Two separate identical containers contain Gas $A$ $(Mw = 40 \ g \ mol^{-1})$ and gas $B$ $(Mw = x \ g \ mol^{-1})$ in the mass ratio $5 : 8$ under similar conditions of temperature and pressure. The value of $x$ is $:-$

Match the following graphs of an ideal gas with their respective axes ($X$ and $Y$).
$(A)$ $P$ vs $V$ (at constant $T$)
$(B)$ $V$ vs $T$ (at constant $P$)
$(C)$ $P$ vs $T$ (at constant $V$)
List-$I$:
$(1)$ $P$ on $Y$-axis,$T$ on $X$-axis
$(2)$ $P$ on $Y$-axis,$1/V$ on $X$-axis
$(3)$ $V$ on $Y$-axis,$T$ on $X$-axis

The pressure of an $LPG$ gas cylinder is $14.9 \ bar$,which is considered safe. If the pressure is $12 \ bar$ at $27 \ ^oC$,at what temperature will the cylinder blast (in $K$)?

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	$(E)$ $V = k_2T$

$A$ and $B$ are ideal gases. At $T(K)$,$2 \ L$ of $A$ with a pressure of $1 \ bar$ is mixed with $4 \ L$ of $B$ with a pressure $p_B \ bar$ in a $100 \ L$ flask. The pressure exerted by the gaseous mixture is $0.1 \ bar$. What is the value of $p_B$ in $bar$?

$1 \ L$ closed flask contains a mixture of $4 \ g$ of methane and $4.4 \ g$ of carbon dioxide. The pressure inside the flask at $27^{\circ} C$ is [Assume ideal behaviour of gases] (in $atm$)