The curves $$\frac{x^2}{a^2}+\frac{y^2}{4}=1$$ and $$y^3=16 x$$ intersect each other orthogonally, then $$a^2=$$

The magnetic potential energy stored in a certain inductor is $$25 \mathrm{~mJ}$$, when the current in the inductor is $$50 \mathrm{~mA}$$. This inductor is of inductance

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