The underlined word in the given sentence is :
"Notwithstanding the late hour, she attended the meeting as scheduled".

The correct answer is Option C (Preposition).

Key Points:
• Core Language Concept Tested: The question primarily tests the candidate's understanding of Parts of Speech in English grammar. Being able to identify the grammatical function of a word based on its context is a crucial area in competitive exams.
• Why the Correct Option is Right: The official answer key marks option 3 as correct. In this sentence, the word "Notwithstanding" functions as a Preposition. It is followed by a noun phrase ("the late hour") which acts as its object. In this context, it means 'in spite of' or 'despite'. When a word introduces a noun phrase and shows its relationship to the rest of the sentence, it is acting prepositionally.
• Common Exam Traps and Pitfalls: MPSC often uses large, complex-looking words that candidates rarely use in daily speech. A common mistake is assuming it's an adverb or conjunction because of its length and '-ing' ending, which is a flawed approach.
• Elimination of Incorrect Options: Looking at the other choices, it is clearly not a definite article (which is 'the'). It is not an auxiliary verb (like is, am, are, have). It is not an adverb modifying a verb here; it takes an object. Thus, by systematic elimination, we arrive safely at 'Preposition'.
• Preparation Strategy: For future exams, aspirants should review lists of compound and participle prepositions (like considering, regarding, notwithstanding) and understand their usage.
• Key Takeaway: Remember: 'Notwithstanding' acts as a preposition when it is followed by a noun phrase, meaning 'in spite of'.