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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) Non-linear equation of order 1

© Linear equation of order 1 (D) Non-linear equation of order 2

Answer: (D)

2. The eigen values of symmetric matrix are all

(A) Complex with non-zero positive imaginary part

(B) Complex with non-zero 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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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 one-dimensional 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 3-wire 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 one-dimensional steady state heat conduction along x-axis (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 mid-plane 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 cross-section 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)

.