Equal masses of $CH_4$ and $H_2$ are mixed in an empty container at $25\,^oC$. The fraction of the total pressure exerted by methane is

When a sample of gas is compressed at constant temperature from $15 \, atm$ to $60 \, atm$,its volume changes from $76 \, cm^3$ to $20.5 \, cm^3$. Which of the following statements are possible explanations of this behaviour?
$(1)$ The gas behaves non-ideally
$(2)$ The gas dimerises
$(3)$ The gas is adsorbed into the vessel walls

Two flasks $I$ and $II$ shown below are connected by a valve of negligible volume. When the valve is opened,the final pressure of the system in bar is $x \times 10^{-2}$. The value of $x$ is $.....$ . (Integer answer) [Assume-Ideal gas; $1 \, bar = 10^{5} \, Pa$; Molar mass of $N_{2} = 28.0 \, g \, mol^{-1}$; $R = 8.31 \, J \, mol^{-1} \, K^{-1}$]

The rate of diffusion of methane at $1.0 \ atm$ pressure is twice that of another gas '$X$' kept at $1.45 \ atm$. The molecular weight of the gas '$X$' is
[$T$ kept constant]

$20 \, L$ of $SO_2$ diffuses through a porous partition in $60 \, s$. Volume of $O_2$ diffused under similar conditions in $30 \, s$ will be ................ $L$. (in $.14$)

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 $T_A : T_B =$