A body of mass M moving at speed V₀ collides elastically with a mass 'm' at rest. After the collision, the two masses move at angles $$\theta$$₁ and $$\theta$$₂ with respect to the initial direction of motion of the body of mass M. The largest possible value of the ratio M/m, for which the angles $$\theta$$₁ and $$\theta$$₂ will be equal, is :

Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. The masses of A, B and C are m, 2m and 2m respectively. A moves towards B with a speed of 9 m/s and makes an elastic collision with it. Thereafter B makes a completely inelastic collision with C. All motions occur along same straight line. The final speed of C is :

Two billiard balls of equal mass 30g strike a rigid wall with same speed of 108 kmph (as shown) but at different angles. If the balls get reflected with the same speed then the ratio of the magnitude of impulses imparted to ball 'a' and ball 'b' by the wall along 'X' direction is :

A bullet of '4 g' mass is fired from a gun of mass 4 kg. If the bullet moves with the muzzle speed of 50 ms^$$-$$1, the impulse imparted to the gun and velocity of recoil of gun are :