ANS:E - All the above.

1. "If two equal and perfectly elastic smooth spheres impinge directly, they interchange their velocities."
   • This statement is true. In a perfectly elastic collision, when two equal spheres collide directly, they exchange velocities.
2. "If a sphere impinges directly on an equal sphere which is at rest, then a fraction (1 - e^2) of the original kinetic energy is lost by the impact."
   • This statement is also true. In an elastic collision, a fraction of the original kinetic energy is lost, and the rest remains conserved. The fraction lost is 1−e^2, where e is the coefficient of restitution.
3. "If a smooth sphere impinges on another sphere, which is at rest, the latter will move along the line of centers."
   • This statement is true. In a collision where one sphere is initially at rest, conservation of momentum dictates that the sphere initially at rest will move along the line of centers after the collision.
4. "If two equal spheres which are perfectly elastic impinge at right angles, their direction after impact will still be at right angles."
   • This statement is also true. In a perfectly elastic collision at right angles, the directions of the velocities after the collision will still be at right angles to each other.