(Take $\gamma$ for nitrogen and $CO_2$ as $1.4$ and $1.3$ respectively)
$(A)$ The average energy per mole of the gas mixture is $2RT$.
$(B)$ The ratio of speed of sound in the gas mixture to that in helium gas is $\sqrt{6 / 5}$.
$(C)$ The ratio of the rms speed of helium atoms to that of hydrogen molecules is $1 / 2$.
$(D)$ The ratio of the rms speed of helium atoms to that of hydrogen molecules is $1 / \sqrt{2}$.