A slit of width $a$ is illuminated by light of wavelength $\lambda$. The linear separation between $1^{\text {st }}$ and $3^{\text {rd }}$ minima in the diffraction pattern produced on a screen placed at a distance $D$ from the slit system is $\_\_\_\_$ .

A string $A$ of length 0.314 m and Young's modulus $2 \times 10^{10} \mathrm{~N} / \mathrm{m}^2$ is connected to another string $B$ of length and Young's modulus both twice of those of $A$. This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass 0.8 kg . The net change in length of the combination is $\_\_\_\_$ mm.

(radius of both the strings is 0.2 mm and acceleration due to gravity $=10 \mathrm{~m} / \mathrm{s}^2$ ) (Mass of both strings is to be neglected as compared to the mass of load)

One gas of $n_1$ mole of molecules at temperature $T_1$, volume $V_1$, and pressure $P_1$, and another gas of $n_2$ mole of molecules at temperature $T_2$, volume $V_2$, and pressure $P_2$, are mixed resulting in pressure $P$ and volume $V$ of the mixture. The temperature of the mixture is $\_\_\_\_$ .

An ideal gas undergoes a process maintaining relation between pressure $(P)$ and $\operatorname{volume}(V)$ as $P=P_{\mathrm{o}}\left(1+\left(\frac{V_{\mathrm{o}}}{V}\right)^2\right)^{-1}$, where $P_{\mathrm{o}}$ and $V_{\mathrm{o}}$ are constants. If two samples $A$ and $B$ (two moles each) with initial volumes $V_{\mathrm{o}}$ and $3 V_{\mathrm{o}}$ respectively undergo above mentioned process and attain same pressure, then the difference at the temperatures of these samples, $T_B-T_A$ is $\_\_\_\_$ .

( $R=$ gas constant)