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What was the problem? Why _______ leave early?
 a. Have you to
b. Did you have to
c. Must you
d. You had to

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Answer
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Hint: The student should go through the options carefully after reading the sentence to understand what the sentence implies. Then the student must recall the structure of sentences. This will help the student in finding the right answer for the given question.

Complete step by step answer:
An auxiliary verb is a verb that combines with another verb in a verb phrase to help form tense, mood, voice, or condition of the verb it combines with.
Let us thus analyze the options given to us in this question -
Option (a.), 'have you to', refers to ‘present tense’.
Therefore, option (a.) is incorrect as the usage of ‘was’ in the first sentence indicates that past tense should be used here.
Option (b.), ‘did you have to', refers to ‘past tense’.
Therefore, option (b.) is correct as we need past tense here since the usage of ‘was’ in the first sentence indicates that past tense should be used.
Option (c.), ‘must you', refers to the modal ‘must’ in the present tense which indicates a requirement or compulsion.
Therefore, option (c.) is incorrect as the usage of ‘was’ in the first sentence indicates that past tense should be used here.
Option (d.), ‘you had to', refers to ‘you’ before ‘had’.
Therefore, option (d.) is incorrect as this structure is incorrect in a question sentence since the subject does not come before the auxiliary.

Note:
 In this question, it will be helpful for the student to recall the concept of verbs. A verb is a content word that denotes an action, occurrence, or state of existence. A verb is the word class that serves as the predicate of a sentence.