If one mole of an ideal monoatomic gas $\left(\gamma = \frac{5}{3}\right)$ is mixed with one mole of a diatomic gas $\left(\gamma = \frac{7}{5}\right)$,the value of $\gamma$ for the mixture is:

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

The pressure of a mixture of $64 \ g$ of oxygen, $28 \ g$ of nitrogen, and $132 \ g$ of carbon dioxide gases in a closed vessel is $P$. Under isothermal conditions, if the entire oxygen is removed from the vessel, the pressure of the mixture of the remaining two gases is:

$A$ mixture of ideal gas containing $5$ moles of monatomic gas and $1$ mole of rigid diatomic gas is initially at pressure $P_0$,volume $V_0$ and temperature $T_0$. If the gas mixture is adiabatically compressed to a volume $V_0 / 4$,then the correct statement$(s)$ is/are:
(Given $2^{1.2}=2.3$; $2^{3.2}=9.2$; $R$ is gas constant)
$(1)$ The final pressure of the gas mixture after compression is in between $9 P_0$ and $10 P_0$.
$(2)$ The average kinetic energy of the gas mixture after compression is in between $18 RT_0$ and $19 RT_0$.
$(3)$ The work $|W|$ done during the process is $13 RT_0$.
$(4)$ Adiabatic constant of the gas mixture is $1.6$.

$A$ gas mixture consists of molecules of $A, B$ and $C$ with masses $m_A > m_B > m_C$. Rank the three types of molecules in decreasing order of $(a)$ average $K.E.$,$(b)$ $rms$ speeds.

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: