Instructions

For the following questions answer them individually

Question 1

Starting from the same initial conditions, an ideal gas expands from volume $$V_1$$, to $$V_2$$, in three different ways, the work done by the gas is $$W_1$$, if the process is purely isothermal, $$W_2$$, if purely isobaric and $$W_3$$, if purely adiabatic, then

Question 2

A beaker filled with hot water in a room cools from $$70^\circ C$$ to $$65^\circ C$$ in $$t_1$$ minutes, $$65^\circ C$$ to $$60^\circ C$$ in $$t_2$$ minutes and from $$60^\circ C$$ to $$55^\circ C$$ in $$t_3$$ minutes. Then,

Question 3

A house refrigerator with its door open is switched on in a closed room. Theair in the room is

Question 4

An elevator has a mass of 5000 kg. When thetension in the supporting cable is 60 kN, the acceleration of the elevator is nearly

Question 5

The piston of a steam engine moves with simple harmonic motion. The speed of rotation of crank is 120 rpm with a stroke of 2m. Whatis the velocity of piston whenit is 0.5 m from

the centre?

Question 6

The sine of the angle between the two vectors $$a = 3i + j + k$$ and $$b = 2i - 2j + k$$ is

Question 7

Equation of the line normal to function $$f(x) = (x - 8)^{\frac{2}{3}} + 1$$ at P(0, 5) is

Question 8

There are 20 locks and 20 matching keys. Maximum number of trials required to match all the locks is

Question 9

If $$\phi(x, y, z)$$ is a scalar function and $$\triangledown^2 f = 0$$, then $$\phi$$ is

Question 10

A and B are two candidates appearing for an interview by a company. The probability that A is selected is 0.5 and the probability that both A and B are selected is at most 0.3. The probability of B getting selected is