In an $LC$ parallel resonance circuit,choose the wrong statement.

In a series $LCR$ resonant circuit,the quality factor is measured as $100$. If the inductance is increased by two fold and resistance is decreased by two fold,then the quality factor after this change will be .........

Two circuits are shown in the figures $(a)$ and $(b)$. At a frequency of $....\,rad/s$,the average power dissipated in one cycle will be the same in both circuits.

Figure $(a)$ shows the plot of voltage across the capacitor as a function of the driving frequency for a sinusoidally driven electromagnetic $LCR$ oscillator circuit. Figure $(b)$ shows the phase angle $\phi$ (phase difference between voltage and current) vs $\omega/\omega_0$ graph for the same circuit,for three different quality factors corresponding to graphs $1, 2, 3$ of figure $(a)$. Each graph in figure $(a)$ can be matched by one of the graphs $a, b, c$ in figure $(b)$. Choose the correct statement:

The capacitor of an oscillatory circuit is enclosed in a container. When the container is evacuated,the resonance frequency of the circuit is $10\, kHz$. When the container is filled with a gas,the resonance frequency changes by $50\, Hz$. The dielectric constant of the gas is

$A$ series $LCR$ circuit of $R=5 \, \Omega, L=20 \, \text{mH}$ and $C=0.5 \, \mu \text{F}$ is connected across an $AC$ supply of $250 \, \text{V}$,having variable frequency. The power dissipated at resonance condition is $..... \times 10^{2} \, \text{W}$.