Resonance, Bandwidth & Q Factor question from MHT CET 2025 (23 Apr, Shift 1)

Answer: (d)

1. $L$ and $2L$ are in series: $L_{eq} = 3L$.
2. $C$ and $2C$ both join the same two nodes, so they are in parallel: $C_{eq} = 3C$.
3. $f = \frac{1}{2\pi\sqrt{L_{eq}C_{eq}}} = \frac{1}{2\pi\sqrt{9LC}} = \frac{1}{6\pi\sqrt{LC}}$
4. So the answer is (d) $\frac{1}{6\pi\sqrt{LC}}$.