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Fill in the blank with the most appropriate option-
“What is your sister doing?”
“She _____ be watching TV.”
A) may
B) can’t
C) needn’t
D) has to
E) could

Answer
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Hint: An Auxiliary or Modal Verb is one that helps other verbs to form other Tenses than the Simple Present or Simple Past. Thus, they are also known as helping verbs. Auxiliaries that help to express conceptions of the mind are called Modal Auxiliaries.

Complete answer:
A modal verb is a sort of action word that is utilized to indicate modality– that is probability, capacity, authorization, demand, limit, ideas, request, commitment, or exhortation. The person in the question has been asked about what his or her sister is doing and he or she is unsure about the answer.

Let us analyze the given options:
Option A) may: ‘May’ is used when you are unsure of what you are saying or to express a possibility, to ask permission and to express a wish. It is also used in subordinate clauses that express purpose.
In the question, the person is unsure about the answer to the question he was asked to. Thus, “May” is the correct answer.

Option B) can’t: ‘Can’t’ is used to express inability or to express that something is impossible at the present moment and to not grant permissions. So, “Can’t” cannot be used to fill the blank given in the question and thus, it is an incorrect answer.

Option C) needn’t: ‘Needn’t’ is used to express the lack of requirement of something or to convey something that was done is unnecessary. So, “Needn’t” cannot be used to fill the blank given in the question and thus, it is an incorrect answer.

Option D) has to: ‘Has to’ is used to express compulsion or general obligations. So, “Has to” cannot be used to fill the blank given in the question and thus, it is an incorrect answer.

Option E) could: ‘Could’ is used to express an ability that existed in the past, to express possibility or uncertainty or something dependent or unreal conditions and to ask polite questions. So, “Could” cannot be used to fill the blank given in the question and thus, it is an incorrect answer.

Thus the correct answer is option ‘A’.

Note: Three basic rules to follow while using Auxiliaries are:
- Use the modal or auxiliary verb as it is. Don't change its form and convert it into the present, future, or paste forms.
- Use the base or root form of the verb after a modal. Don't use “to” or the full infinitive verb “to”.
- While using modals in the negative form, use them only with “not” after the modal verb.