A pendulum is oscillating with frequency '$$n$$' on the surface of the earth. It is taken to a depth $$\frac{R}{2}$$ below the surface of earth. New frequency of oscillation at depth $$\frac{R}{2}$$ is

[ $$R$$ is the radius of earth]

The molar specific heats of an ideal gas at constant pressure and volume are denoted by '$$\mathrm{C}_{\mathrm{p}}$$' and '$$C_v$$' respectively. If $$\gamma=\frac{C_p}{C_v}$$ and '$$R$$' is universal gas constant, then $$C_v$$ is equal to

In a pure silicon, number of electrons and holes per unit volume are $$1.6 \times 10^{16} \mathrm{~m}^{-3}$$. If silicon is doped with Boron in a way that on doping hole density increases to $$4 \times 10^{22} \mathrm{~m}^{-3}$$. Then electron density in doped semiconductor will be

A charge moves with velocity '$$V$$' through electric field $$(E)$$ as well as magnetic field (B). then the force acting on it is