If the speed of sound in a mixture of $2$ moles of Helium and $2$ moles of Hydrogen at temperature $\frac{972}{5} \,K$ is $n \times 100 \,ms^{-1}$, then the value of $n$ is (Take, $R=\frac{25}{3} \,J \,mol^{-1} \,K^{-1}$)

$A$ 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 $1.6$.

$A$ vessel of volume $20 \ L$ contains a mixture of hydrogen and helium at a temperature of $27^{\circ} C$ and pressure $2 \ atm$. The mass of the mixture is $5 \ g$. Assuming the gases to be ideal,the ratio of the mass of hydrogen to that of helium in the given mixture will be:

$A$ gaseous mixture has $2$ moles of oxygen and $4$ moles of Argon at a temperature $T$. Neglecting all vibrational modes of the molecules,the total internal energy of the system is ($R$ = Universal gas constant). (in $RT$)

An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume $V_1$ and contains ideal gas at pressure $P_1$ and temperature $T_1$. The other chamber has volume $V_2$ and contains ideal gas at pressure $P_2$ and temperature $T_2$. If the partition is removed without doing any work on the gas,the final equilibrium temperature of the gas in the container will be

$A$ gaseous mixture contains $7 \ g$ of nitrogen and $20 \ g$ of argon. Assuming the gases are ideal,what are the specific heats $C_P$ and $C_V$ (in $J/g \ K$) for the mixture?