The correct answer is: A. Slave
The name Bihar was given to this place in the reign of the Slave dynasty. The Slave dynasty was a Muslim dynasty that ruled over the Indian subcontinent from 1206 to 1290. The dynasty was founded by Qutb-ud-din Aibak, a former slave of Muhammad Ghori. Qutb-ud-din Aibak conquered Delhi in 1206 and established the Slave dynasty. The dynasty reached its peak under the reign of Iltutmish, who ruled from 1211 to 1236. Iltutmish expanded the empire and consolidated his rule. He also built many mosques and other buildings in Delhi. The Slave dynasty declined after the death of Iltutmish. The last ruler of the dynasty, Muiz-ud-din Bahram Shah, was defeated by the Khalji dynasty in 1290.
The other options are incorrect. The Khilji dynasty ruled over the Indian subcontinent from 1290 to 1320. The Tughlaq dynasty ruled over the Indian subcontinent from 1320 to 1414. The Noohani dynasty was a short-lived dynasty that ruled over parts of Bihar in the 16th century.