Under standard conditions,the density of a gas is $\frac{1400}{1089} \ kg \ m^{-3}$ and the speed of sound propagation in it is $330 \ ms^{-1}$. The number of degrees of freedom of the gas molecules is:

Given below are two statements:
Statement $I :$ In a diatomic molecule,the rotational energy at a given temperature obeys Maxwell's distribution.
Statement $II :$ In a diatomic molecule,the rotational energy at a given temperature equals the translational kinetic energy for each molecule.
In the light of the above statements,choose the correct answer from the options given below:

$A$ polyatomic gas with $n$ degrees of freedom has a mean energy per molecule given by (where $k$ is Boltzmann's constant and $T$ is temperature).

For two different gases $X$ and $Y,$ having degrees of freedom $f_1$ and $f_2$ and molar heat capacities at constant volume $C_{v_1}$ and $C_{v_2}$ respectively, for an adiabatic process, the $\ln P$ versus $\ln V$ graph is plotted as shown:

The ratio of the kinetic energy of a diatomic gas molecule at a high temperature to that at $NTP$ is:

$A$ container holds $1 \, \text{mole}$ of oxygen and $2 \, \text{moles}$ of nitrogen at a temperature of $300 \, K$. What is the ratio of the average rotational kinetic energy of $O_2$ to that of $N_2$?