GATE  >  Mechanical Engineering (ME) 2006 GATE Paper without solution

# 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
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
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
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
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
```

## GATE Past Year Papers for Practice (All Branches)

407 docs|127 tests

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

 1. What is the significance of the Mechanical Engineering (ME) 2006 GATE Paper?
Ans. The Mechanical Engineering (ME) 2006 GATE Paper is an important examination paper conducted by GATE (Graduate Aptitude Test in Engineering). It serves as a benchmark for assessing the knowledge and skills of candidates in the field of mechanical engineering.
 2. What are the topics covered in the Mechanical Engineering (ME) 2006 GATE Paper?
Ans. The topics covered in the Mechanical Engineering (ME) 2006 GATE Paper include engineering mathematics, mechanics of solids, thermodynamics, manufacturing engineering, fluid mechanics, and heat transfer, among others. It aims to evaluate the understanding and proficiency of candidates in these areas.
 3. How can I prepare for the Mechanical Engineering (ME) 2006 GATE Paper?
Ans. To prepare for the Mechanical Engineering (ME) 2006 GATE Paper, candidates can follow a systematic study plan. They should thoroughly revise the core concepts and formulas of each topic, practice previous year question papers, and attempt mock tests for time management and self-assessment. Referring to standard textbooks and online resources can also enhance their preparation.
 4. What is the difficulty level of the Mechanical Engineering (ME) 2006 GATE Paper?
Ans. The difficulty level of the Mechanical Engineering (ME) 2006 GATE Paper can be considered moderate to difficult. It requires a comprehensive understanding of the subject matter and the ability to apply concepts to solve complex problems. Candidates should be well-prepared and practice extensively to achieve a good score.
 5. How can the Mechanical Engineering (ME) 2006 GATE Paper benefit me in my career?
Ans. Clearing the Mechanical Engineering (ME) 2006 GATE Paper with a good score can open up various opportunities for a career in mechanical engineering. It can be a gateway to pursue higher studies (M.Tech or Ph.D.) in reputed institutes or secure job positions in industries, public sector undertakings (PSUs), and research organizations. GATE scores are widely accepted and recognized, providing candidates with a competitive edge in the job market.

## GATE Past Year Papers for Practice (All Branches)

407 docs|127 tests

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