For a fixed number of moles of a gas at constant volume,the pressure of the gas increases with an increase in temperature because:

$X$ and $Y$ are two volatile liquids with molar weights of $10 \ g \ mol^{-1}$ and $40 \ g \ mol^{-1}$ respectively. Two cotton plugs,one soaked in $X$ and the other soaked in $Y$,are simultaneously placed at the ends of a tube of length $L = 24 \ cm$. The tube is filled with an inert gas at $1 \ atmosphere$ pressure and a temperature of $300 \ K$. Vapours of $X$ and $Y$ react to form a product which is first observed at a distance $d \ cm$ from the plug soaked in $X$. Take $X$ and $Y$ to have equal molecular diameters and assume ideal behaviour for the inert gas and the two vapours.
$1.$ The value of $d$ in $cm$,as estimated from Graham's law,is:
$(A) \ 8 \ (B) \ 12 \ (C) \ 16 \ (D) \ 20$
$2.$ The experimental value of $d$ is found to be smaller than the estimate obtained using Graham's law. This is due to:
$(A)$ larger mean free path for $X$ as compared to that of $Y$.
$(B)$ larger mean free path for $Y$ as compared to that of $X$.
$(C)$ increased collision frequency of $Y$ with the inert gas as compared to that of $X$ with the inert gas.
$(D)$ increased collision frequency of $X$ with the inert gas as compared to that of $Y$ with the inert gas.
Give the answer for question $1$ and $2$.

Which of the following is an incorrect postulate of the kinetic molecular theory of gases?

Two gases $A$ and $B$ are released from the two ends of a tunnel of length $100 \ m$. $A$ travels $40 \ m$ before meeting the gas $B$ in the tunnel. If the molecular weight of $B$ is $18$,what is the molecular weight of $A$ (in $.5$)?

$A$ helium molecule is two times heavier than a hydrogen molecule at $298 \ K$. According to the kinetic theory,the average kinetic energy of helium at $298 \ K$ is

The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolute temperature of an ideal gas is increased $4$ times and its pressure is increased $2$ times. As a result,the diffusion coefficient of this gas increases $x$ times. The value of $x$ is