Combination of Inductors, LR & LC Circuits question from MHT CET 2025 (25 Apr, Shift 1)

Answer: (a)

1. The top wire joins $A$ to the junction after 4 H, and the bottom wire joins the junction after 2 H to $B$.
2. So all four coils (2 H, 3 H, 4 H, 6 H) are connected directly between $A$ and $B$: all in parallel.
3. $\frac{1}{L} = \frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{6} = \frac{15}{12}$
4. So the answer is (a) $\frac{4}{5}\text{ H}$.