A copper wire of length 3 m is stretched by 3 mm by applying an external force. The volume of the wire is $600 \times 10^{-6} \mathrm{~m}^3$. The elastic potential energy stored in the wire in stretched condition would be

$\_\_\_\_$ J.

(Given Young modulus of copper $=1.1 \times 10^{11} \mathrm{~N} / \mathrm{m}^2$ )

The heat extracted out of $x$ gram of water initially at $50^{\circ} \mathrm{C}$ to $\operatorname{cool}$ it down to $0^{\circ} \mathrm{C}$ is sufficient to evaporate $(1000-x)$ gram of water also initially at $50^{\circ} \mathrm{C}$. The value of $x$ (closest integer) is $\_\_\_\_$ .

(Take latent heat of water $2256 \mathrm{~kJ} / \mathrm{kg} . \mathrm{K}$, specific heat capacity of water $4200 \mathrm{~J} / \mathrm{kg} . \mathrm{K}$ )

A series LCR circuit with $R=20 \Omega, L=1.6 \mathrm{H}$ and $C=40 \mu \mathrm{~F}$ is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is $\_\_\_\_$ $\Omega$.

When an external resistance of $5 \Omega$ is connected across terminals of a cell, a current of 0.25 A flows through it. When the $5 \Omega$ resistor is replaced by a $2 \Omega$ resistor, a current of 0.5 A flows through it. The internal resistance of the cell is $\_\_\_\_$ $\Omega$.