$A$ $x : 1$ molar mixture of $He$ and $CH_4$ is contained in a vessel at $20 \ bar$ pressure. Due to a hole in the vessel,the gas mixture leaks out. If the composition of the mixture effusing out initially is $8 : 1$,then the value of $x$ will be

Two thin circular discs $A$ and $B$ of radii $2 \ cm$ and $4 \ cm$ are in a liquid at the same depth. $T_A$ is the thrust on $A$ and $T_B$ is the thrust on $B$. Then $T_A : T_B =$

Equal moles of hydrogen and oxygen gases are placed in a container with a pin-hole through which both can escape. What fraction of the oxygen escapes in the time required for one-half of the hydrogen to escape?

The vapor pressure of water at $80\,^oC$ is $355.5\, mm\, of\, Hg$. $A$ $100\, mL$ vessel contains $O_2$ saturated with water vapor at $80\,^oC$,and the total pressure is $760\, mm\, of\, Hg$. If the contents are transferred to a $50\, mL$ vessel at the same temperature,what will be the partial pressure of $O_2$ in $mm\, Hg$?

$1 \text{ mole}$ of gas $A$ and $1 \text{ mole}$ of gas $B$ at $27^{\circ} C$ were pumped into a $24.6 \ L$ volume pre-evacuated isolated flask. The catalyst coated inside the flask catalyses the following reaction $A_{(g)} + B_{(g)} \longrightarrow 2 D_{(g)}$. The kinetic energy of $D$ is $98.03 \ L \ atm$. Calculate the pressure realized at the end of the reaction. (in $atm$)

Which of the following sets consists of gases with the same rate of diffusion?