When we sit on a chair and study for 2-3 hours, we are not doing work from a physicists point of view. Why?

In the context of physics, work is defined to be the movement of an object when you apply a (pushing or pulling) force.

If you lifted a box to move it upward, then you are doing work. If you slide that box along the floor, then you are also doing work. However, if you try to lift something very heavy, but cannot move it at all, then 0 work is being applied. This is because the object hasn't moved. You need displacement to have work happen.

So that's why a physicist would not consider studying doing "work" (in the context of physics), though I'm sure they would be able to agree that studying does exercise the mind.