When air is filled in a balloon, both the pressure and volume increase while the temperature remains constant. Why is Boyle's law not obeyed in this case?

An open glass tube is immersed in mercury such that a length of $8 \ cm$ extends above the mercury level. The open end of the tube is then closed and sealed,and the tube is raised vertically by an additional $46 \ cm$. What will be the length of the air column above the mercury in the tube now? (Atmospheric pressure = $76 \ cm$ of $Hg$)

The $P-T$ graph shows a gas being heated. During this process from point $1$ to $2$,the volume of the gas:

An oxygen cylinder of volume $30 \; L$ has an initial gauge pressure of $15 \; atm$ and a temperature of $27 \; ^{\circ}C$. After some oxygen is withdrawn from the cylinder,the gauge pressure drops to $11 \; atm$ and its temperature drops to $17 \; ^{\circ}C$. Estimate the mass (in $kg$) of oxygen taken out of the cylinder ($R = 8.31 \; J \; mol^{-1} K^{-1}$,molecular mass of $O_{2} = 32 \; u$).

If the pressure of an ideal gas contained in a closed vessel is increased by $0.5\%,$ the increase in temperature is $2 \, K.$ The initial temperature of the gas is ...... $^\circ C$

$A$ box contains $n$ molecules of a gas. How will the pressure of the gas be affected if the number of molecules is made $2n$?