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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
− © 3
5
(D) 4
5
2. The divergence of the vector field 3xzi 2xyj yz k ˆ ˆ + − 2ˆ at a point (1,1,1 ) is equal to
(A) 7 (B) 4 © 3 (D) 0
3. The inverse Laplace transform of ( ) 2
1
s s +
is
(A) t 1 e + (B) t 1 e − © 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 © 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
© 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 (B) 1 © 5 (D) 10
7. 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 © 554.67 (D) 8320.00
ME GATE Paper 2009 www.gateforum.com
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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 © 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 ∫
© ( ) v P P 1 2 1 − (D) ( ) P v v 2 1 2 − −
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 © 481.0 (D) 981.0
11. If the principal stresses in a plane stress problem, are σ = σ = 1 2 100MPa, 40MPa ,
the magnitude of the maximum shear stress (in MPa) will be
(A) 60 (B) 50 © 30 (D) 20