Which of the following shows the correct relationship between the pressure $P$ and density $\rho$ of an ideal gas at constant temperature?

The temperature of a gas at pressure $P$ and volume $V$ is $27^{\circ}C$. Keeping its volume constant,if its temperature is raised to $927^{\circ}C$,then its pressure will be (in $P$)

$A$ monoatomic ideal gas of two moles is taken through a cyclic process starting from $1$ as shown. Given $\frac{V_2}{V_1} = 2$ and $\frac{V_4}{V_1} = 4$. The temperature at state $1$ is $T_1 = 27\,^oC$. Find the temperature at state $2$,i.e.,$T_2$ in $K$.

$A$ closed vessel contains $8\,g$ of oxygen and $7\,g$ of nitrogen. The total pressure is $10\,atm$ at the given temperature. If all the oxygen is removed from the system without permitting any change in temperature,then the pressure will become (in atmosphere):

$2 \, g$ of ${O_2}$ gas is taken at $27^{\circ}C$ and a pressure of $76 \, cm$ of $Hg$. Find the volume of the gas (in liters).

$A$ narrow glass tube,$80 \,cm$ long and open at both ends,is half-immersed in mercury. Now,the top of the tube is closed and it is taken out of the mercury. $A$ column of mercury $20 \,cm$ long remains in the tube. Find the atmospheric pressure.