JEE Main · 2019 · 09 Apr 2019 · Shift 1 · Chemical Thermodynamics

A path function depends on how a change is carried out, not just on its endpoints, and heat $q$ and work $w$ are both like this. But their sum $q+w$ equals $\Delta U$, the internal energy change, which is a state function, and $H-TS$ is the Gibbs energy $G$, again a state function. So the only path functions among these are $q$ and $w$.