✅ In option C, "She greeted Professor Davies at the conference," "Professor Davies" is a proper noun because it is a specific person's title and name. The verb "greeted" is a transitive verb, and "Professor Davies" directly receives the action of being greeted, thereby functioning as the direct object of the verb.

❌ In option A, "Mathematics" is a proper noun (the name of a specific subject), but it functions as a subject complement. It follows the linking verb "is" and renames the subject "subject," rather than receiving the action of a verb.

❌ In option B, "blocks" is a common noun, not a proper noun. Additionally, it is the object of the preposition "with," not the direct object of a verb.

❌ In option D, "Australia" is a proper noun, but it functions as the subject of the sentence. It performs the action (or is the topic) of the sentence, rather than receiving the action of a verb as a direct object would.

✅ In option B, the clause "what he meant" functions as the direct object of the verb "wondered," answering the question "wondered what?".

❌ In option A, the clause "Whoever arrives first" functions as the subject of the sentence, performing the action of "will receive."

❌ In option C, "that they had no money" functions as a subject complement (predicate nominative), following the linking verb "was" and renaming or describing the subject "problem."

❌ In option D, "that you came" acts as an adverbial clause of reason or an adjectival complement modifying the adjective "glad," explaining why the speaker is glad, rather than a noun clause functioning as a direct object.

✅ "The diligent students" is the correct answer because it is the complete noun phrase that performs the action in the sentence, acting as the subject. It includes the head noun "students" and all its modifiers: the determiner "The" and the adjective "diligent."

❌ "students" is only the head noun of the phrase, not the complete noun phrase itself. A noun phrase includes all words that modify the noun.

❌ "completed their challenging assignment" is the predicate of the sentence, which includes the verb and the object, describing what the students did.

❌ "their challenging assignment" is also a noun phrase, but it functions as the direct object of the verb "completed," not the subject of the sentence.

✅ The phrase "a talented artist" is a noun phrase that renames or clarifies "My younger sister," placed directly beside it and set off by commas, thus functioning as an appositive.

❌ Option A is incorrect because "My younger sister" is the subject of the sentence, performing the action of painting.

❌ Option C is incorrect because "this beautiful portrait" is the direct object, receiving the action of the verb "painted."

❌ Option D is incorrect because "last month" is a noun phrase functioning as an adverbial phrase of time, indicating when the painting occurred, not as a direct object.

✅ The word "clock" is the central noun in the noun phrase "the antique clock" because "antique" is an adjective modifying "clock," and "the" is a determiner. It is the core element of that specific phrase.

❌ "Intricate" is an adjective modifying "design," which is part of a different noun phrase ("The intricate design").

❌ "Design" is the head noun of the initial noun phrase "The intricate design," not the one specified in the question ("the antique clock").

❌ "Visitors" is the direct object of the verb "captivated," representing a different noun within the sentence, not the head noun of "the antique clock."