a
Quality factor of an \(L-C-R\) circuit is given by,

\({Q=\frac{1}{R} \sqrt{\frac{L}{C}}} \)

\({Q_{1}=\frac{1}{15} \sqrt{\frac{3.5}{30 \times 10^{-6}}}=\frac{100}{15} \sqrt{\frac{35}{3}}=22.77} \)

\({Q_{2}=\frac{1}{25} \times \sqrt{\frac{1.5}{45 \times 10^{-6}}}=40 \times \sqrt{\frac{5}{90}}=9.43} \)

\({Q_{3}=\frac{1}{20} \sqrt{\frac{1.5}{35 \times 10^{-6}}}=50 \times \sqrt{\frac{3}{70}}=10.35} \)

\({Q_{4}=\frac{1}{25} \times \sqrt{\frac{2.5}{45 \times 10^{-6}}}=\frac{40}{\sqrt{30}}=7.30}\)

Clearly \(Q_{1}\) is maximum of \(Q_{1}, Q_{2}, Q_{3},\) and \(Q_{4}\).

Hence, option \((a)\) should be selected for better tuning of an \(L-C-R\) circuit.