Two small balls A and B of mass$M$  and $3M$ hang from the ceiling by strings of equal length. The ball A is drawn aside so that it is raised to a height $H$. It is then released and collides with ball B. Select the correct answer(s).

 

If the collision is perfectly inelastic, the combined mass will rise to a height $\frac{H}{16}$

If collision is elastic, ball B will rise to a height $\frac{H}{2}$

If collision is elastic, ball A will rise upto a height $\frac{H}{2}$

If the collision is perfectly inelastic, the combined mass will rise to a height $\frac{H}{4}$