Collisions in two dimensions

2012 AIPMT-PRE 1 question

1. 1 Work, Energy and Power
   Two spheres A and B of masses $m_1$ and $m_2$ respectively collide. A is at rest initially and B is moving with velocity v along x-axis. After collision B has a velocity $\frac{v}{2}$ in a direction perpendicular to the original direction. The mass A moves after collision in the direction
   A $\theta = \tan^{-1}\left(-\frac{1}{2}\right)$ to the x-axis B same as that of B C opposite to that of B D $\theta = \tan^{-1}\left(\frac{1}{2}\right)$ to the x-axis
   Check Answer