Rotational mechanics

Options A and B can be eliminated immediately: if there is friction, there can be rolling.

Option D ( a smooth flat plane) can be eliminated, even though there is no friction. This is because as long as the ball is moving with the "correct" translational speed and the "correct" angular velocity, there will be no sliding between the sphere and the plane surface.

Option C is the only one left, but here is (specifically) why a ball can't roll on a smooth inclined surface: it's accelerating. The normal force must point perpendicular to the plane, so it cannot be cancelled out by gravity. Therefore there will be a net force on the sphere, and it will accelerate. Therefore it cannot have the "correct" translation and angular speed for more than instant, and then sliding will occur.

Rolling possible only if there is friction. On a plane surface, there is no force acting so no accelerated motion. It is on an inclined surface there is gravity to cause accelerated motion. But if the surface is smooth, there will be no rolling.

When a sphere is in smooth plane no frictional force works only transitional motion takes place instead of rolling motion i.e it slips.