In the question below, four sentences have been given. Out of four sentences, one sentence is error-free. Find out which of the following sentence is error-free. If all the given sentences have errors, then choose option ‘None is correct’ as the answer choice.

To identify the error-free sentence, let's analyze each option step-by-step:

1. "She insisted to take the blame even though the mishap was clearly not her fault."
- Error: The verb "insisted" is incorrectly followed by an infinitive ("to take").
- Correction: The verb "insist" should be followed by the preposition "on" followed by a gerund ("insisted on taking") or by a "that" clause ("insisted that she take"). Therefore, the correct form is: "She insisted on taking the blame..." or "She insisted that she take the blame..."

2. "The committee members, many of whom has served over a decade, voiced their dissent vehemently."
- Error: There is a subject-verb agreement error. The relative pronoun "whom" refers to "committee members" (plural). Therefore, the modifying clause "many of whom" requires a plural verb.
- Correction: "has served" (singular) should be replaced with "have served" (plural). The corrected phrase is: "...many of whom have served..."

3. "Had they adhered strictly to the guidelines, the irregularities would not have occurred."
- Analysis: This sentence uses a conditional structure (inverted third conditional) correctly. "Had they adhered..." is equivalent to "If they had adhered...", which matches the past conditional result "would not have occurred". The adverb "strictly" correctly modifies the verb "adhered", and the preposition "to" is correct. This sentence is completely error-free.

4. "The number of applicants, regardless of their credentials, do not guarantee selection."
- Error: There is a subject-verb agreement error. The subject of the sentence is "The number", which is singular (unlike "A number", which is plural). The parenthetical phrase "regardless of their credentials" does not change the singular nature of the subject.
- Correction: The plural verb "do not" should be replaced with the singular verb "does not". The corrected form is: "The number of applicants... does not guarantee selection."

Thus, the third sentence is the only one that is grammatically correct.