The correct answer is option 3: a republican tribe. The Yaudheyas were an ancient republic tribe in India. Republics were a common form of government in ancient India, where power was shared among the people rather than being held by a single ruler. The Yaudheyas were known for their warrior skills and were involved in various conflicts and battles with other tribes and kingdoms.

Option 1, a sect of Buddhism, is incorrect. The Yaudheyas were not associated with Buddhism.

Option 2, a sect of Jainism, is also incorrect. The Yaudheyas were not a sect of Jainism either.

Option 4, vassals of the Cholas, is incorrect. The Cholas were a dynasty in South India, but the Yaudheyas were not their vassals or subjects. They were an independent tribe that had their own territory and governance.

To summarize, the Yaudheyas were an ancient republican tribe in India known for their warrior skills. They were not associated with Buddhism, Jainism, or the Cholas.