Which statements are correct about degrees of freedom?

A. A molecule with $n$ degrees of freedom has $n^2$ different ways of storing energy.

B. Each degree of freedom is associated with $\frac{1}{2}RT$ average energy per mole.

C. A monoatomic gas molecule has $1$ rotational degree of freedom where as diatomic molecule has $2$ rotational degrees of freedom

D. ${\mathrm{CH}}_4$ has a total to $6$ degrees of freedom.

Choose the correct answer from the option given below:

Given below are two statements:

Statement I :The average momentum of a molecule in a sample of an ideal gas depends on temperature.

Statement II : The rms speed of oxygen molecules in a gas is $v$. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become $2v$.

In the light of the above statements, choose the correct answer from the options given below :

The root mean square speed of smoke particles of mass $5\times {10}^{-17} \mathrm{kg}$ in their Brownian motion in air at NTP is approximately.

[Given $k=1.38\times {10}^{-23}\mathrm{J} {\mathrm{K}}^{-1}$]