The correct answer is: C. three years
The apostrophe is used to show possession. In this case, the diploma course does not belong to Dr. Mukhtar, so the apostrophe is not needed.
The word “years” is plural, so it takes a plural verb. In this case, the verb is “joined,” which is a regular verb that forms its past tense by adding -ed.
The word “three” is an adjective, so it comes before the noun it modifies. In this case, the noun is “years,” so the adjective “three” comes before it.
Therefore, the correct sentence is: “Dr. Mukhtar joined a three-year diploma course in Chennai.”