If the density of gas $A$ is $1.5$ times that of gas $B$,and the molecular mass of $A$ is $M$,then the molecular mass of $B$ is:

Match the laws given in List-$I$ with their mathematical forms given in List-$II$.

List-$I$	List-$II$
$(1)$ Boyle's Law	$(A)$ $p \propto T$
$(2)$ Charles's Law	$(B)$ $V \propto n$
$(3)$ Gay-Lussac's Law	$(C)$ $p \propto \frac{1}{V}$
$(4)$ Avogadro's Law	$(D)$ $pV = nRT$
$(5)$ Ideal Gas Equation	$(E)$ $V = k_2T$

An open vessel containing air was heated from $27^{\circ} C$ to $727^{\circ} C$. Some air was expelled. What is the fraction of air remaining in the vessel? (Assume air as an ideal gas)

At very low pressure,the compressibility factor $Z$ of a $CO_2$ gas with constant molar volume is:

What is the volume of $n$ moles of gas? Derive the formula for the combined gas law.

An ideal gas expands isothermally and reversibly from $10 \ m^{3}$ to $20 \ m^{3}$ at $300 \ K$ performing $5.187 \ kJ$ of work on surroundings. Calculate the number of moles of gas undergoing expansion? $(R = 8.314 \ J \ K^{-1} \ mol^{-1})$