotating with a constant angular velocity of 2 rad/s in counter
clockwise direction and a block is sliding radially outward on it with an uniform
velocity of 0.75 m/s with respect to the rod, as shown in the figure below. If
OA = 1m, the magnitude of the absolute acceleration of the block at location A in
2
m / s is
(A) 3 (B) 4 (C) 5 (D) 6
Explanation:
t
2
r
2 2
2v 2 0.75 2 3
v
4
r
Resultant 3 4 5
a = ? = × × =
a = =
? a = + =
7. For steady, fully developed flow inside a straight pipe of diameter D, neglecting
gravity effects, the pressure drop p ? over a length L and the wall shear stress
w
t
are related by
(A)
w
pD
4L
?
t = (B)
2
w 2
pD
4L
?
t = (C)
w
pD
2L
?
t = (D)
w
4 pL
D
?
t =
Explanation:
( )
2
pD
DL D p
4 4L
? ?
p ?
t p = ·? ?t =
A
B
O
|ME-GATE-2013 PAPER|
3
8. The pressure, dry bulb temperature, and relative humidity of air in a room are
1bar, 30ºC and 70% respectively. If the saturated steam pressure at 30ºC is
4.25kPa, the specific humidity of the room air in kg water vapour / kg dry air is
(A) 0.0083 (B) 0.0101 (C) 0.0191 (D) 0.0232
Explanation:
5
P 1 bar 10 Pa 100 KPa = = =
sat
P 4.25KPa =
( )
× ×
= =
-
p
0.622 0.7 4.25
S .humidity 0.019
100 4.25

9. Consider one-dimensional steady state heat conduction, without heat generation,
in a plane wall; with boundary conditions as shown in the figure below. The
conductivity of the wall is given by
0
k k bT = + ; where
0
k and b are positive
constants and T is temperature.
As x increases, the temperature gradient ( ) dT / dx will
(A) Remain constant (B) Be zero (C) Increase (D) Decrease
10. In a rolling process, the state of stress of the material undergoing deformation is
(A) Pure compression   (B) Pure shear
(C) Compression and shear (D) Tension and shear
11. Match the CORRECT pairs.
Processes Characteristics / Application
P. Friction Welding 1. Non-consumable electrode
Q. Gas Metal Arc Welding 2. Joining of thick plates
R. Tungsten Inert Gas Welding 3. Consumable electrode wire
S. Electroslag Welding 4. Joining of cylindrical dissimilar materials
(A) P-4;Q-3;R-1;S-2 (B) P-4;Q-2;R-3;S-1
(C) P-2;Q-3;R-4;S-1 (D) P-2;Q-4;R-1;S-3
1
T
2 2 1
T where T T >
x
|ME-GATE-2013 PAPER|
4
12. A metric thread of pitch 2mm and thread angle 60º is inspected for its pitch
diameter using 3-wire method. The diameter of the best size wire in mm is
(A) 0.866 (B) 1.000 (C) 1.154 (D) 2.000
Explanations:- For 60
o
thread angle, best wire size =0.57135xP=1.154
13. Customers arrive at a ticket counter at a rate of 50 per hour and tickets are
issued in the order of their arrival. The average time taken for issuing a ticket is
1min. Assuming that customer arrivals form a Poisson process and service times
are exponentially distributed, the average waiting time in queue in minutes is:
(A) 3 (B) 4 (C) 5 (D) 6
Explanation:
( )
50 / hr 60 / hr W.T 0.083hr 5min
?
? = µ = = = =
µ µ - ?

14. In simple exponential smoothing forecasting, to give higher weightage to recent
demand information, the smoothing constant must be close to
(A) -1 (B) zero (C) 0.5 (D) 1
Explanations:- Value of a close to one have less of a smoothing effect and give greater
weight to recent changes in the data.
15. A steel bar 200 mm in diameter is turned at a feed of 0.25 mm/rev with a depth
of cut of 4 mm. The rotational speed of the workpiece is 160 rpm. The material
removal rate in
3
mm / s is
(A) 160 (B) 167.6 (C) 1600 (D) 1675.5
Explanations:- f d v × ×
( )( )
200 160
0.25 4
60
p× ×
= × 1675.5 =
16. A cube shaped casting solidifies in 5 minutes. The solidification time in minutes
for a cube of the same material, which is 8 times heavier than the original casting
will be
(A) 10 (B) 20 (C) 24 (D) 40

Explanations:-
2
2
1
1
1
V V
t C ; t 5 C
A A
? ?
? ?
= = =
? ?
? ?
? ?
? ?
2 1
Now V 8V =
Which implies each ride is getting doubled.  So
2 1
A 4A =
2 2
2 1
2 1
2 2
V V
t c c 4 t 4 5 20min
A 4A
? ? ? ?
= = = × = × =
? ? ? ?
? ? ? ?

|ME-GATE-2013 PAPER|
5
17. For a ductile material, toughness is a measure of
(A) Resistance to scratching
(B) Ability to absorb energy up to fracture
(C) Ability to absorb energy till elastic limit
(D) Resistance to indentation
Explanations:- Since, toughness has ability to absorb energy up to fracture.
18. In order to have maximum power from a Pelton turbine, the bucket speed must
be
(A) Equal to the jet speed (B) Equal to half the jet speed
(C) Equal to twice the jet speed (D) Independent of the jet speed
Explanation: Since, velocity of bucket = ½ times the velocity of jet.
19. Consider one-dimensional steady state heat conduction along x-axis ( ) 0 x L = = ,
through a plane wall with the boundary surfaces ( ) x 0 and x = L = maintained at
temperatures 0ºC and 100ºC. Heat is generated uniformly throughout the wall.
Choose the CORRECT statement.
(A) The direction of heat transfer will be from the surface at 100ºC to surface at
0ºC.
(B) The maximum temperature inside the wall must be greater than 100ºC
(C) The temperature distribution is linear within the wall
(D) The temperature distribution is symmetric about the mid-plane of the wall
20. A cylinder contains
3
5m of ideal gas at a pressure of 1 bar. This gas is
compressed in a reversible isothermal process till its pressure increases to 5 bar.
The work in kJ required for this process is
(A) 804.7 (B) 953.2 (C) 981.7 (D) 1012.2
Explanations:-
2
1 1
1
P
P V ln wD
P
=
5
5
wD 10 5 ln 804718.95 804.71 kJ
1
? ?
? = × = =
? ?
? ?

21. A long thin walled cylindrical shell, closed at both ends, is subjected to an internal
pressure. The ratio of the hoop stress (circumferential stress) to longitudinal
stress developed in the shell is
(A) 0.5 (B) 1.0 (C) 2.0 (D) 4.0
```
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## GATE Past Year Papers for Practice (All Branches)

380 docs|127 tests

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