Resonance, Bandwidth & Q Factor question from MHT CET 2024 (10 May, Shift 2)

Answer: (d)

1. To stay at resonance, $f = \frac{1}{2\pi\sqrt{LC}}$ must equal the supply frequency.
2. Doubling $f$ needs $LC$ to become $\frac{1}{4}$ of its value.
3. Halving both: $\frac{L}{2}\cdot\frac{C}{2} = \frac{LC}{4}$
4. So the answer is (d) both halved simultaneously.