A series circuit has R=10 Ω, L=0.10 H and C=100 muF connected to a variable-frequency source of constant rms emf 100 V.

At resonance $X_L=X_C$, so the impedance equals $R$ and the rms current is $100/10=10\ \mathrm{A}$. The power is $I^2R=1000\ \mathrm{W}$, so (A) is true. The resonant frequency is $\omega_0=1/\sqrt{LC}=1/\sqrt{10^{-5}}=316\ \mathrm{rad\,s^{-1}}$, so $Q=\omega_0L/R=31.6/10=3.16$, not $10$; (B) is false. At $2\omega_0$ we have $X_L=2\omega_0L$ doubled and $X_C$ halved, so $X_L>X_C$ and the circuit is inductive: the current lags the voltage, hence (C) is false. The half-power bandwidth of a series RLC circuit is $\Delta\omega=R/L=100\ \mathrm{rad\,s^{-1}}$, not $50$, so (D) is false. Only (A) is correct.