$A$ $10 \ g$ mixture of hydrogen and helium is contained in a vessel of capacity $0.0125 \ m^{3}$ at $6 \ bar$ and $27^{\circ}C$. The mass of helium in the mixture is $g$. (nearest integer) Given : $R = 8.3 \ J \ K^{-1} \ mol^{-1}$ (Atomic masses of $H$ and $He$ are $1 \ u$ and $4 \ u$,respectively)

The pressure exerted by a mixture of $3.2 \ g$ of methane $(CH_4)$ and $4.4 \ g$ of $CO_2$ contained in a $9 \ dm^3$ flask at $27^{\circ}C$ is: (in $atm$)

$A$ fixed mass '$m$' of a gas is subjected to a transformation of states from $K$ to $L$ to $M$ to $N$ and back to $K$ as shown in the figure.
$1.$ The succeeding operations that enable this transformation of states are:
$(A)$ Heating,cooling,heating,cooling
$(B)$ Cooling,heating,cooling,heating
$(C)$ Heating,cooling,cooling,heating
$(D)$ Cooling,heating,heating,cooling
$2.$ The pair of isochoric processes among the transformation of states is:
$(A)$ $K$ to $L$ and $L$ to $M$
$(B)$ $L$ to $M$ and $N$ to $K$
$(C)$ $L$ to $M$ and $M$ to $N$
$(D)$ $M$ to $N$ and $N$ to $K$
Give the answer for question $1$ and $2$.

Equal volumes of two monoatomic gases,$A$ and $B$ at same temperature and pressure are mixed. The ratio of specific heats $(C_P/C_V)$ of the mixture will be

Densities of two gases are in the ratio $1:2$ and their temperatures are in the ratio $2:1$,then the ratio of their respective pressures is

Which of the following is a superfluid?