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

Two gases $X$ (molecular weight $M_{X}$) and $Y$ (molecular weight $M_{Y}$; $M_{Y} > M_{X}$) are at the same temperature $T$ in two different containers. Their root mean square velocities are $C_{X}$ and $C_{Y}$ respectively. If the average kinetic energies per molecule of two gases $X$ and $Y$ are $E_{X}$ and $E_{Y}$ respectively, then which of the following relation$(s)$ is(are) true?

Choose the incorrect statement from the following:

The magnitude of surface tension of a liquid depends on the attractive forces between the molecules. Arrange the following in increasing order of surface tension: Water,alcohol $(C_2H_5OH)$,and hexane $(CH_3(CH_2)_4CH_3)$.

At $290 \ K$,a vessel $(I)$ contains equal moles of three liquids $(A, B, C)$. The boiling points of $A, B$ and $C$ are $350 \ K, 373 \ K$ and $308 \ K$ respectively. Vessel $(I)$ is heated to $300 \ K$ and vapours were collected into vessel $(II)$. Identify the correct statements. (Assume vessel $(I)$ contains liquids and vapours and vessel $(II)$ contains only vapours)
$I.$ Vessel $- I$ is rich in liquid $B$
$II.$ Vessel $- II$ is rich in vapour of $C$
$III.$ The vapour pressures of $A, B, C$ in Vessel $(I)$ at $290 \ K$ follows the order $C > A > B$.

Equal volumes of monoatomic and diatomic gases at same initial temperature and pressure are mixed. The ratio of specific heats of the mixture $({C_p}/{C_v})$ will be