One mole of a gas having $\gamma = \frac{7}{5}$ is mixed with one mole of a gas having $\gamma = \frac{4}{3}$. The value of $\gamma$ for the mixture is ($\gamma$ is the ratio of the specific heats of the gas).

Two moles of helium are mixed with $n$ moles of hydrogen. If $\frac{C_P}{C_V} = \frac{3}{2}$ for the mixture,then the value of $n$ is:

$A$ mixture of ideal gases consists of $7 \, kg$ of nitrogen and $11 \, kg$ of $CO_2$. Then (Take $\gamma$ for nitrogen and $CO_2$ as $1.4$ and $1.3$ respectively):

$A$ cylindrical container of volume $4.0 \times 10^{-3} \, m^3$ contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is $400 \, K$. The pressure of the mixture of gases is:
[Take gas constant as $R = 8.3 \, J \, mol^{-1} \, K^{-1}$]

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

$A$ vessel of volume $0.02 \, m^3$ contains a mixture of hydrogen and helium at $20 \, ^oC$ and $2$ atmospheric pressure. The mass of the mixture is $5 \, g$. Find the ratio of the mass of hydrogen to that of helium in the mixture.