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 ..........?

Two ideal polyatomic gases at temperatures $T_{1}$ and $T_{2}$ are mixed such that there is no loss of energy. If $F_{1}$ and $F_{2}$,$m_{1}$ and $m_{2}$,$n_{1}$ and $n_{2}$ are the degrees of freedom,masses,and number of molecules of the first and second gas respectively,then the temperature of the mixture of these two gases is:

$A$ gas mixture consists of $2$ moles of $O_2$ and $4$ moles of $Ar$ at temperature $T$. Neglecting all vibrational modes,the total internal energy of the system is (in $RT$)

One mole of a monoatomic ideal gas is mixed with one mole of a diatomic ideal gas. The molar specific heat of the mixture at constant volume is

In a container of volume $16.62 \ m^3$ at $0 \ ^{\circ}C$ temperature,$2 \ moles$ of oxygen,$5 \ moles$ of nitrogen,and $3 \ moles$ of hydrogen are present. Then,the pressure in the container is (Universal gas constant $R = 8.31 \ J \ mol^{-1} \ K^{-1}$) (in $Pa$)

$A$ mixture of hydrogen and oxygen has volume $500 \, cm^3$,temperature $300 \, K$,pressure $400 \, kPa$,and mass $0.76 \, g$. The ratio of the mass of oxygen to the mass of hydrogen is: