Grammer

In English grammar, it is essential to ensure subject-verb agreement and correct pronoun usage. Let's evaluate each sentence option:

1. Neither of the answers are correct.
   In this sentence, "neither" is a singular pronoun, so the verb should agree in number. The correct form is "Neither of the answers is correct," since "neither" implies not one and thus denotes singularity.

2. Each of the boys have their own books.
   "Each" is singular, requiring a singular verb, so "have" should be "has." Correct sentence: "Each of the boys has his own book." The pronoun "their" should also agree with "each," so it should be "his" or "his or her."

3. The jury were divided in their opinions.
   Collective nouns like "jury" can be singular or plural based on context. However, when the group acts as one unit, the singular form is used: "The jury was divided in its opinion." If used in the plural context where the individuals are acting separately, "were divided" can still be appropriate, but the pronoun should be their own opinions if the sentence context truly calls for that distinction.

4. It is I who am responsible for the mistake.
   This sentence is grammatically correct. The pronoun "I" is the predicate nominative following the verb "is," and the phrase "who am responsible" correctly uses "am" to agree with "I."

Thus, the correct and grammatically appropriate sentence is: It is I who am responsible for the mistake.