A block is kept on a frictionless inclined surface with angle of inclination $\alpha$. The incline is given an acceleration $a$ to keep the block stationary. Then $a$ is equal to:

In the frame of the incline, a pseudo force $ma$ acts horizontally on the block.For the block to be stationary, the components of force along the incline must balance:Component of gravity down the incline $=mg\sin \alpha$.Component of pseudo force up the incline $=ma\cos \alpha$.
$$mg\sin \alpha =ma\cos \alpha$$
$$a=g\frac{\sin \alpha }{\cos \alpha }=g\tan \alpha$$