Mechanical Engineering (ME) 2006 GATE Paper without solution - GATE Past Year Papers for Practice (All Branches)

 Page 1


GATE ME – 2006 
Q.1 – Q.20 Carry One Mark Each. 
1. Match the items in columns I and II.
Column I Column II 
(P) Gauss-Seidel method (1) Interpolation 
(Q) Forward Newton-Gauss method (2) Non-linear differential equations 
(R) Runge-Kutta method (3) Numerical integration 
(S) Trapezoidal Rule (4) Linear algebraic equations 
(A)  P  -  1   Q  -  4   R  -  3   S  -  2 
(B) P  -  1   Q  -  4   R  -  2   S  -  3 
(C) P  -  1   Q  -  3   R  -  2   S  -  4 
(D) P  -  4   Q  -  1   R  -  2   S  -  3 
2. The solution of the differential equation
( )
2
2 with 0 1
x
dy
xy e y
dx
-
+ = = is: 
(A) ( )
2
1
x
x e
+
+
(B) ( )
2
1
x
x e
-
+
(C) ( )
2
1
x
x e
+
-
(D) ( )
2
1
x
x e
-
-
3. Let x denote a real number. Find out the INCORRECT statement.
(A) { } : 3 S x x = > represents the set of all real numbers greater than 3
(B)
{ }
2
: 0 S x x = < represents the empty set 
(C) { } : and S x x A x B = ? ? represents the union of set A and set B
(D) { } : S x a x b = < < represents the set of all real numbers between a and b,
where a and b are real numbers. 
4. A box contains 20 defective items and 80 non-defective items. If two items are
selected at random without replacement, what will be the probability that both
items are defective.?
(A)
1
5
Page 2


GATE ME – 2006 
Q.1 – Q.20 Carry One Mark Each. 
1. Match the items in columns I and II.
Column I Column II 
(P) Gauss-Seidel method (1) Interpolation 
(Q) Forward Newton-Gauss method (2) Non-linear differential equations 
(R) Runge-Kutta method (3) Numerical integration 
(S) Trapezoidal Rule (4) Linear algebraic equations 
(A)  P  -  1   Q  -  4   R  -  3   S  -  2 
(B) P  -  1   Q  -  4   R  -  2   S  -  3 
(C) P  -  1   Q  -  3   R  -  2   S  -  4 
(D) P  -  4   Q  -  1   R  -  2   S  -  3 
2. The solution of the differential equation
( )
2
2 with 0 1
x
dy
xy e y
dx
-
+ = = is: 
(A) ( )
2
1
x
x e
+
+
(B) ( )
2
1
x
x e
-
+
(C) ( )
2
1
x
x e
+
-
(D) ( )
2
1
x
x e
-
-
3. Let x denote a real number. Find out the INCORRECT statement.
(A) { } : 3 S x x = > represents the set of all real numbers greater than 3
(B)
{ }
2
: 0 S x x = < represents the empty set 
(C) { } : and S x x A x B = ? ? represents the union of set A and set B
(D) { } : S x a x b = < < represents the set of all real numbers between a and b,
where a and b are real numbers. 
4. A box contains 20 defective items and 80 non-defective items. If two items are
selected at random without replacement, what will be the probability that both
items are defective.?
(A)
1
5
GATE ME – 2006 
(B)
1
25
(C) 
20
99
(D) 
19
495
5. For a circular shaft of diameter d subjected to torque T, the maximum value of
the shear stress is:
(A) 
3
64T
d p
(B) 
3
32T
d p
(C) 
3
16T
d p
(D) 
3
8T
d p
6. For a four-bar linkage in toggle position, the value of mechanical advantage is:
(A) 0.0
(B) 0.5
(C) 1.0
(D) 8
7. The differential equation governing the vibrating system is:
(A) ( ) 0 mx cx k x y + + - =
&& &
(B) ( ) ( ) 0 m x y c x y kx - + - + =
&& && & &
C 
y x 
m 
k 
Page 3


GATE ME – 2006 
Q.1 – Q.20 Carry One Mark Each. 
1. Match the items in columns I and II.
Column I Column II 
(P) Gauss-Seidel method (1) Interpolation 
(Q) Forward Newton-Gauss method (2) Non-linear differential equations 
(R) Runge-Kutta method (3) Numerical integration 
(S) Trapezoidal Rule (4) Linear algebraic equations 
(A)  P  -  1   Q  -  4   R  -  3   S  -  2 
(B) P  -  1   Q  -  4   R  -  2   S  -  3 
(C) P  -  1   Q  -  3   R  -  2   S  -  4 
(D) P  -  4   Q  -  1   R  -  2   S  -  3 
2. The solution of the differential equation
( )
2
2 with 0 1
x
dy
xy e y
dx
-
+ = = is: 
(A) ( )
2
1
x
x e
+
+
(B) ( )
2
1
x
x e
-
+
(C) ( )
2
1
x
x e
+
-
(D) ( )
2
1
x
x e
-
-
3. Let x denote a real number. Find out the INCORRECT statement.
(A) { } : 3 S x x = > represents the set of all real numbers greater than 3
(B)
{ }
2
: 0 S x x = < represents the empty set 
(C) { } : and S x x A x B = ? ? represents the union of set A and set B
(D) { } : S x a x b = < < represents the set of all real numbers between a and b,
where a and b are real numbers. 
4. A box contains 20 defective items and 80 non-defective items. If two items are
selected at random without replacement, what will be the probability that both
items are defective.?
(A)
1
5
GATE ME – 2006 
(B)
1
25
(C) 
20
99
(D) 
19
495
5. For a circular shaft of diameter d subjected to torque T, the maximum value of
the shear stress is:
(A) 
3
64T
d p
(B) 
3
32T
d p
(C) 
3
16T
d p
(D) 
3
8T
d p
6. For a four-bar linkage in toggle position, the value of mechanical advantage is:
(A) 0.0
(B) 0.5
(C) 1.0
(D) 8
7. The differential equation governing the vibrating system is:
(A) ( ) 0 mx cx k x y + + - =
&& &
(B) ( ) ( ) 0 m x y c x y kx - + - + =
&& && & &
C 
y x 
m 
k 
GATE ME – 2006 
    
(C) m
&
x
& 
+ c (x
& 
- y
& 
) + kx = 0
(D) m ( 
&
x
& 
- 
&
y
&
) + c (x
& 
- y
& 
) + k (x - y ) = 0
8. A pin-ended column of length L, modulus of elasticity E and second moment of
the cross-sectional area I is loaded centrically by a compressive load P. the
critical buckling load ( )
cr
P is given by
(A) 
2 2 cr
EI
P
L p
=
(B) 
2
2
3
cr
EI
P
L
p
=
(C) 
2 cr
EI
P
L
p
=
(D) 
2
2 cr
EI
P
L
p
=
9. The number of inversions for a slider crank mechanism is:
(A) 6
(B) 5
(C) 4
(D) 3
10. For a Newtonian fluid
(A) shear stress is proportional to shear strain
(B) rate of shear stress is proportional to shear strain
(C) shear stress is proportional to rate of shear strain
(D) rate of shear stress is proportional to rate of shear strain
11. In a two-dimensional velocity field with velocities u and ? along the x and y
directions respectively, the convective acceleration along the x-direction is given
by
(A) 
u u
u
x y
?
? ?
+
? ?
(B) 
u
u
x y
?
?
? ?
+
? ?
(C) 
u
u
x y
?
?
? ?
+
? ?
(D) 
u u
u
x y
?
? ?
+
? ?
Page 4


GATE ME – 2006 
Q.1 – Q.20 Carry One Mark Each. 
1. Match the items in columns I and II.
Column I Column II 
(P) Gauss-Seidel method (1) Interpolation 
(Q) Forward Newton-Gauss method (2) Non-linear differential equations 
(R) Runge-Kutta method (3) Numerical integration 
(S) Trapezoidal Rule (4) Linear algebraic equations 
(A)  P  -  1   Q  -  4   R  -  3   S  -  2 
(B) P  -  1   Q  -  4   R  -  2   S  -  3 
(C) P  -  1   Q  -  3   R  -  2   S  -  4 
(D) P  -  4   Q  -  1   R  -  2   S  -  3 
2. The solution of the differential equation
( )
2
2 with 0 1
x
dy
xy e y
dx
-
+ = = is: 
(A) ( )
2
1
x
x e
+
+
(B) ( )
2
1
x
x e
-
+
(C) ( )
2
1
x
x e
+
-
(D) ( )
2
1
x
x e
-
-
3. Let x denote a real number. Find out the INCORRECT statement.
(A) { } : 3 S x x = > represents the set of all real numbers greater than 3
(B)
{ }
2
: 0 S x x = < represents the empty set 
(C) { } : and S x x A x B = ? ? represents the union of set A and set B
(D) { } : S x a x b = < < represents the set of all real numbers between a and b,
where a and b are real numbers. 
4. A box contains 20 defective items and 80 non-defective items. If two items are
selected at random without replacement, what will be the probability that both
items are defective.?
(A)
1
5
GATE ME – 2006 
(B)
1
25
(C) 
20
99
(D) 
19
495
5. For a circular shaft of diameter d subjected to torque T, the maximum value of
the shear stress is:
(A) 
3
64T
d p
(B) 
3
32T
d p
(C) 
3
16T
d p
(D) 
3
8T
d p
6. For a four-bar linkage in toggle position, the value of mechanical advantage is:
(A) 0.0
(B) 0.5
(C) 1.0
(D) 8
7. The differential equation governing the vibrating system is:
(A) ( ) 0 mx cx k x y + + - =
&& &
(B) ( ) ( ) 0 m x y c x y kx - + - + =
&& && & &
C 
y x 
m 
k 
GATE ME – 2006 
    
(C) m
&
x
& 
+ c (x
& 
- y
& 
) + kx = 0
(D) m ( 
&
x
& 
- 
&
y
&
) + c (x
& 
- y
& 
) + k (x - y ) = 0
8. A pin-ended column of length L, modulus of elasticity E and second moment of
the cross-sectional area I is loaded centrically by a compressive load P. the
critical buckling load ( )
cr
P is given by
(A) 
2 2 cr
EI
P
L p
=
(B) 
2
2
3
cr
EI
P
L
p
=
(C) 
2 cr
EI
P
L
p
=
(D) 
2
2 cr
EI
P
L
p
=
9. The number of inversions for a slider crank mechanism is:
(A) 6
(B) 5
(C) 4
(D) 3
10. For a Newtonian fluid
(A) shear stress is proportional to shear strain
(B) rate of shear stress is proportional to shear strain
(C) shear stress is proportional to rate of shear strain
(D) rate of shear stress is proportional to rate of shear strain
11. In a two-dimensional velocity field with velocities u and ? along the x and y
directions respectively, the convective acceleration along the x-direction is given
by
(A) 
u u
u
x y
?
? ?
+
? ?
(B) 
u
u
x y
?
?
? ?
+
? ?
(C) 
u
u
x y
?
?
? ?
+
? ?
(D) 
u u
u
x y
?
? ?
+
? ?
GATE ME – 2006 
12. Dew point temperature is the temperature at which condensation begins when
the air is cooled at constant.
(A) volume
(B) entropy
(C) pressure
(D) enthalpy
13. In a composite slab, the temperature at the interface ( )
inter
T between two 
materials is equal to the average of the temperatures at the two ends. Assuming
steady one-dimensional heat conduction, which of the following statements is
true about the respective thermal conductivities?
(A) 
1 2
2k k =
(B) 
1 2
k k =
(C) 
1 2
2 3 k k =
(D) 
1 2
2 k k =
14. In a Pelton wheel, the bucket peripheral speed is 10 m/s, the water jet velocity is
25 m/s and volumetric flow rate of the jet is 0.1 
3
/ . m s If the jet deflection angle 
is 120° and the flow is ideal, the owe developed is:
(A) 7.5 kW
(B) 15.0 kW
(C) 22.5 kW
(D) 37.5 kW
15. An expendable pattern is used in
(A) slush casting
(B) squeeze casting
(C) centrifugal casting
(D) investment casting
T 1
T 2
k 1 k 2 
T inter 
2b b
Page 5


GATE ME – 2006 
Q.1 – Q.20 Carry One Mark Each. 
1. Match the items in columns I and II.
Column I Column II 
(P) Gauss-Seidel method (1) Interpolation 
(Q) Forward Newton-Gauss method (2) Non-linear differential equations 
(R) Runge-Kutta method (3) Numerical integration 
(S) Trapezoidal Rule (4) Linear algebraic equations 
(A)  P  -  1   Q  -  4   R  -  3   S  -  2 
(B) P  -  1   Q  -  4   R  -  2   S  -  3 
(C) P  -  1   Q  -  3   R  -  2   S  -  4 
(D) P  -  4   Q  -  1   R  -  2   S  -  3 
2. The solution of the differential equation
( )
2
2 with 0 1
x
dy
xy e y
dx
-
+ = = is: 
(A) ( )
2
1
x
x e
+
+
(B) ( )
2
1
x
x e
-
+
(C) ( )
2
1
x
x e
+
-
(D) ( )
2
1
x
x e
-
-
3. Let x denote a real number. Find out the INCORRECT statement.
(A) { } : 3 S x x = > represents the set of all real numbers greater than 3
(B)
{ }
2
: 0 S x x = < represents the empty set 
(C) { } : and S x x A x B = ? ? represents the union of set A and set B
(D) { } : S x a x b = < < represents the set of all real numbers between a and b,
where a and b are real numbers. 
4. A box contains 20 defective items and 80 non-defective items. If two items are
selected at random without replacement, what will be the probability that both
items are defective.?
(A)
1
5
GATE ME – 2006 
(B)
1
25
(C) 
20
99
(D) 
19
495
5. For a circular shaft of diameter d subjected to torque T, the maximum value of
the shear stress is:
(A) 
3
64T
d p
(B) 
3
32T
d p
(C) 
3
16T
d p
(D) 
3
8T
d p
6. For a four-bar linkage in toggle position, the value of mechanical advantage is:
(A) 0.0
(B) 0.5
(C) 1.0
(D) 8
7. The differential equation governing the vibrating system is:
(A) ( ) 0 mx cx k x y + + - =
&& &
(B) ( ) ( ) 0 m x y c x y kx - + - + =
&& && & &
C 
y x 
m 
k 
GATE ME – 2006 
    
(C) m
&
x
& 
+ c (x
& 
- y
& 
) + kx = 0
(D) m ( 
&
x
& 
- 
&
y
&
) + c (x
& 
- y
& 
) + k (x - y ) = 0
8. A pin-ended column of length L, modulus of elasticity E and second moment of
the cross-sectional area I is loaded centrically by a compressive load P. the
critical buckling load ( )
cr
P is given by
(A) 
2 2 cr
EI
P
L p
=
(B) 
2
2
3
cr
EI
P
L
p
=
(C) 
2 cr
EI
P
L
p
=
(D) 
2
2 cr
EI
P
L
p
=
9. The number of inversions for a slider crank mechanism is:
(A) 6
(B) 5
(C) 4
(D) 3
10. For a Newtonian fluid
(A) shear stress is proportional to shear strain
(B) rate of shear stress is proportional to shear strain
(C) shear stress is proportional to rate of shear strain
(D) rate of shear stress is proportional to rate of shear strain
11. In a two-dimensional velocity field with velocities u and ? along the x and y
directions respectively, the convective acceleration along the x-direction is given
by
(A) 
u u
u
x y
?
? ?
+
? ?
(B) 
u
u
x y
?
?
? ?
+
? ?
(C) 
u
u
x y
?
?
? ?
+
? ?
(D) 
u u
u
x y
?
? ?
+
? ?
GATE ME – 2006 
12. Dew point temperature is the temperature at which condensation begins when
the air is cooled at constant.
(A) volume
(B) entropy
(C) pressure
(D) enthalpy
13. In a composite slab, the temperature at the interface ( )
inter
T between two 
materials is equal to the average of the temperatures at the two ends. Assuming
steady one-dimensional heat conduction, which of the following statements is
true about the respective thermal conductivities?
(A) 
1 2
2k k =
(B) 
1 2
k k =
(C) 
1 2
2 3 k k =
(D) 
1 2
2 k k =
14. In a Pelton wheel, the bucket peripheral speed is 10 m/s, the water jet velocity is
25 m/s and volumetric flow rate of the jet is 0.1 
3
/ . m s If the jet deflection angle 
is 120° and the flow is ideal, the owe developed is:
(A) 7.5 kW
(B) 15.0 kW
(C) 22.5 kW
(D) 37.5 kW
15. An expendable pattern is used in
(A) slush casting
(B) squeeze casting
(C) centrifugal casting
(D) investment casting
T 1
T 2
k 1 k 2 
T inter 
2b b
GATE ME – 2006 
16. The main purpose of spheroidising treatment is to improve
(A) hardenability of low carbon steels
(B) machinability of low carbon steels
(C) hardenability of high carbon steels
(D) machinability of high carbon steels
17. NC contouring is an example of
(A) continuous path positioning
(B) point-to-point positioning
(C) absolute positioning
(D) incremental positioning
18. A ring gage is used to measure
(A) outside diameter but not roundness
(B) roundness but not outside diameter
(C) both outside diameter and roundness
(D) only external threads
19. The number of customers arriving at a railway reservation counter is Poisson
distributed with an arrival rate of eight customers per hour. The reservation clerk
at this counter takes six minutes per customer on an average with an
exponentially distributed service time. The average number of the customers in
the queue will be
(A) 3
(B) 3.2
(C) 4
(D) 4.2
20. In an MRP system, component demand is:
(A) forecasted
(B) established by the master production schedule
(C) calculated by the MRP system from the master production schedule
(D) ignored
Q.21 to Q.75 Carry Two Marks Each. 
21. Eigen values of a matrix