Final answer:
The correct term for a Buddhist monastery in Indian architecture, often carved from rock with a central chamber and surrounding cells is A) Vihara.
Step-by-step explanation:
The term that best describes a Buddhist monastery in Indian architecture, often excavated from solid rock, consisting of a central pillared chamber surrounded by a verandah onto which open small sleeping cells, is A) Vihara. This type of monastery can be found as part of the ancient Buddhist tradition, and such structures were pivotal in the development of Buddhist religious architecture. The structure typically includes residential cells for monks and may also have been used for educational purposes.
During the Gupta period, such architectural designs were prevalent, combining architecture, sculpture, and paintings, such as those found at the famous Buddhist monastery, Nalanda University. The period also saw the construction of imposing structures like the Mahabodhi Temple, which played an important role in showcasing Indian Buddhism's architectural grandeur, heights of artistry, and symbolisms of enlightenment.