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# BARC 2021 ME: Full Syllabus Test 3

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Question 1

The area bounded by that parabola 2y=x2 and the line x = y-4 is equal to

Question 2

A long column of uniform cross-section hinged at one end and clamped at another able to sustain a buckling load P. What will be the maximum Euler buckling load when the length of the column is doubled and both ends are hinged.

Question 3

A DC arc welding has its voltage-arc length characteristics given by V= 5+10L , where L=arc length in cm. The power source is approximated as a straight line for which the open circuit voltage is 20 V and the short circuit current is 250 A. The optimum arc length is :

Question 4

Air at 100 kPa, 2 °C occupies a 10 liter piston-cylinder device that is arranged to maintain constant air pressure. This device is now heated until its volume is 20 liters. The work produced by the air is

Question 5

Given a function f( x ,y) = 5x2 – 4xy + 2y2 + 4x – 4y + 10 ,the optimum value of f(x, y) is

Question 6

Which is correct in case of flywheel?

Question 7

The process of reheating the martensitic steel to reduce its brittleness without any significant loss in its hardness is

Question 8

A 300 mm thick slab is being cold rolled using roll of 600 mm diameter. If the coefficient of friction is 0.08, the maximum possible reduction (in mm) is __________

Question 9

Steady one-dimensional heat conduction takes place across the faces 1 and 3 of a composite slab consisting of slabs A and B in perfect contact as shown in the figure, where kA, kB denote the respective thermal conductivities. Using the data as given in the figure, the interface temperature T2 (in oC. is ____

Question 10

For two springs having same stiffness (k) are in series, the equivalent stiffness would be __________.

Question 11

A block whose mass is 650 gm is fastened to a spring of spring constant K equals 65 N/m whose other end is fixed. The block is pulled a distance x = 11 cm from its equilibrium position at x = 0 on a smooth surface, and released from rest at t=0. The maximum speed ‘S ’ of the oscillating

Question 12

A solid disc of mass 2.5 kg is rolling without slipping from the top of an incline whose angle of inclination is 30° with the horizontal. The speed of the center of mass of the disc at the bottom of the incline is __________.

Question 13

For the matrix eigen vector corresponding to eigen value 2 is ___________.

Question 14

During a rolling process, a sheet of  thick is rolled down to  thickness. If the roll of diameter rotates at , calculate the velocity of strip  at the neutral point.

Question 15

GO and NO-GO plug gauges are to be designed for a hole mm. Gauge tolerances can be taken as 10% of the hole tolerance. The sizes of GO and NO-GO gauge will be respectively(On the basis of workshop gauge)______.

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