The correct option is C
'While' can function as various parts of speech (noun, conjunction, adverb, etc.). The nature of the word can be found out through its position in the sentence.
Options B and D: The given sentence ends with the word 'while'. A preposition usually precedes a noun and connects it with the rest of the sentence. Since this sentence ends with 'while', the word cannot be a preposition. Hence D is not the right option.
Similarly, adjectives also come before nouns that they modify. Since this word comes last, and also it does not modify any other word, option B is wrong.
Option C: Adverbs modify verbs, adjectives and other adverbs. The word 'while' does not modify any of these parts of speech. Hence C is incorrect.
Option A: 'While' refers to a 'period of time' in the given sentence. It functions as a noun as it names a 'period of time'. Nouns name things, here it names a certain amount of time. Hence option A is correct.