$A$ 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 ...... $^\circ C$.

$A$ vessel contains hydrogen and nitrogen gases in the ratio $2: 3$ by mass. If the temperature of the mixture of the gases is $30^{\circ} C$, then the ratio of the average kinetic energies per molecule of hydrogen and nitrogen gases is $($Molecular mass of hydrogen gas $= 2$ and molecular mass of nitrogen gas $= 28)$.

$A$ box contains a mixture of ${H_2}$ and $He$ gases. Which of the following statements are correct?

One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of the mixture at constant volume is $\frac{\alpha^{2}}{4} R \ J/mol \ K$; then the value of $\alpha$ will be $.......$ (Assume that the given diatomic gas has no vibrational mode.)

Two containers of equal volume contain identical gases at pressures $P_1$ and $P_2$ and absolute temperatures $T_1$ and $T_2$ respectively. The vessels are joined and the gas reaches a common pressure $P$ and a common temperature $T$. Then: