$A$ mixture of hydrogen and oxygen has a volume of $2000 \; cm^{3}$,a temperature of $300 \; K$,a pressure of $100 \; kPa$,and a mass of $0.76 \; g$. The ratio of the number of moles of hydrogen to the number of moles of oxygen in the mixture is:

If $22 \, g$ of $CO_2$ gas at $27 \, ^\circ C$ and $16 \, g$ of $O_2$ gas at $37 \, ^\circ C$ are mixed,the final temperature of the mixture will be ...... $^\circ C$.

$A$ 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 $1.6$.

$A$ mixture of two moles of hydrogen and one mole of argon gas is taken in a closed container at room temperature. Consider the following two statements:
$(i)$ The average kinetic energy of each molecule of $H_2$ and $Ar$ are the same.
$(ii)$ The partial pressure due to argon gas is more than that due to hydrogen gas.

The specific heat of the mixture of two gases at constant volume is $\frac{13}{6} R$. The ratio of the number of moles of the first gas to the second is $1:2$. The respective gases may be:

One mole of a gas with $\gamma = 7/5$ is mixed with one mole of a gas with $\gamma = 4/3$. What will be the $\gamma$ of the mixture?