Dr. Mukhtar joined a . . . . . . . . diploma course in Chennai.

Whether to use 'year' or 'years' depends on how the sentence is phrased.
All of the following are correct:
Tom is three years old,
Tom is a three-year-old child,
It is a six-horse race,
This race is for three-year-olds,
My contract is for two years,
Mine is a two-year contract.