This is the … he has submitted his assignment since joining the class.

Analyze the question

The sentence is: "This is the __ he has submitted his assignment since joining the class." The blank comes after "the" and before a clause ("he has submitted..."). So we need a word that works after "the" and describes how early the submission is compared with all the others.

Explain the concept

The definite article "the" is followed by a superlative when we compare one occasion with all the others: the best, the most, the earliest. The pattern is:

This is the + superlative + (that) + subject + present perfect...

Examples: "This is the fastest he has ever run." "This is the latest she has come to school."

Check each option

• A. early is a base adjective/adverb. "The early he has submitted" is ungrammatical, because "the" needs a superlative here.
• B. later is a comparative. "The later he has submitted" does not fit, since there is no "the... the..." comparison structure.
• C. earliest is a superlative. "This is the earliest he has submitted his assignment since joining the class" is correct. It means that out of all the times since joining, this is the earliest.
• D. lately is an adverb meaning "recently". It cannot follow "the" in this way.

Answer

The correct option is C. earliest.

Tip: When you see "the ___ (that) he has ever/since...", think superlative. Words like since joining, ever, and so far often signal a comparison against all previous occasions. Also remember that "the" followed by a gap before a clause usually means a superlative is needed.