Conservation of Momentum Questions

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 $v/2$ in a direction perpendicular to the original direction. The mass $A$ moves after collision in the direction:

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass $1\text{kg}$ moves with a speed of $12\text{m/s}$ and the second part of mass $2\text{kg}$ moves with $8\text{m/s}$ speed. If the third part flies off with $4\text{m/s}$ speed, then its mass is:

A body of mass ($4m$) is lying in $x-y$ plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass ($m$) move perpendicular to each other with equal speeds ($v$). The total kinetic energy generated due to explosion is: