The density of a gas at $27\,^oC$ and $1\, atm$ is $d$. At constant pressure,at which of the following temperatures will its density become $0.75\, d$?

Three flasks of equal volumes contain $CH_4$,$CO_2$,and $Cl_2$ gases respectively. They will contain equal number of molecules if

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 correct value of the gas constant $R$ is close to

An ideal gas weighing $9.0 \ g$ occupies a volume of $8.2 \ L$ at $300 \ K$ and $1 \ atm$ pressure. The molar mass of the gas is .....

An $LPG$ (Liquefied Petroleum Gas) cylinder weighs $15.0 \ kg$ when empty. When full, it weighs $30.0 \ kg$ and shows a pressure of $3.0 \ atm$. In the course of usage at $27^{\circ}C$, the mass of the full cylinder is reduced to $24.2 \ kg$. The volume of the used gas in cubic metre at the normal usage condition ($1 \ atm$ and $27^{\circ}C$) is (assume $LPG$ to be normal butane and it behaves ideally). (in $m^3$)