For the series LCR circuit, \(R=\frac{X_L}{2}=2 X_c\). The impedance of the circuit and the phase difference between V and I will be

\(\operatorname{Impedance}(\mathrm{Z})=\sqrt{\mathrm{R}^2+\left(\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}\right)^2}...(i)\)
Given \(R=\frac{X_L}{2} \Rightarrow X_L=2 R\)...(ii)
Also, \(\mathrm{R}=2 \mathrm{X}_{\mathrm{C}} \Rightarrow \mathrm{X}_{\mathrm{C}}=\frac{\mathrm{R}}{2}\)...(iii)
Substituting (ii) and (iii) in (i),
\(Z=\sqrt{R^2+\left(2 R-\frac{R}{2}\right)^2}=\sqrt{\frac{13}{4} R^2}=\frac{\sqrt{13}}{2} R\)
Phase difference \(\phi=\tan ^{-1}\left(\frac{\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}}{\mathrm{R}}\right)=\tan ^{-1}\left(\frac{3}{2}\right)\)
Since the impedance values provided in the options are all different, calculating the impedance will be enough to identify the correct answer.