The natural frequency of an $L-C$ circuit is equal to:

The natural frequency of an $L-C$ circuit is $1,25,000 \text{ cycle/s}$. Then the capacitor $C$ is replaced by another capacitor with a dielectric medium of dielectric constant $K$. In this case,the frequency decreases by $25 \text{ kHz}$. The value of $K$ is

$A$ charged $10 \mu F$ capacitor is connected to a $16 \text{ mH}$ inductor. What is the angular frequency of free oscillations of the circuit?

In the $LC$ circuit shown below,the current is in the direction shown. At this time :-

In an $LC$ oscillator,if values of inductance and capacitance become twice and eight times,respectively,then the resonant frequency of the oscillator becomes $x$ times its initial resonant frequency $\omega_0$. The value of $x$ is:

The carrier frequency generated by a tank circuit containing $1 \,nF$ capacitor and $10 \, \mu H$ inductor is