There's a door at either end of the building?
The correct answer is A. The building has two ends and two doors
Either as used before the first of two given alternatives. When it is used as a determiner, it refers to both choices or possibilities
This means that there are two alternatives. At each end of the building, there is a door.
Either is used only when there are two persons or things. The statement can be interpreted as
''There are two ends in the building, and each of the ends has a door.
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