A book falls of the table and hits the floor. Is work done? Why?

Yes, work is done when a book falls of the table.

This is because:

When the book falls, it's potential energy is converted into kinetic energy.   As it reaches the floor down, this kinetic energy is converted to heat energy and sound energy due to the impact.

When a force is imposed on an object to cause displacement of that object, work is done on that object. For a force to do work on an object, there should be a displacement and this force should cause the displacement. So here, since the book falls from the table and causes the displacement of the book from the table to the floor. It is said that work is done.

Work can be given by the formula:

W = F • d

where F is the force and d is the displacement.