JEE Main 2017 · 8 Apr · Shift 1, Physics question 4

The official answer, $\frac53h$, corresponds to the speed being halved at each bounce ($e=\frac12$, so each rebound height is $\frac14$ of the previous one):
$$d=h+2\left(\frac h4+\frac h{16}+\dots\right)=h+\frac{2h/4}{1-1/4}=\frac53h.$$
Read literally, losing 50% of the kinetic energy makes each rebound height $\frac12$ of the previous, which gives $h+2h=3h$, not among the options. The answer follows the official key.