The correct answer is D. Narsimha : Chalukya.
The Sangama dynasty ruled the Vijayanagara Empire from 1336 to 1485. The Tuluva dynasty ruled the Vijayanagara Empire from 1485 to 1505. The Aravidu dynasty ruled the Vijayanagara Empire from 1505 to 1565. The Chalukya dynasty ruled the Deccan region of India from the 6th to the 12th centuries.
Narsimha was a ruler of the Sangama dynasty. He was the son of Bukka Raya I and the grandson of Harihara Raya I. He ruled from 1491 to 1505. He was a successful military commander and expanded the Vijayanagara Empire. He was also a patron of the arts and literature.
The Chalukya dynasty was a different dynasty that ruled the Deccan region of India from the 6th to the 12th centuries. They were not related to the Sangama dynasty.