We use the preposition "in" to refer to a point of time when something occurred, especially with years. Example: "He graduated in 1990."
Therefore, "He passed the undergraduate degree course in the year 1983" is the grammatically correct choice.
Why other options are incorrect:
- "of" indicates possession or belonging, not time.
- "since" indicates a time from which something has continued, and doesn't fit in this sentence.
- "at" is used for specific times or places, not years.