If $P$,$V$,$M$,$T$ and $R$ are pressure,volume,molar mass,temperature and gas constant respectively,then for an ideal gas,the density is given by

Containers $A$ and $B$ contain the same gas. If the pressure,volume,and temperature of container $A$ are all twice those of container $B$,what is the ratio of the number of molecules in $A$ to those in $B$?

$A$ box contains $0.90 \ g$ of liquid water in equilibrium with water vapour at $27^{\circ} C$. The equilibrium vapour pressure of water at $27^{\circ} C$ is $32.0 \ Torr$. When the volume of the box is increased,some of the liquid water evaporates to maintain the equilibrium pressure. If all the liquid water evaporates,then the volume of the box must be $.... \ litre$. [nearest integer]
(Given $R = 0.082 \ L \ atm \ K^{-1} \ mol^{-1}$)
(Ignore the volume of the liquid water and assume water vapours behave as an ideal gas.)

From the following plots,find the correct option.

An ideal gas undergoes a cyclic transformation starting from the point $A$ and coming back to the same point by tracing the path $A$ $\rightarrow B$ $\rightarrow C$ $\rightarrow A$ as shown in the diagram. The total work done in the process is . . . . . . $J$.

$A$ mass of gas occupies $11.2 \ dm^3$ at $105 \ kPa$. What is its volume if the pressure is increased to $210 \ kPa$ at constant temperature (in $dm^3$)?