Find the ratio of the density of air at the top of a mountain to the density of air at the bottom of the mountain,given the conditions shown in the image.

When air is pumped into a cycle tyre, the volume and pressure of the air in the tyre both increase. What about Boyle's law in this case?

An insulated container is divided into two parts by a partition. The same gas is filled in both parts. In the right part,the volume,temperature,and pressure are $2V$,$T$,and $2P$ respectively. In the left part,the same parameters are $V$,$T$,and $P$. What is the ratio of the number of molecules in the right part to the left part?

In the relation $n = \frac{PV}{RT}$,what does $n$ represent?

Air is filled in a bottle at atmospheric pressure and it is corked at $35^{\circ}C$. If the cork can come out at $3$ atmospheric pressure,then up to what temperature should the bottle be heated in order to remove the cork? (in $^{\circ}C$)

At a pressure $P$ and temperature $T$, $7 \text{ g}$ of oxygen occupies a volume $V$. The equation of state will be (Molecular weight of Oxygen = $32$).