Mechanical Engineering (ME) 2009 GATE Paper without solution Mechanical Engineering Notes | EduRev

Mock Test Series - Mechanical Engineering (ME) for GATE 2020

Mechanical Engineering : Mechanical Engineering (ME) 2009 GATE Paper without solution Mechanical Engineering Notes | EduRev

 Page 1


ME? GATE Paper 2009
Q. No. 1 – 20 Carry One Mark Each 
1. For a matrix [M]=
3 4
5 5
3
x
5
? ?
? ?
? ?
? ?
? ?
? ?
, the transpose of the matrix is equal to the inverse of 
the matrix 
T 1
M M
-
= ? ? ? ?
? ? ? ?
. The value of x is given by
(A) 
4
5
- (B) 
3
5
- (C) 
3
5
(D) 
4
5
2. The divergence of the vector field 
2
ˆ ˆ ˆ
3xzi 2xyj yz k + - at a point (1,1,1 ) is equal to
(A) 7  (B) 4 (C) 3 (D) 0
3. The inverse Laplace transform of
( )
2
1
s s +
 is 
(A) 
t
1 e + (B) 
t
1 e - (C) 
t
1 e
-
- (D) 
t
1 e
-
+
4. If three coins are tossed simultaneously, the probability of getting at least one
head
(A) 1/8  (B) 3/8      (C) 1/2  (D) 7/8
5. If a closed system is undergoing an irreversible process, the entropy of the
system
(A)  Must increase
(B)  Always remains constant
(C)  Must decrease
(D) Can increase, decrease or remain constant
6. A coolant fluid at 30°C flows over a heated flat plate maintained at a constant 
temperature of 100°C. The boundary layer temperature distribution at a given 
location on the plate may be approximated as ( ) T 30 70exp y = + - where y (in m)
is the distance normal to the plate and T is in °C. If thermal conductivity of the 
fluid is 1.0W/mK, the local convective heat transfer coefficient (in W/m
2
K) at that 
location will be 
(A) 0.2 (B) 1 (C) 5 (D) 10 
7. A frictionless piston-cylinder device contains a gas initially at 0.8MPa and 0.015
m
3
. It expands quasi-statically at constant temperature to a final volume of 0.030
m
3
. The work output (in kJ) during this process will be
(A) 8.32 (B) 12.00 (C) 554.67 (D) 8320.00 
Page 2


ME? GATE Paper 2009
Q. No. 1 – 20 Carry One Mark Each 
1. For a matrix [M]=
3 4
5 5
3
x
5
? ?
? ?
? ?
? ?
? ?
? ?
, the transpose of the matrix is equal to the inverse of 
the matrix 
T 1
M M
-
= ? ? ? ?
? ? ? ?
. The value of x is given by
(A) 
4
5
- (B) 
3
5
- (C) 
3
5
(D) 
4
5
2. The divergence of the vector field 
2
ˆ ˆ ˆ
3xzi 2xyj yz k + - at a point (1,1,1 ) is equal to
(A) 7  (B) 4 (C) 3 (D) 0
3. The inverse Laplace transform of
( )
2
1
s s +
 is 
(A) 
t
1 e + (B) 
t
1 e - (C) 
t
1 e
-
- (D) 
t
1 e
-
+
4. If three coins are tossed simultaneously, the probability of getting at least one
head
(A) 1/8  (B) 3/8      (C) 1/2  (D) 7/8
5. If a closed system is undergoing an irreversible process, the entropy of the
system
(A)  Must increase
(B)  Always remains constant
(C)  Must decrease
(D) Can increase, decrease or remain constant
6. A coolant fluid at 30°C flows over a heated flat plate maintained at a constant 
temperature of 100°C. The boundary layer temperature distribution at a given 
location on the plate may be approximated as ( ) T 30 70exp y = + - where y (in m)
is the distance normal to the plate and T is in °C. If thermal conductivity of the 
fluid is 1.0W/mK, the local convective heat transfer coefficient (in W/m
2
K) at that 
location will be 
(A) 0.2 (B) 1 (C) 5 (D) 10 
7. A frictionless piston-cylinder device contains a gas initially at 0.8MPa and 0.015
m
3
. It expands quasi-statically at constant temperature to a final volume of 0.030
m
3
. The work output (in kJ) during this process will be
(A) 8.32 (B) 12.00 (C) 554.67 (D) 8320.00 
ME? GATE Paper 2009
8. In an ideal vapour compression refrigeration cycle, the specific enthalpy of
refrigerant (in kJ/kg) at the following states is given as:
Inlet of condenser: 283 
Exit of condenser: 116 
Exit of evaporator: 232 
The COP of this cycle is
(A) 2.27 (B) 2.75 (C) 3.27 (D) 3.75 
9. A compressor undergoes a reversible, steady flow process. The gas at inlet and
outlet of the compressor is designated as state 1 and state 2 respectively.
Potential and kinetic energy changes are to be ignored. The following notations
are used:
v= specific volume and P=pressure of the gas.
The specific work required to be supplied to the compressor for this gas
compression process is
(A) 
2
1
Pdv
?
(B) 
2
1
vdP
?
(C) ( )
1 2 1
v P P - (D) ( )
2 1 2
P v v - -
10. A block weighing 981N is resting on a horizontal surface. The coefficient of 
friction between the block and the horizontal surface is µ = 0.2A vertical cable 
attached to the block provides partial support as shown. A man can pull 
horizontally with a force of 100N. What will be the tension, T (in N) in the cable if 
the man is just able to move the block to the right? 
(A) 176.2 (B) 196.0 (C) 481.0 (D) 981.0 
11. If the principal stresses in a plane stress problem, are
1 2
100MPa, 40MPa s = s = , 
the magnitude of the maximum shear stress (in MPa) will be
(A) 60  (B) 50                    (C) 30 (D) 20 
12. A simple quick return mechanism is shown in the figure. The forward to return
ratio of the quick return mechanism is 2:1. If the radius of the crank O
1
P is 125
mm, then the distance 'd' (in mm) between the crank centre to lever pivot centre
point should be
100N
T
G
0.2 µ =
Page 3


ME? GATE Paper 2009
Q. No. 1 – 20 Carry One Mark Each 
1. For a matrix [M]=
3 4
5 5
3
x
5
? ?
? ?
? ?
? ?
? ?
? ?
, the transpose of the matrix is equal to the inverse of 
the matrix 
T 1
M M
-
= ? ? ? ?
? ? ? ?
. The value of x is given by
(A) 
4
5
- (B) 
3
5
- (C) 
3
5
(D) 
4
5
2. The divergence of the vector field 
2
ˆ ˆ ˆ
3xzi 2xyj yz k + - at a point (1,1,1 ) is equal to
(A) 7  (B) 4 (C) 3 (D) 0
3. The inverse Laplace transform of
( )
2
1
s s +
 is 
(A) 
t
1 e + (B) 
t
1 e - (C) 
t
1 e
-
- (D) 
t
1 e
-
+
4. If three coins are tossed simultaneously, the probability of getting at least one
head
(A) 1/8  (B) 3/8      (C) 1/2  (D) 7/8
5. If a closed system is undergoing an irreversible process, the entropy of the
system
(A)  Must increase
(B)  Always remains constant
(C)  Must decrease
(D) Can increase, decrease or remain constant
6. A coolant fluid at 30°C flows over a heated flat plate maintained at a constant 
temperature of 100°C. The boundary layer temperature distribution at a given 
location on the plate may be approximated as ( ) T 30 70exp y = + - where y (in m)
is the distance normal to the plate and T is in °C. If thermal conductivity of the 
fluid is 1.0W/mK, the local convective heat transfer coefficient (in W/m
2
K) at that 
location will be 
(A) 0.2 (B) 1 (C) 5 (D) 10 
7. A frictionless piston-cylinder device contains a gas initially at 0.8MPa and 0.015
m
3
. It expands quasi-statically at constant temperature to a final volume of 0.030
m
3
. The work output (in kJ) during this process will be
(A) 8.32 (B) 12.00 (C) 554.67 (D) 8320.00 
ME? GATE Paper 2009
8. In an ideal vapour compression refrigeration cycle, the specific enthalpy of
refrigerant (in kJ/kg) at the following states is given as:
Inlet of condenser: 283 
Exit of condenser: 116 
Exit of evaporator: 232 
The COP of this cycle is
(A) 2.27 (B) 2.75 (C) 3.27 (D) 3.75 
9. A compressor undergoes a reversible, steady flow process. The gas at inlet and
outlet of the compressor is designated as state 1 and state 2 respectively.
Potential and kinetic energy changes are to be ignored. The following notations
are used:
v= specific volume and P=pressure of the gas.
The specific work required to be supplied to the compressor for this gas
compression process is
(A) 
2
1
Pdv
?
(B) 
2
1
vdP
?
(C) ( )
1 2 1
v P P - (D) ( )
2 1 2
P v v - -
10. A block weighing 981N is resting on a horizontal surface. The coefficient of 
friction between the block and the horizontal surface is µ = 0.2A vertical cable 
attached to the block provides partial support as shown. A man can pull 
horizontally with a force of 100N. What will be the tension, T (in N) in the cable if 
the man is just able to move the block to the right? 
(A) 176.2 (B) 196.0 (C) 481.0 (D) 981.0 
11. If the principal stresses in a plane stress problem, are
1 2
100MPa, 40MPa s = s = , 
the magnitude of the maximum shear stress (in MPa) will be
(A) 60  (B) 50                    (C) 30 (D) 20 
12. A simple quick return mechanism is shown in the figure. The forward to return
ratio of the quick return mechanism is 2:1. If the radius of the crank O
1
P is 125
mm, then the distance 'd' (in mm) between the crank centre to lever pivot centre
point should be
100N
T
G
0.2 µ =
ME? GATE Paper 2009
(A) 144.3 (B) 216.5 (C) 240.0 (D) 250.0 
13. The rotor shaft of a large electric motor supported between short bearings at
both deflection of 1.8mm in the middle of the rotor. Assuming the rotor to be
perfectly balanced and supported at knife edges at both the ends, the likely
critical speed (in rpm) of the shaft is
(A) 350 (B) 705 (C) 2810 (D) 4430 
14. A solid circular shaft of diameter d is subjected to a combined bending moment M
and torque, T. The material property to be used for designing the shaft using the
relation
2 2
3
16
M T
d
+
p
is 
(A) ultimate tensile strength (S
u
) (B) tensile yield strength (S
y
) 
(C) torsional yield strength (S
sy
)  (D) endurance strength (S
e
) 
15. The effective number of lattice points in the unit cell of simple cubic, body
centered cubic, and face centered cubic space lattices, respectively, are
(A) 1,2,2 (B) 1,2,4         (C) 2,3,4        (D) 2,4,4
16. Friction at the tool-chip interface can be reduced by 
(A)  decreasing the rake angle  (B) increasing the depth of cut 
(C)  decreasing the cutting speed (D) increasing the cutting speed 
17. Two streams of liquid metal, which are not hot enough to fuse properly, result
into a casting defect known as
(A) cold shut  (B) swell                (C) sand wash        (D) scab
18. The expected time (t
e
) of a PERT activity in terms of optimistic time (t
0
),
pessimistic time (t
p
) and most likely time (t
l
) is given by
(A) 
o l p
e
t 4t t
t
6
+ +
= (B) 
o p l
e
t 4t t
t
6
+ +
=
(C) 
o l p
e
t 4t t
t
3
+ +
= (D) 
o l l
e
t 4t t
t
3
+ +
=
Q
P
1
O
2
O
d
Page 4


ME? GATE Paper 2009
Q. No. 1 – 20 Carry One Mark Each 
1. For a matrix [M]=
3 4
5 5
3
x
5
? ?
? ?
? ?
? ?
? ?
? ?
, the transpose of the matrix is equal to the inverse of 
the matrix 
T 1
M M
-
= ? ? ? ?
? ? ? ?
. The value of x is given by
(A) 
4
5
- (B) 
3
5
- (C) 
3
5
(D) 
4
5
2. The divergence of the vector field 
2
ˆ ˆ ˆ
3xzi 2xyj yz k + - at a point (1,1,1 ) is equal to
(A) 7  (B) 4 (C) 3 (D) 0
3. The inverse Laplace transform of
( )
2
1
s s +
 is 
(A) 
t
1 e + (B) 
t
1 e - (C) 
t
1 e
-
- (D) 
t
1 e
-
+
4. If three coins are tossed simultaneously, the probability of getting at least one
head
(A) 1/8  (B) 3/8      (C) 1/2  (D) 7/8
5. If a closed system is undergoing an irreversible process, the entropy of the
system
(A)  Must increase
(B)  Always remains constant
(C)  Must decrease
(D) Can increase, decrease or remain constant
6. A coolant fluid at 30°C flows over a heated flat plate maintained at a constant 
temperature of 100°C. The boundary layer temperature distribution at a given 
location on the plate may be approximated as ( ) T 30 70exp y = + - where y (in m)
is the distance normal to the plate and T is in °C. If thermal conductivity of the 
fluid is 1.0W/mK, the local convective heat transfer coefficient (in W/m
2
K) at that 
location will be 
(A) 0.2 (B) 1 (C) 5 (D) 10 
7. A frictionless piston-cylinder device contains a gas initially at 0.8MPa and 0.015
m
3
. It expands quasi-statically at constant temperature to a final volume of 0.030
m
3
. The work output (in kJ) during this process will be
(A) 8.32 (B) 12.00 (C) 554.67 (D) 8320.00 
ME? GATE Paper 2009
8. In an ideal vapour compression refrigeration cycle, the specific enthalpy of
refrigerant (in kJ/kg) at the following states is given as:
Inlet of condenser: 283 
Exit of condenser: 116 
Exit of evaporator: 232 
The COP of this cycle is
(A) 2.27 (B) 2.75 (C) 3.27 (D) 3.75 
9. A compressor undergoes a reversible, steady flow process. The gas at inlet and
outlet of the compressor is designated as state 1 and state 2 respectively.
Potential and kinetic energy changes are to be ignored. The following notations
are used:
v= specific volume and P=pressure of the gas.
The specific work required to be supplied to the compressor for this gas
compression process is
(A) 
2
1
Pdv
?
(B) 
2
1
vdP
?
(C) ( )
1 2 1
v P P - (D) ( )
2 1 2
P v v - -
10. A block weighing 981N is resting on a horizontal surface. The coefficient of 
friction between the block and the horizontal surface is µ = 0.2A vertical cable 
attached to the block provides partial support as shown. A man can pull 
horizontally with a force of 100N. What will be the tension, T (in N) in the cable if 
the man is just able to move the block to the right? 
(A) 176.2 (B) 196.0 (C) 481.0 (D) 981.0 
11. If the principal stresses in a plane stress problem, are
1 2
100MPa, 40MPa s = s = , 
the magnitude of the maximum shear stress (in MPa) will be
(A) 60  (B) 50                    (C) 30 (D) 20 
12. A simple quick return mechanism is shown in the figure. The forward to return
ratio of the quick return mechanism is 2:1. If the radius of the crank O
1
P is 125
mm, then the distance 'd' (in mm) between the crank centre to lever pivot centre
point should be
100N
T
G
0.2 µ =
ME? GATE Paper 2009
(A) 144.3 (B) 216.5 (C) 240.0 (D) 250.0 
13. The rotor shaft of a large electric motor supported between short bearings at
both deflection of 1.8mm in the middle of the rotor. Assuming the rotor to be
perfectly balanced and supported at knife edges at both the ends, the likely
critical speed (in rpm) of the shaft is
(A) 350 (B) 705 (C) 2810 (D) 4430 
14. A solid circular shaft of diameter d is subjected to a combined bending moment M
and torque, T. The material property to be used for designing the shaft using the
relation
2 2
3
16
M T
d
+
p
is 
(A) ultimate tensile strength (S
u
) (B) tensile yield strength (S
y
) 
(C) torsional yield strength (S
sy
)  (D) endurance strength (S
e
) 
15. The effective number of lattice points in the unit cell of simple cubic, body
centered cubic, and face centered cubic space lattices, respectively, are
(A) 1,2,2 (B) 1,2,4         (C) 2,3,4        (D) 2,4,4
16. Friction at the tool-chip interface can be reduced by 
(A)  decreasing the rake angle  (B) increasing the depth of cut 
(C)  decreasing the cutting speed (D) increasing the cutting speed 
17. Two streams of liquid metal, which are not hot enough to fuse properly, result
into a casting defect known as
(A) cold shut  (B) swell                (C) sand wash        (D) scab
18. The expected time (t
e
) of a PERT activity in terms of optimistic time (t
0
),
pessimistic time (t
p
) and most likely time (t
l
) is given by
(A) 
o l p
e
t 4t t
t
6
+ +
= (B) 
o p l
e
t 4t t
t
6
+ +
=
(C) 
o l p
e
t 4t t
t
3
+ +
= (D) 
o l l
e
t 4t t
t
3
+ +
=
Q
P
1
O
2
O
d
ME? GATE Paper 2009
19. Which of the following is the correct data structure for solid models?
(A)  solid part  faces  edges  vertices
(B)  solid part  edges  faces  vertices
(C) vertices  edges  faces  solid parts
(D) vertices  faces  edges  solid parts
20. Which of the following forecasting methods takes a fraction of forecast error into 
account for the next period forecast? 
(A) simple average method  (B) moving average method 
(C) weighted moving average method   (D) exponential smoothening method 
Q. No. 21 – 56 Carry Two Marks Each 
21. An analytic function of a complex variable z = x + iy is expressed as
( ) ( ) ( ) f z u x,y iv x,y = + where i 1 = - . If u = xy, the expression for v should be
(A) 
( )
2
x y
k
2
+
+ (B) 
2 2
x y
k
2
-
+ (C) 
2 2
y x
k
2
-
+ (D) 
( )
2
x y
k
2
-
+
22. The solution of 
4
dy
x y x
dx
+ = with the condition ( )
6
y 1
5
= is 
(A) 
4
x 1
y
5 x
= + (B) 
4
4x 4
y
5 5x
= + (C) 
4
x
y 1
5
= + (D) 
5
x
y 1
5
= +
23. A path AB in the form of one quarter of a circle of unit radius is shown in the
figure. Integration of ( )
2
x y + on path AB traversed in a counter-clockwise sense
is 
(A) 1
2
p
- (B) 1
2
p
+ 
(C) 
2
p
(D) 1 
24. The distance between the origin and the point nearest to it on the surface
2
z 1 xy = + is
(A) 1 (B) 
3
2
(C)  3 (D) 2 
25. The area enclosed between the curves y
2
 = 4x and x
2
 = 4y is
(A)
16
3
(B) 8 (C) 
32
3
(D) 16 
A
B
Y
X
Page 5


ME? GATE Paper 2009
Q. No. 1 – 20 Carry One Mark Each 
1. For a matrix [M]=
3 4
5 5
3
x
5
? ?
? ?
? ?
? ?
? ?
? ?
, the transpose of the matrix is equal to the inverse of 
the matrix 
T 1
M M
-
= ? ? ? ?
? ? ? ?
. The value of x is given by
(A) 
4
5
- (B) 
3
5
- (C) 
3
5
(D) 
4
5
2. The divergence of the vector field 
2
ˆ ˆ ˆ
3xzi 2xyj yz k + - at a point (1,1,1 ) is equal to
(A) 7  (B) 4 (C) 3 (D) 0
3. The inverse Laplace transform of
( )
2
1
s s +
 is 
(A) 
t
1 e + (B) 
t
1 e - (C) 
t
1 e
-
- (D) 
t
1 e
-
+
4. If three coins are tossed simultaneously, the probability of getting at least one
head
(A) 1/8  (B) 3/8      (C) 1/2  (D) 7/8
5. If a closed system is undergoing an irreversible process, the entropy of the
system
(A)  Must increase
(B)  Always remains constant
(C)  Must decrease
(D) Can increase, decrease or remain constant
6. A coolant fluid at 30°C flows over a heated flat plate maintained at a constant 
temperature of 100°C. The boundary layer temperature distribution at a given 
location on the plate may be approximated as ( ) T 30 70exp y = + - where y (in m)
is the distance normal to the plate and T is in °C. If thermal conductivity of the 
fluid is 1.0W/mK, the local convective heat transfer coefficient (in W/m
2
K) at that 
location will be 
(A) 0.2 (B) 1 (C) 5 (D) 10 
7. A frictionless piston-cylinder device contains a gas initially at 0.8MPa and 0.015
m
3
. It expands quasi-statically at constant temperature to a final volume of 0.030
m
3
. The work output (in kJ) during this process will be
(A) 8.32 (B) 12.00 (C) 554.67 (D) 8320.00 
ME? GATE Paper 2009
8. In an ideal vapour compression refrigeration cycle, the specific enthalpy of
refrigerant (in kJ/kg) at the following states is given as:
Inlet of condenser: 283 
Exit of condenser: 116 
Exit of evaporator: 232 
The COP of this cycle is
(A) 2.27 (B) 2.75 (C) 3.27 (D) 3.75 
9. A compressor undergoes a reversible, steady flow process. The gas at inlet and
outlet of the compressor is designated as state 1 and state 2 respectively.
Potential and kinetic energy changes are to be ignored. The following notations
are used:
v= specific volume and P=pressure of the gas.
The specific work required to be supplied to the compressor for this gas
compression process is
(A) 
2
1
Pdv
?
(B) 
2
1
vdP
?
(C) ( )
1 2 1
v P P - (D) ( )
2 1 2
P v v - -
10. A block weighing 981N is resting on a horizontal surface. The coefficient of 
friction between the block and the horizontal surface is µ = 0.2A vertical cable 
attached to the block provides partial support as shown. A man can pull 
horizontally with a force of 100N. What will be the tension, T (in N) in the cable if 
the man is just able to move the block to the right? 
(A) 176.2 (B) 196.0 (C) 481.0 (D) 981.0 
11. If the principal stresses in a plane stress problem, are
1 2
100MPa, 40MPa s = s = , 
the magnitude of the maximum shear stress (in MPa) will be
(A) 60  (B) 50                    (C) 30 (D) 20 
12. A simple quick return mechanism is shown in the figure. The forward to return
ratio of the quick return mechanism is 2:1. If the radius of the crank O
1
P is 125
mm, then the distance 'd' (in mm) between the crank centre to lever pivot centre
point should be
100N
T
G
0.2 µ =
ME? GATE Paper 2009
(A) 144.3 (B) 216.5 (C) 240.0 (D) 250.0 
13. The rotor shaft of a large electric motor supported between short bearings at
both deflection of 1.8mm in the middle of the rotor. Assuming the rotor to be
perfectly balanced and supported at knife edges at both the ends, the likely
critical speed (in rpm) of the shaft is
(A) 350 (B) 705 (C) 2810 (D) 4430 
14. A solid circular shaft of diameter d is subjected to a combined bending moment M
and torque, T. The material property to be used for designing the shaft using the
relation
2 2
3
16
M T
d
+
p
is 
(A) ultimate tensile strength (S
u
) (B) tensile yield strength (S
y
) 
(C) torsional yield strength (S
sy
)  (D) endurance strength (S
e
) 
15. The effective number of lattice points in the unit cell of simple cubic, body
centered cubic, and face centered cubic space lattices, respectively, are
(A) 1,2,2 (B) 1,2,4         (C) 2,3,4        (D) 2,4,4
16. Friction at the tool-chip interface can be reduced by 
(A)  decreasing the rake angle  (B) increasing the depth of cut 
(C)  decreasing the cutting speed (D) increasing the cutting speed 
17. Two streams of liquid metal, which are not hot enough to fuse properly, result
into a casting defect known as
(A) cold shut  (B) swell                (C) sand wash        (D) scab
18. The expected time (t
e
) of a PERT activity in terms of optimistic time (t
0
),
pessimistic time (t
p
) and most likely time (t
l
) is given by
(A) 
o l p
e
t 4t t
t
6
+ +
= (B) 
o p l
e
t 4t t
t
6
+ +
=
(C) 
o l p
e
t 4t t
t
3
+ +
= (D) 
o l l
e
t 4t t
t
3
+ +
=
Q
P
1
O
2
O
d
ME? GATE Paper 2009
19. Which of the following is the correct data structure for solid models?
(A)  solid part  faces  edges  vertices
(B)  solid part  edges  faces  vertices
(C) vertices  edges  faces  solid parts
(D) vertices  faces  edges  solid parts
20. Which of the following forecasting methods takes a fraction of forecast error into 
account for the next period forecast? 
(A) simple average method  (B) moving average method 
(C) weighted moving average method   (D) exponential smoothening method 
Q. No. 21 – 56 Carry Two Marks Each 
21. An analytic function of a complex variable z = x + iy is expressed as
( ) ( ) ( ) f z u x,y iv x,y = + where i 1 = - . If u = xy, the expression for v should be
(A) 
( )
2
x y
k
2
+
+ (B) 
2 2
x y
k
2
-
+ (C) 
2 2
y x
k
2
-
+ (D) 
( )
2
x y
k
2
-
+
22. The solution of 
4
dy
x y x
dx
+ = with the condition ( )
6
y 1
5
= is 
(A) 
4
x 1
y
5 x
= + (B) 
4
4x 4
y
5 5x
= + (C) 
4
x
y 1
5
= + (D) 
5
x
y 1
5
= +
23. A path AB in the form of one quarter of a circle of unit radius is shown in the
figure. Integration of ( )
2
x y + on path AB traversed in a counter-clockwise sense
is 
(A) 1
2
p
- (B) 1
2
p
+ 
(C) 
2
p
(D) 1 
24. The distance between the origin and the point nearest to it on the surface
2
z 1 xy = + is
(A) 1 (B) 
3
2
(C)  3 (D) 2 
25. The area enclosed between the curves y
2
 = 4x and x
2
 = 4y is
(A)
16
3
(B) 8 (C) 
32
3
(D) 16 
A
B
Y
X
ME? GATE Paper 2009
26. The standard deviation of a uniformly distributed random variable between 0 and 
1 is 
(A) 
1
12
(B) 
1
3
(C) 
5
12
(D) 
7
12
27. Consider steady, incompressible and irrotational flow through a reducer in a
horizontal pipe where the diameter is reduced from 20cm to 10cm. The pressure
in the 20cm pipe just upstream of the reducer is 150kPa. The fluid has a vapour
pressure of 50kPa and a specific weight of 5 kN/m
3
. Neglecting frictional effects,
the maximum discharge (in m
3
/s) that can pass through the reducer without
causing cavitation is
(A) 0.05 (8) 0.16 (C) 0.27 (D) 0.38 
28. In a parallel flow heat exchanger operating under steady state, the heat capacity
rates (product of specific heat at constant pressure and mass flow rate) of the
hot and cold fluid are equal. The hot fluid, flowing at 1kg/s with C
p
 = 4kJ/kgK,
enters the heat exchanger at 102°C while the cold fluid has an inlet temperature
of 15°C. The overall heat transfer coefficient for the heat exchanger is estimated
to be 1kW/m
2
K and the corresponding heat transfer surface area is 5m
2
. Neglect
heat transfer between the heat exchanger and the ambient. The heat exchanger
is characterized by the following relation:
( ) 2 1 exp 2NTU e = - - .
The exit temperature (in °C) for the cold fluid is
(A) 45 (B)55 (C) 65 (D) 75 
29. In an air-standard Otto cycle, the compression ratio is 10. The condition at the
beginning of the compression process is 100kPa and 27°C. Heat added at
constant volume is 1500kJ/kg, while 700kJ/kg of heat is rejected during the other
constant volume process in the cycle. Specific gas constant for air=0.287 kJ/kgK.
The mean effective pressure (in kPa) of the cycle is
(A) 103 (B) 310 (C) 515 (D) 1032 
30. An irreversible heat engine extracts heat from a high temperature source at a 
rate of 100kW and rejects heat to a sink at a rate of 50kW. The entire work 
output of the heat engine is used to drive a reversible heat pump operating 
between a set of independent isothermal heat reservoirs at 17°C and 75°C. The 
rate (in kW) at which the heat pump delivers heat to its high temperature sink is 
(A) 50 (B) 250 (C) 300 (D) 360 
31. You are asked to evaluate assorted fluid flows for their suitability in a given
laboratory application. The following three flow choices, expressed in terms of the
two-dimensional velocity fields in the xy-plane, are made available.
P. u 2y, v 3x
Q. u 3xy, v 0
R. u 2x, v 2y
= = -
= =
= - =
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