Kinetic energy before the collision should be equal to kinetic energy after the collision
In an elastic collision, the "total" kinetic energy and "total" momentum of the system will be conserved. You missed that point. The individual kinetic energy of the ball and wall could change. But the total kinetic energy of the system is conserved before and after collision. That is
where the primed quantities denote kinetic energy after collision and unprimed quantities denote kinetic energy after collision. This is what it is meant by kinetic energy of the system is conserved in elastic collision.
- the massive wall is static (and the ball is not so fast enough to break the wall on collision), or
- the ball and the wall have equal masses and equal velocities
then only we can say that the kinetic energy of each constituents of the system is conserved before and after collisions. But, in general, it is the total kinetic energy of the system (the sum of kinetic energies of all constituents making up the system) that is conserved.
Hence option (d) is incorrect, as the given problem does not satisfy any of the above mentioned criterions. So, on impact, the momentum of the ball increases and hence its kinetic energy also increases. This increase in kinetic energy of the ball will be equal to the decrease in the kinetic energy of the wall. Hence the kinetic energy of the system is conserved in the elastic collision.