If a mixture of $28 \, g$ of Nitrogen $(N_2)$,$4 \, g$ of Hydrogen $(H_2)$,and $8 \, g$ of Helium $(He)$ is contained in a vessel at temperature $400 \, K$ and pressure $8.3 \times 10^5 \, Pa$,the density of the mixture will be:

The molar specific heat of a mixture at constant volume,if one mole of $He$ gas is mixed with three moles of $O_2$ gas,is: (in $R$)

Two gases $A$ and $B$ having same pressure $P$,volume $V$,and absolute temperature $T$ are mixed. If the mixture has the volume and temperature as $V$ and $T$ respectively,then the pressure of 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 $M_2=2\ g$. If the internal energy of the $He$ sample is $100\ J$ and that of the hydrogen sample is $200\ J$,then the internal energy of the mixture is ..... $J$.

Two identical containers contain the same gas at pressures $P_1$ and $P_2$ and temperatures $T_1$ and $T_2$,respectively. If the containers are connected,the common pressure is $P$ and the common temperature is $T$. What is the value of $P/T$?

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, $R=\frac{25}{3} \,J \,mol^{-1} \,K^{-1}$)