One mole of ideal monoatomic gas $(\gamma = 5/3)$ is mixed with one mole of diatomic gas $(\gamma = 7/5)$. What is $\gamma$ for the mixture? $\gamma$ denotes the ratio of specific heat at constant pressure to that at constant volume.

Three perfect gases at absolute temperatures $T_1, T_2$ and $T_3$ are mixed. The masses of molecules are $m_1, m_2$ and $m_3$ and the number of molecules are $n_1, n_2$ and $n_3$ respectively. Assuming no loss of energy,the final temperature of the mixture is

$A$ gas mixture consists of $2$ moles of oxygen and $4$ moles of neon at temperature $T$. Neglecting all vibrational modes,the total internal energy of the system will be $...........\,RT$.

Sound travels in a mixture of $2$ moles of helium and $n$ moles of hydrogen. If the root-mean-square (rms) speed of gas molecules in the mixture is $\sqrt{2}$ times the speed of sound,then the value of $n$ will be:

Five moles of helium are mixed with two moles of hydrogen to form a mixture. Take the molar mass of helium $M_1 = 4 \ g/mol$ and that of hydrogen $M_2 = 2 \ g/mol$. The equivalent value of $\gamma$ for the mixture is:

$A$ container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium at temperature $T$. Assuming the gases are ideal,the correct statement$(s)$ is(are):
$(A)$ 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 $1/\sqrt{2}$.