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: 'Either' means any one. Hence, the subject of the sentence is singular. If 'pants' was given after 'or', then the subject would have been plural and we would need a plural verb. As 'coat' is the subject which has to be considered, we can say that the subject is singular and hence we need a singular verb.
Option B - 'Are' is a plural verb. Hence, option B is incorrect.
Option C - 'Were' is a plural verb. Hence, option C is incorrect.
Option D - 'Been' is a verb which can't be used without an auxiliary/ helping verb. Hence, option D is incorrect.
Option A - 'Is' is a singular verb, which agrees with the singular subject of the given sentence. Hence, option A is the correct answer.
'Either my pants or your coat is in the laundry.'