If $L$ and $C$ are inductance and capacitance respectively, then the dimensional formula of $(LC)^{-\frac{1}{2}}$ is

The magnetic energy in an inductor changes from maximum value to minimum value in $5 \ ms$. When connected to an $A.C.$ source,the frequency of the source is (in $Hz$)

In the given circuit, the resonant frequency is (in $ Hz$)

The charge of the capacitor in an $LC$ oscillatory circuit,when the energy associated with the inductor and capacitor are equal,is . . . . . . . ($Q_{0}$ is the initial charge on the capacitor.)

An $L-C$ resonant circuit contains a $400 \ pF$ capacitor and an inductor of $400 \ \mu H$. It is coupled to an antenna. The wavelength of the radiated electromagnetic wave is:

$A$ charged $30 \mu\text{F}$ capacitor is connected to a $27 \text{ mH}$ inductor. What is the angular frequency of free oscillations of the circuit (in $\text{ rad/s}$)?