Given $L = \frac{50}{\pi} \text{ mH} = \frac{50}{\pi} \times 10^{-3} \text{ H}$, $C = \frac{10^3}{\pi} \text{ } \mu\text{F} = \frac{10^{-3}}{\pi} \text{ F}$, $R = 10 \text{ } \Omega$, $f = 50 \text{ Hz}$. Inductive reactance $X_L = 2\pi f L = 2\pi \times 50 \times \frac{50}{\pi} \times 10^{-3} = 5 \text{ } \Omega$. Capacitive reactance $X_C = \frac{1}{2\pi f C} = \frac{1}{2\pi \times 50 \times \frac{10^{-3}}{\pi}} = \frac{1}{0.1} = 10 \text{ } \Omega$. Impedance $Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{10^2 + (5 - 10)^2} = \sqrt{100 + 25} = \sqrt{125} = 5\sqrt{5} \text{ } \Omega$.