How many degrees of freedom does a diatomic gas have due to its translational motion?

Consider two ideal diatomic gases $A$ and $B$ at some temperature $T$. Molecules of the gas $A$ are rigid,and have a mass $m$. Molecules of the gas $B$ have an additional vibrational mode,and have a mass $\frac{m}{4}$. The ratio of the specific heats $(C_{v}^{A}$ and $C_{v}^{B})$ of gas $A$ and $B$,respectively,is

Ratio of translational degrees of freedom to rotational degrees of freedom of a polyatomic linear gas molecule is

The temperature of argon,kept in a vessel,is raised by $1^\circ C$ at a constant volume. The total heat supplied to the gas is a combination of translational and rotational energies. Their respective shares are

The value of $\gamma \left( = \frac{C_{p}}{C_{v}} \right)$ for hydrogen,helium,and another ideal diatomic gas $X$ (whose molecules are not rigid but have an additional vibrational mode) are respectively equal to:

$A$ polyatomic ideal gas has $24$ vibrational modes. What is the value of $\gamma$ ?