$A$ cylinder of $5 \, L$ capacity,filled with air at $NTP$,is connected to another evacuated cylinder of $30 \, L$ capacity. The resultant air pressure in both the cylinders will be .............. $cm$ of $Hg$.

The gas equation $PV = nRT$ is obeyed by:

$A$ plot of volume $(V)$ of the gas versus temperature ($T$ in $K$) is shown below. Which of the following options is correct for the plot?

$A$ home owner uses $4.00 \times 10^{3} \ m^{3}$ of methane $(CH_{4})$ gas (assume $CH_{4}$ is an ideal gas) in a year to heat his home. Under the pressure of $1.0 \ atm$ and $300 \ K$,the mass of gas used is $X \times 10^{5} \ g$. The value of $X$ is $.......$ (Nearest integer).
(Given $R = 0.083 \ L \ atm \ K^{-1} \ mol^{-1}$)

At $25 \, ^\circ C$ temperature and $760 \, mm \, Hg$ pressure,the volume of a gas is $600 \, mL$. Calculate the pressure when the volume of this gas becomes $640 \, mL$ at $10 \, ^\circ C$ temperature. Use the ideal gas equation: $\frac{p_1 V_1}{T_1} = \frac{p_2 V_2}{T_2}$

Which amongst the given plots is the correct plot for pressure $(p)$ $vs$ density $(d)$ for an ideal gas?