$A$ gas at $27^oC$ has a volume $V$ and pressure $P$. On heating,its pressure is doubled and volume becomes three times. The resulting temperature of the gas will be ...... $^oC$.

For container $A$,the pressure is $P$,volume is $V$,and temperature is $T$. For container $B$,the pressure is $2P$,volume is $V/4$,and temperature is $2T$. Find the ratio of the number of molecules in container $A$ to that in container $B$.

For an ideal gas at constant pressure,if the volume is $V$ at a temperature of $27^{\circ}C$,what will be its final volume when the temperature is increased to $327^{\circ}C$?

One mole of an ideal gas undergoes a process in which pressure $P$ varies with volume $V$ as $P = 3 - g \left(\frac{V}{V_0}\right)^2$,where $V_0$ and $g$ are constants. The maximum temperature attainable by the ideal gas during this process is ($All$ quantities are in $SI$ units and $R$ is the gas constant).

Column-$I$ represents a graph and Column-$II$ represents a physical quantity or condition that is constant for that graph. Match them correctly:

Column-$I$	Column-$II$
$(a)$ Top graph	$(i)$ Constant pressure
$(b)$ Bottom graph	$(ii)$ Constant volume
	$(iii)$ For ideal gas

Which of the following graphs correctly represents the variation of $\beta = - \left( \frac{dV}{dP} \right)/V$ with $P$ for an ideal gas at constant temperature?