Topic: Conjunction,

Best Answer Explained in Below-:

In the sentence "By the end of the day we were tired but happy," the word "but" functions as a conjunction. Conjunctions are words that connect clauses, sentences, or words within the same clause. In this case, "but" is used to link two contrasting adjectives: "tired" and "happy."

The use of "but" indicates a contrast between these two states. While being "tired" suggests fatigue and a sense of weariness, being "happy" conveys a sense of joy and contentment. The conjunction effectively combines these opposing ideas, highlighting that despite their tiredness, the subjects still experienced happiness.

In contrast, let's briefly consider the other options:

- A preposition (Option A) usually indicates relationships of direction, location, or time, as in "in," "on," or "at."
- An adjective (Option B) describes a noun, giving us more information about it, such as "blue" or "happy."
- An adverb (Option D) modifies a verb, an adjective, or another adverb, often denoting manner, degree, or frequency.

Thus, the clear role of "but" in conveying contrast establishes it firmly as a conjunction, making option C the correct answer.