The Vijayanagara Empire was established by:

Harihara and Bukka Raya
Krishna Deva Raya
Deva Raya II
Saluva Narasimha Raya

The correct answer is: a) Harihara and Bukka Raya.

Harihara and Bukka Raya were brothers who founded the Vijayanagara Empire in 1336. They were members of the Sangama dynasty, which ruled the empire until 1565. The Vijayanagara Empire was one of the largest and most powerful empires in Indian history. It was a major center of Hindu culture and learning.

Option b) Krishna Deva Raya was a ruler of the Vijayanagara Empire from 1509 to 1529. He was a great military leader and expanded the empire to its greatest extent. He was also a patron of the arts and literature.

Option c) Deva Raya II was a ruler of the Vijayanagara Empire from 1424 to 1446. He was a successful military leader and expanded the empire. He was also a patron of the arts and literature.

Option d) Saluva Narasimha Raya was a ruler of the Vijayanagara Empire from 1542 to 1543. He was a member of the Saluva dynasty, which ruled the empire for a brief period. He was a successful military leader and expanded the empire.