The density of a mixture of $He$ and $O_2$ gases at $27\,^{\circ}C$ and $760\, torr$ pressure is $0.543\, g\, dm^{-3}$. Calculate the percentage by mass of $He$ in the mixture.

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

The graph shows the characteristics of one mole of an ideal gas at a pressure of $1 \ atm$ with respect to volume $(V)$ and temperature $(T)$. Identify the correct graph.

Which of the following statements is incorrect?
$1$. The property of liquid drops to have minimum surface area is called surface tension.
$2$. Surface tension of liquids decreases with rise in temperature.
$3$. The $SI$ unit of surface tension is $N \ m^{-1}$.
$4$. Magnitude of surface tension is less,when there is strong attractive force between the molecules.

$A$ box of $1 \, L$ capacity is divided into two equal parts by a thin partition,which are filled with $2 \, g$ of $H_2$ and $16 \, g$ of $CH_4$ respectively. The temperature of each part is $T$. The pressure in each part is $P$. If the partition is removed,the total pressure will be:

The force $(F)$ required to maintain the flow of layers of a liquid is equal to ($A = \text{area of contact of layers}$, $dz = \text{distance between the layers}$, $du = \text{change in velocity}$, $\eta = \text{coefficient of viscosity}$)