At the equivalence point of a titration of acid-base reactions, the pH?

The answer: a. changes rapidly

Suppose an alkali (a base) is placed in the conical flask and an acid is placed in the burette to run the titration. When one small drop of titer before the equivalence point, the reaction mixture is still alkaline (basic). At equivalence point, the reaction mixture becomes neutral. When one small drop of titer is added, the reaction mixture becomes acidic. The change of alkaline to neutral and then to acidic is very sharp when a very small amount of titer is added. Hence, the pH changes rapidly.

On the other hand, if an acid is placed in the conical flask and an alkali is placed in the burette instead, the change of acid to neutral and then to alkali is also very sharp and thus the pH also changes rapidly.

a. changes rapidly

This is because there is no longer any of the other reactant in the solution so none of the added acid or base is consumed, causing a rapid change in the pH of the solution.