The correct answer is: b) Vijayanagara Empire.
The Vijayanagara Empire was a Hindu empire that ruled over southern India from the 14th to the 16th centuries. It was founded 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, who expanded its territory to include much of southern India. The Vijayanagara Empire declined in the 16th century due to a number of factors, including internal conflicts, the rise of the Muslim Deccan sultanates, and the Portuguese invasion of Goa.
Sivagangai was a princely state that emerged after the decline of the Vijayanagara Empire. It was founded by Muthu Vaduganatha Nayak, a Nayak of Madurai. The state was ruled by the Nayak dynasty until it was annexed by the British in 1801.
The other options are incorrect because:
- The Madurai Nayaks were a dynasty that ruled over the Madurai region of southern India from the 16th to the 18th centuries. They were feudatories of the Vijayanagara Empire.
- The Chola Empire was a Tamil empire that ruled over southern India from the 9th to the 13th centuries. It was one of the largest and most powerful empires in Indian history.
- The Pallavas were a Tamil dynasty that ruled over southern India from the 3rd to the 9th centuries. They were the first major power to unify southern India.