Combination of Inductors, LR & LC Circuits question from JEE Main 2020 (8 Jan, Shift 2)

Answer: (a)

1. Growth of current: $i = \frac{\varepsilon}{R}\left(1 - e^{-t/\tau}\right)$, $\tau = L/R$.
2. $q = \int_0^{\tau} i\,dt = \frac{\varepsilon}{R}\left[t + \tau e^{-t/\tau}\right]_0^{\tau} = \frac{\varepsilon}{R}\left(\tau + \frac{\tau}{e} - \tau\right)$
3. $q = \frac{\varepsilon\tau}{eR} = \frac{\varepsilon L}{eR^2}$
4. So the answer is (a).