Escape Velocity question from NEET 2021

Answer: (a)

1. Energy conservation: $\frac{1}{2}mk^2\frac{2GM}{R} = GMm\left(\frac{1}{R} - \frac{1}{R+h}\right)$.
2. $\frac{1}{R+h} = \frac{1-k^2}{R} \Rightarrow R+h = \frac{R}{1-k^2}$.
3. $h = \frac{Rk^2}{1-k^2}$.
4. So the answer is (a) $\frac{Rk^{2}}{1-k^{2}}$.