If $1 \text{ mole}$ of a monoatomic gas $\left[ \gamma = \frac{5}{3} \right]$ is mixed with $1 \text{ mole}$ of a diatomic gas $\left[ \gamma = \frac{7}{5} \right]$,then the $\gamma$ of the mixture is ..........?

$A$ closed container contains a homogeneous mixture of two moles of an ideal monatomic gas $(\gamma=5/3)$ and one mole of an ideal diatomic gas $(\gamma=7/5)$. Here,$\gamma$ is the ratio of the specific heats at constant pressure and constant volume of an ideal gas. The gas mixture does a work of $66 \ J$ when heated at constant pressure. The change in its internal energy is . . . . . . $J$.

$A$ gas mixture consists of $16 \ g$ of helium and $16 \ g$ of oxygen. For this mixture,the ratio $C_P/C_V$ is equal to:

Two gases have temperature $T$,pressure $P$,and volume $V$ each. If they are mixed in a container of volume $V$ at the same temperature $T$,what will be the new pressure and mass of the mixture?

$A$ gas mixture contains monoatomic and diatomic molecules of $2$ moles each. The mixture has a total internal energy of (symbols have usual meanings): (in $R T$)

$A$ 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 $1/\sqrt{2}$.