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ME GATE Paper 2009

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_____________Download from wQ. No. 1 – 20 Carry OnePowered By © JbigDeaL____________ ww.JbigDeaL.com Mark Each

1.

3
5
For a matrix [M]= 
x


T

4
5
 , the transpose of the matrix is equal to the inverse of 3
5


−1

the matrix M = M . The value of x is given by


(A) −

2.

4
5

3
5

(D)

4
5

(B) 1 − et

(C) 3

(s

2

1
+s

)

(D) 0

(C) 1 − e− t

(D) 1 + e− t

is

If three coins are tossed simultaneously, the probability of getting at least one head
(A) 1/8

5.

(C)

(B) 4

The inverse Laplace transform of

(A) 1 + et
4.

3
5

ˆ
ˆ
The divergence of the vector field 3xzˆ + 2xyj − yz2k at a point (1,1,1 ) is equal to i

(A) 7

3.

(B) −

(B) 3/8

(C) 1/2

(D) 7/8

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 + 70 exp ( −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/m2K) at that location will be

(A) 0.2

7.

(B) 1

(C) 5

(D) 10

A frictionless piston-cylinder device contains a gas initially at 0.8MPa and 0.015 m3. It expands quasi-statically at constant temperature to a final volume of 0.030 m3. The work output (in kJ) during this process will be

(A) 8.32

(B) 12.00

(C) 554.67

(D) 8320.00

1

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ME GATE Paper 2009

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8.
In an ideal vapour compression refrigeration cycle, the specific enthalpy of _____________Download from www.JbigDeaL.com Powered By © JbigDeaL____________ 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
9.

(B) 2.75

(C) 3.27

(D) 3.75

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
2

(A)

∫ Pdv
1

10.

2

(B)

(C) v1 (P2 − P1 )

∫ vdP

(D) −P2 ( v1 − v2 )

1

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?

T

G

100N

µ = 0.2

(A) 176.2
11.

(C) 481.0

(D) 981.0

If the principal stresses in a plane stress problem, are σ1 = 100MPa, σ2 = 40MPa , the magnitude of the maximum shear stress (in MPa) will be
(A) 60

12.

(B) 196.0

(B) 50

(C) 30

(D) 20

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 O1P is 125 mm, then the distance 'd' (in mm) between the crank centre to lever pivot centre point should be

2

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