Explanation:

 The Vijayanagara Empire was based in the Deccan Plateau region in South India. The empire is named after its capital city of Vijayanagara, whose ruins surround present day Hampi, now a World Heritage Site in Karnataka, India. It was established in 1336 by Harihara I and his brother Bukka Raya I  The Vijayanagara Empire was based in the Deccan Plateau region in South India. The empire is named after its capital city of Vijayanagara, whose ruins surround present day Hampi, now a World Heritage Site in Karnataka, India. It was established in 1336 by Harihara I and his brother Bukka Raya I of Sangama Dynasty.

•  The first dynasty, the Sangama, lasted until about 1485, when at a time of pressure from the Bahmani sultan and the raja of Orissa, Narasimha of the Saluva dynasty usurped power.
•  By 1503 the Saluva dynasty had been supplanted by the Tuluva dynasty. The outstanding Tuluva king was Krishna Deva Raya. During his reign (1509–29) the land between the Tungabhadra and Krishna rivers (the Raichur doab) was acquired (1512), the Orissa Hindus were subdued by the capture of Udayagiri (1514) and other towns, and severe defeats were inflicted on the Bijapur sultan(1520).
• Krishna Deva’s successors, however, allowed their enemies to unite against them. In 1565 Rama Raya, the chief minister of Vijayanagar, led the empire into the fatal battle at Talikota, in which its army was routed by the combined forces of the Muslim states of Bijapur, Ahmadnagar, and Golconda and the city of Vijayanagar was destroyed.
• Tirumala, brother of Rama Raya, then seized control of the empire and founded the Aravidu dynasty, which established a new capital at Penukonda and kept the empire intact for a time.
• ?Hence, option (a) is the correct answer..