The correct answer is A) Hampi.
Hampi was the capital of the Vijayanagara Empire, a major power in South India from the 14th to the 16th centuries. The city was located on the banks of the Tungabhadra River in present-day Karnataka state. Hampi is a UNESCO World Heritage Site and is known for its ruins of temples, palaces, and other monuments.
The Vijayanagara Empire was founded in 1336 by Harihara I and Bukka Raya I, two brothers who were feudatories of the Hoysala Empire. The empire reached its peak under the reign of Krishnadevaraya (1509-1529), who expanded its territory and made it a major center of trade and culture. The empire declined in the 16th century due to a number of factors, including internal conflicts and the invasion of the Deccan sultanates.
Hampi was abandoned in the 16th century after the fall of the Vijayanagara Empire. The city was rediscovered in the 18th century by European travelers, and it has been a popular tourist destination since the 19th century.
Hampi is a UNESCO World Heritage Site because of its well-preserved ruins of temples, palaces, and other monuments. The city is a major center of Hindu pilgrimage, and it is also a popular destination for tourists interested in Indian history and culture.
The other options are incorrect because they are not the capital of the Vijayanagara Empire. Mysore was the capital of the Mysore Kingdom, which was a rival of the Vijayanagara Empire. Srirangapatana was the capital of the Nayak of Madurai, which was another rival of the Vijayanagara Empire. Madurai was the capital of the Madurai Nayak Kingdom.