$A$ gaseous mixture consists of $16 \ g$ of helium and $16 \ g$ of hydrogen. The ratio $\frac{C_p}{C_v}$ of the mixture is

Ferric sulphate on heating gives:

On stretching a wire,the elastic energy stored per unit volume is

In the circuit shown in the figure,the $AC$ source gives a voltage $V = 20 \cos(2000t)$. Neglecting source resistance,the voltmeter and ammeter readings will be

If $\int \sec ^2 x \operatorname{cosec}^4 x \, dx = -\frac{1}{3} \cot ^3 x + k \tan x - 2 \cot x + C$, then $k$ is equal to

$A$ parallel plate capacitor of capacity $C_0$ is charged to a potential $V_0$. $(i)$ The energy stored in the capacitor when the battery is disconnected and the plate separation is doubled is $E_1$. (ii) The energy stored in the capacitor when the charging battery is kept connected and the separation between the capacitor plates is doubled is $E_2$. Then,the value of $E_1 / E_2$ is: