The correct option is
B Is
In order to fill in the blank with the correct auxiliary verb, let's understand what auxiliary verbs are. Auxiliary verbs are used to form tenses, moods and forms of other verbs. For example - I am a woman. Here, 'am' is an auxiliary verb as it indicates that the sentence is in simple present tense.
Option A - 'Are' is the plural form of the auxiliary verb used with a plural subject. As the subject in the given question is singular, we can't use 'are'. Hence, optipn A is incorrect.
Option C - 'Do' is the plural form of the auxiliary verb used with a plural subject. As the verb in the given question is singular, we can't use 'do' here. Hence, option C is incorrect.
Option D - 'Does' is the singular form of the auxiliary verb, but it indicates the 'doing' actions and not the state of being. The given question requires an auxiliary verb that explains the subject's state of being. Hence, option D is incorrect.
Option B - 'Is' is the singular form of the auxiliary verb used with a singular subject. It indicates the subject's state of being. Hence, we can use 'is' here. Thus option B is the correct answer.
'Is he a university professor?'