The correct answer is (a). The Bahmani Sultanate emerged as a powerful kingdom in the Deccan in the 14th century. It had frequent conflicts with the Vijayanagara Empire, which was another powerful kingdom in the Deccan. The two kingdoms fought over control of territory and resources. The Bahmani Sultanate was eventually defeated by the Vijayanagara Empire in the 16th century.
The Gajapatis were a Hindu dynasty that ruled over the eastern Deccan in the 14th and 15th centuries. They were not as powerful as the Bahmani Sultanate or the Vijayanagara Empire, and they did not have frequent conflicts with either kingdom.
The Delhi Sultanate was a Muslim dynasty that ruled over northern India from the 12th to the 16th centuries. It had frequent conflicts with the Bahmani Sultanate, but it did not have frequent conflicts with the Vijayanagara Empire.
The Cholas were a Hindu dynasty that ruled over southern India from the 9th to the 13th centuries. They were a powerful kingdom, but they did not have frequent conflicts with the Bahmani Sultanate.