Topic: Sequence of Tense,

Best Answer Explained in Below-:

The phrase "No sooner had" is used to express that one event happened immediately after another event in a way that emphasizes the quick succession of actions. In the sentence "..... we reached the exam hall than the door closed," the intended meaning is that as soon as they arrived, the door closed right after, highlighting the immediacy of the actions.

Option A, "No sooner had," is grammatically correct because it sets up the expectation of a subsequent event using an inversion structure, making it clear that the first action (reaching the exam hall) occurred with such immediacy that it was followed closely by the second action (the door closing). It suggests a causal or sequential relationship.

In contrast, options B ("As sooner as") is incorrect due to improper phrasing, and C ("As soon as") does not use the required syntax for the context. Option D ("No sooner") is incomplete without the necessary follow-up clause and is therefore not suitable. Thus, "No sooner had" is the correct choice, establishing a clear and grammatically sound relationship between the two events.