The correct option is
A is
In order to fill in the blank with the most appropriate verb, we must understand the 'subject and verb agreement'. A subject is a person, thing, or a concept, in a sentence. A sentence always describes a person, thing or a concept and that is called 'subject' of the sentence. The rest of the sentence is a complement (which has the object in it). A subject and a verb should always agree in a sentence. If the subject is singular (example: Raj), the verb will also be singular (does). If the subject is plural (We), the verb will also be plural (do).NOTE: In order to choose the best verb, let's find the subject first. The question mainly asks about the book's state. Hence, 'the fat book' is the subject. As the subject is singular, the verb should be singular too.
Option B - 'Are' is a plural verb and hence, it can't be used here. Thus option B is incorrect.
Option C - 'Has' is used to explain possession or perfect/perfect continuous tenses. As we see, the sentence asks about the state of the book, we can't use 'has' (as the question is neither in the perfect tense nor asks about possession). Hence, option C is incorrect.
Option D - 'Does' is used to explain the state of 'doing' something (and not the state of 'being'). Though 'does' is in the singular form of the verb, we can't use it here. Hence, option D is incorrect.
Option A - 'Is' is a be verb and it explains the state of being of an object or a person in simple present tense. As the sentence is a general sentence, we will use simple present tense here. Hence, option A is the correct answer.
'Is the fat book in the drawer?'