$A$ rough inclined plane is placed on a car moving with a constant velocity $u$ on horizontal ground. $A$ block of mass $M$ rests on the inclined plane. Is any work done by the force of friction between the block and the inclined plane? Is there any dissipation of energy?

(N/A) Yes,there is a static friction force $f$ acting on the block.
Since the block is at rest relative to the inclined plane,the force of friction is given by $f = Mg \sin \theta$.
Work done by a force is defined as $W = \vec{F} \cdot \vec{d}$. Since the block is not in motion relative to the inclined plane (displacement $d = 0$),the work done by the friction force is zero.
Because the work done is zero and there is no relative motion between the surfaces,there is no dissipation of energy.