Pressure-temperature graph of the ideal gas at constant volume $V$ is shown by a straight line $A.$ Now, pressure $P$ of the gas is doubled and the volume is halved; then the corresponding pressure temperature graph will be shown by the line

Two balloons are filled; one with pure $\mathrm{He}$ gas and the other with air, respectively. If the pressure and temperature of these balloons are the same, then the number of molecules per unit volume is

The density $\left(\rho \right)$ versus pressure $\left(P\right)$ graphs of a given mass of an ideal gas is shown at two temperatures $T_1$ and $T_2.$ Then relation between $T_1$ and $T_2$ may be

The given curve represents the variations of temperature as a function of volume for one mole of an ideal gas. Which of the following curves best represent the variation of pressure as a function of volume?