The equation of state of a gas is given by $\left( P + \frac{aT^2}{V} \right) V^c = (RT + b)$,where $a, b, c$ and $R$ are constants. The isotherms can be represented by $P = AV^m - BV^n$,where $A$ and $B$ depend only on temperature. Then:

To determine the Young's modulus of a wire,the formula is $Y = \frac{FL}{A\Delta L}$,where $L$ is the length,$A$ is the area of cross-section of the wire,and $\Delta L$ is the change in length of the wire when stretched with a force $F$. The conversion factor to change the unit of Young's modulus from $CGS$ to $MKS$ system is $x \times 10^{-1} \ N/m^2$. Find the value of $x$.

Match the entries in List-$I$ with those in List-$II$.

$A$. Unified interaction reducing the number of fundamental forces from four to three	$(i)$ Strong interaction
$B$. Force between two molecules separated by a distance near about the sum of the molecular radii	$(ii)$ Gravitational force
$C$. Nuclear binding force	$(iii)$ Electroweak interaction
$D$. Bodies of astronomical proportions	$(iv)$ Electromagnetic interaction

The unit $J \cdot s^2$ corresponds to which physical quantity?

Match the following. (Take the relative strength of the strongest fundamental forces in nature as $1$)

Which of the following pairs does not have the same dimensions?