Answer:
(d) One of my cousins is a doctor
Step-by-step explanation:
A plural word like “cousins” comes after “one of” to show that we choose a single thing from a group that has more than one thing in it.
The word “one” is the main subject of the sentence and it is singular, so the word “is” matches it.
The word “cousins” is part of the phrase after “of” and it is plural, but it does not affect the verb. The verb should be the same as the subject, not the object.