In an L-C-R circuit capacitance is changed from C to 2C. For the resonant frequency to remain unchanged, the inductance should be changed from L to

At resonance, ${\mathrm{X}}_{\mathrm{L}}={\mathrm{X}}_{\mathrm{C}}\text{ i.e., }\mathrm{\omega L}=1/\left(\mathrm{\omega C}\right)$. For the resonant frequency to remain unchanged, $\sqrt{\mathrm{LC}}=$ constant or LC = constant
$$\begin{gathered} \therefore {\mathrm{L}}_1{\mathrm{C}}_1={\mathrm{L}}_2{\mathrm{C}}_2 \text{ or }\mathrm{LC}={\mathrm{L}}_2\times 2\mathrm{C} \\ \text{ or }{\mathrm{L}}_2=\mathrm{L}/2 \end{gathered}$$