A suction cup is attached a smooth metal ceiling. The maximum weight that can be supported by the suction cup is dependent on

(A) its area of contact with the ceiling.

(B) the air pressure outside the cup.

(C) both (A) and (B).

(D) neither (A) nor (B).

The correct option is (C) both (A) and (B).
When a suction cup is attached a smooth metal ceiling, it is supported by the pressure exerted by its surface on the surface of the ceiling.
The pressure exerted is due to the difference between the pressure inside the suction cup and the air pressure outside the cup. As long as this net pressure is maintained, the suction cup can support any weight attached to it. The net pressure is depending on the area of contact with the ceiling as pressure is the normal force acting per unit area.
Thus, the maximum weight depends on the area of contact with suction cup with the ceiling and the air pressure outside the cup.
Therefore, both the options (A) and (B) are correct.