(b) the linear momentum remains constant
(c) the final kinetic energy is equal to the initial kinetic energy
(d) the final linear momentum is equal to the initial linear momentum.
Explanation:
In a fully elastic collision only during the contact period a part of the kinetic energy is stored as elastic potential energy in the bodies and their shapes are slightly changed. Since the collision is elastic the bodies release the stored elastic potential energy and regain their shape. Again the total energy is in the form of K.E. Hence the final K.E. is equal to the initial K.E. But we can not say that the K.E. remains constant because during the contact period it is reduced. So (c) is true and (a) false.
When there is no external force the momentum is conserved. Hence (b) and (d) is true.