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

$A$ $60\,\mu F$ capacitor is charged to $50\, V$. This charged capacitor is connected across a $1.5\, mH$ coil,so that $LC$ oscillations occur. The max current in the coil is......$A$

$A$ transistor-oscillator using a resonant circuit with an inductor $L$ (of negligible resistance) and a capacitor $C$ in series produces oscillations of frequency $f$. If $L$ is doubled and $C$ is changed to $4C$,the frequency will be

$A$ condenser of capacity $6 \ \mu F$ is fully charged using a $6 \ V$ battery. The battery is removed and a resistanceless $0.2 \ mH$ inductor is connected across the condenser. The current flowing through the inductor when one-third of the total energy is in the magnetic field of the inductor is.....$A$

In an oscillating $LC$ circuit, the maximum charge on the capacitor is $Q$. When the energy is stored equally between the electric and magnetic fields, the charge on the capacitor $(q)$ is:

Write the differential equation for an $LC$ circuit.