The interaction energy of London forces between two particles is proportional to ${\mathrm{r}}^x$, where $\mathrm{r}$ is the distance between the particles. The value of $\mathrm{x}$ is :

A home owner uses $4.00\times {10}^3{ \mathrm{m}}^3$ of methane $\left({\mathrm{CH}}_4\right)$ gas, (assume ${\mathrm{CH}}_4$ is an ideal gas) in a year to heat his home. Under the pressure of $1.0$ atm and $300 \mathrm{K}$, mass of gas used is $\mathrm{x}\times {10}^5 \mathrm{g}$. The value of $\mathrm{x}$ is ______. (Nearest integer)

(Given $\mathrm{R}=0.083 \mathrm{L} \mathrm{atm} {\mathrm{K}}^{-1}{ \mathrm{mol}}^{-1}$)

The volume occupied by $4.75 \mathrm{g}$ of acetylene gas at $50°\mathrm{C}$ and $740 \mathrm{mm} \mathrm{Hg}$ pressure is ____________ $\mathrm{L}.$ (Rounded off to the nearest integer)

[Given $\mathrm{R}=0.0826 \mathrm{L} \mathrm{atm} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}$]

Match the type of interaction in column $\mathrm{A}$ with the distance dependence of their interaction energy in column $\mathrm{B}:$

Which one of the following graphs is not correct for ideal gas?

$\mathrm{d}=$ Density, $\mathrm{P}=$ Pressure, $\mathrm{T}=$Temperature