Two particles A and B, move with constant velocities v₁ and v₂. At the initial moment, their position vectors are r₁ and r₂ respectively. The condition for particles A and B for their collision is 

• 

• r₁.v₁ = r₂.v₂

• r₁ x v₁ = r₂ x v₂

• r₁ x v₁ = r₂ x v₂

A rectangular coil of length 0.12 m and width 0.1 m having turns of wire is suspended vertically in a uniform magnetic field of strength 0.2 Wb/m².The coil carries a current of 2 A. If the plane of the coil is inclined at an angle of 30^o with the direction of the field, the torque required to keep the coil in stable equilibrium will be

• 0.15 Nm

• 0.20 Nm

• 0.24 Nm

• 0.24 Nm

On a frictionless surface, a block of mass M moving at speed v collides elastically with another block of same mass M which is initially at rest. After collision, the first block moves at an angle θ to its initial direction and has a speed v/3/ The second block's speed after the collision is 

• 

• 3/4 v

• 

• 

If dimensions of critical velocity v_c of a liquid flowing through  a tube are expressed as  are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of x, y and z are given by

• 1,-1,-1

• -1,-1,1

• -1,-1,-1

• -1,-1,-1

4.0 g of a gas occupies 22.4 L at NTP. The specific heat capacity of the gas at constant volume is 5.0 JK^-1 mol^-1. If the speed of sound in this gas at NTP is 952 ms^-1, then the heat capacity at constant pressure is.
(Take gas constant R = 8.3 Jk^-1 mol^-1)

• 8.0 JK^-1mol^-1

• 7.5 JK^-1mol^-1

• 7.0 JK^-1mol^-1

• 7.0 JK^-1mol^-1

A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. The lowest resonant frequency for this strings is

• 155 Hz

• 205 Hz

• 10.5 Hz

• 10.5 Hz

The coefficient of performance of a refrigerator is 5. If the temperature inside freezer is -20^o C, th temperature of the surroundings to which it rejects heat is

• 31^o C

• 41^o C

• 11^o C

• 11^o C

The value of the coefficient of volume expansion of glycerin is 5 x 10^-4 K^-1. The fractional change in the density of glycerin for a rise of 40⁰C in its temperature is 

• 0.015

• 0.020

• 0.025

• 0.025

Water rises to a height 'h' in a capillary tube. If the length of capillary tube above the surface of water is made less than 'h' then

• water rises upto the tip of the capillary tube and then starts overflowing like a fountain

• water rises  upto the top of capillary tube and stays there without overflowing 

• water rises upto a point little below the top and stays there

• water rises upto a point little below the top and stays there

20.

The young's modulus of steel is twice that of brass. Two wires of same length and of same area of cross section, one of steel and another of brass are suspended from the same roof. we want the lower ends of the wires to be at the same level, then the weight added to the steel and brass wires must be in the ratio of

• 1:2

• 2:1

• 4:1

• 4:1