MEGATE2013 PAPER

MEGATE2013 PAPER
1377931594MEGATE13.pdf (Size: 232.91 KB / Downloads: 67)
Q. No. 1 – 25 Carry One Mark Each
The partial differential equation
2
2
u u u
u
t x x
¶ ¶ ¶
+ =
¶ ¶ ¶
is a
(A) Linear equation of order 2 (B) Nonlinear equation of order 1
© Linear equation of order 1 (D) Nonlinear equation of order 2
Answer: (D)
2. The eigen values of symmetric matrix are all
(A) Complex with nonzero positive imaginary part
(B) Complex with nonzero negative imaginary part
© Real
(D) Pure imaginary
The threaded bolts A and B of same material and length are subjected to identical
tensile load. If the elastic strain energy stored in bolt A is 4 times that of the bolt B
and the mean diameter of bolt A is 12mm, the mean diameter of bolt B in mm is
(A) 16 (B) 24 © 36 (D) 48
1 E 2 E
S
S
L /2
L
P P
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2
Answer: (B)
Explanation:
2
1 1 2
2
2 1
2
P l
E 2AE A
E P l A
2AE
= =
2
2
2
1
2 1
d
4
d
d 12 d 24
=
= × =
6. A link OB is rotating with a constant angular velocity of 2 rad/s in counter
clockwise direction and a block is sliding radially outward on it with an uniform
velocity of 0.75 m/s with respect to the rod, as shown in the figure below. If
OA = 1m,
The pressure, dry bulb temperature, and relative humidity of air in a room are
1bar, 30ºC and 70% respectively. If the saturated steam pressure at 30ºC is
4.25kPa, the specific humidity of the room air in kg water vapour / kg dry air is
(A) 0.0083 (B) 0.0101 © 0.0191 (D) 0.0232
Answer: ©
Explanation:
P = 1 bar = 105 Pa = 100 KPa
sat P = 4.25KPa
( )
× ×
= =
− p
0.622 0.7 4.25
S .humidity 0.019
100 4.25
9. Consider onedimensional steady state heat conduction, without heat generation,
in a plane wall; with boundary conditions as shown in the figure below. The
conductivity of the wall is given by 0 k = k + bT ; where 0 k and b are positive
constants and T is temperature.
As x increases, the temperature gradient (dT / dx) will
(A) Remain constant (B) Be zero © Increase (D) Decrease
Answer: (D)
A metric thread of pitch 2mm and thread angle 60º is inspected for its pitch
diameter using 3wire method. The diameter of the best size wire in mm is
(A) 0.866 (B) 1.000 © 1.154 (D) 2.000
Answer: ©
Explanations: For 60o thread angle, best wire size =0.57135xP=1.154
13. Customers arrive at a ticket counter at a rate of 50 per hour and tickets are
issued in the order of their arrival. The average time taken for issuing a ticket is
1min. Assuming that customer arrivals form a Poisson process and service times
are exponentially distributed, the average waiting time in queue in minutes is:
(A) 3 (B) 4 © 5 (D) 6
Answer: ©
Explanation:
( )
50 / hr 60 / hrW.T 0.083hr 5min
For a ductile material, toughness is a measure of
(A) Resistance to scratching
(B) Ability to absorb energy up to fracture
© Ability to absorb energy till elastic limit
(D) Resistance to indentation
Answer: (B)
Explanations: Since, toughness has ability to absorb energy up to fracture.
18. In order to have maximum power from a Pelton turbine, the bucket speed must
be
(A) Equal to the jet speed (B) Equal to half the jet speed
© Equal to twice the jet speed (D) Independent of the jet speed
Answer: (B)
Explanation: Since, velocity of bucket = ½ times the velocity of jet.
19. Consider onedimensional steady state heat conduction along xaxis (0 £ x £ L) ,
through a plane wall with the boundary surfaces (x = 0 and x = L) maintained at
temperatures 0ºC and 100ºC. Heat is generated uniformly throughout the wall.
Choose the CORRECT statement.
(A) The direction of heat transfer will be from the surface at 100ºC to surface at
0ºC.
(B) The maximum temperature inside the wall must be greater than 100ºC
© The temperature distribution is linear within the wall
(D) The temperature distribution is symmetric about the midplane of the wall
Answer: (B)
A single degree of freedom system having mass 1 kg and stiffness 10kN/m
initially at rest is subjected to an impulse force of magnitude 5 kN for
4 10− seconds. The amplitude in mm of the resulting free vibration is
(A) 0.5 (B) 1.0 © 5.0 (D)10.0
Answer: ©
40. A bar is subjected to fluctuating tensile load from 20 kN to 100 kN. The material
has yield strength of 240 MPa and endurance limit in reversed bending is 160
MPa. According to the Soderberg principle, the area of crosssection in 2 mm of
the bar for a factor of safety of 2 is
(A) 400 (B) 600 © 750 (D)1000
y
x
(2,0) (3.33,0)
4x + 6y £ 8
(0,1.33)
(0,1.42)
3x + 7y £ 0
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Answer: (D)
m v
y e
1
F.S
s s
+ =
s s
60 40 1
1000
A 240 A 160 2
+ =
× ×
A =1000
41. A simply supported beam of length L is subjected to a varying distributed load
1 x
sin 3 Nm
L
−
p
, where the distance x is measured from the left support. The
magnitude of the vertical force in N at the left support is
(A) zero (B)
L
3p
©
L
p
(D)
2L
p
Answer: (B)
. 

