Three identical containers contain three different gases. The masses of the molecules are $m_1, m_2$,and $m_3$,and the number of molecules in the containers are $N_1, N_2$,and $N_3$,respectively. The pressures of the gases in the containers are $P_1, P_2$,and $P_3$,respectively. If these three gases are mixed and filled into a single container of the same volume,what will be the pressure of the mixture?

Two gases $A$ and $B$ having the same pressure $P$, volume $V$, and absolute temperature $T$ are mixed. If the mixture has the volume $V$ and temperature $T$, then the pressure of the mixture is:

$A$ container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium at temperature $T$. Assuming the gases are ideal,the correct statement$(s)$ is(are):
$(A)$ The average energy per mole of the gas mixture is $2RT$.
$(B)$ The ratio of speed of sound in the gas mixture to that in helium gas is $\sqrt{6/5}$.
$(C)$ The ratio of the rms speed of helium atoms to that of hydrogen molecules is $1/2$.
$(D)$ The ratio of the rms speed of helium atoms to that of hydrogen molecules is $1/\sqrt{2}$.

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

If $\alpha$ moles of a monoatomic gas are mixed with $\beta$ moles of a polyatomic gas and the mixture behaves like a diatomic gas,then [neglect the vibrational mode of freedom]:

$A$ mixture of two non-reactive ideal gases is enclosed in a vessel consisting of one mole of a monatomic gas '$A$' and 'n' moles of a diatomic gas '$B$' at a temperature '$T$'. If the adiabatic constant of the gaseous mixture is $\frac{13}{9}$,then the value of 'n' is: