The translational degrees of freedom $(f_t)$ and rotational degrees of freedom $(f_r)$ of a $CH_4$ molecule are:

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:

For a triatomic gas molecule,if the degrees of freedom for translation,rotation,and vibration are considered,then $C_P/C_V = ?$

Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom. The gas is maintained at a temperature of $T$. The total internal energy,$U$ of a mole of this gas,and the value of $\gamma \left( = \frac{C_P}{C_V} \right)$ are given,respectively,by:

If hydrogen gas is heated to a very high temperature,then the fraction of energy possessed by gas molecules corresponding to rotational motion is ...........

If the internal energy of $n_1$ moles of $He$ at temperature $10T$ is equal to the internal energy of $n_2$ moles of hydrogen $(H_2)$ at temperature $6T$,find the ratio $\frac{n_1}{n_2}$.