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 $R$)

In a cubic container of inner side length $10 \ cm$,nitrogen gas at $100 \ kPa$ pressure is maintained at $300 \ K$. If the pressure inside the container is increased to $300 \ kPa$ by adding oxygen gas,the ratio of the number of $N_2$ molecules to $O_2$ molecules in the container is:

Considering the gases to be ideal,the value of $\gamma = \frac{C_P}{C_V}$ for a gaseous mixture consisting of $3$ moles of carbon dioxide and $2$ moles of oxygen will be $(\gamma_{O_2} = 1.4, \gamma_{CO_2} = 1.3)$.

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 $M_2=2 \ g$. The equivalent degree of freedom $f$ of the mixture is:

Five moles of helium are mixed with two moles of hydrogen to form a mixture. Take the molar mass of helium $M_1 = 4 \ g/mol$ and that of hydrogen $M_2 = 2 \ g/mol$. The equivalent value of $\gamma$ for the mixture is:

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