The sentence is: “You ............. to finish this on time because you have no choice.”
This is a case where we need an auxiliary verb (helping verb) to complete the sentence grammatically and logically.
The phrase “you have no choice” indicates necessity or obligation.
The word that best expresses such compulsion is simply "have" — as in “You have to finish this on time.”
Let’s examine the options:
- (A) may have — suggests possibility in the past; does not fit the context of present obligation.
- (B) could have — indicates a missed opportunity in the past; not suitable.
- (C) have — correct, as it conveys present necessity: “You have to...”
- (D) needn’t — means “no need to,” which contradicts the meaning of “no choice.”
Hence, the correct auxiliary verb is (C) have.