Who, amongst the following, founded the Vijayanagara Empire?

The correct option is Harihara and Bukka.

The Vijayanagara Empire was established in 1336 CE by two brothers, Harihara I (also known as Hakka) and Bukka Raya I, who belonged to the Sangama dynasty.

Here is a step-by-step historical explanation:
1. Historical Origin: Harihara and Bukka were originally in the service of the Kakatiya dynasty of Warangal. After the fall of the Kakatiyas, they served the ruler of Kampili. After Kampili was conquered by the Delhi Sultanate under Muhammad bin Tughlaq, the brothers were taken to Delhi and converted to Islam.
2. Re-establishment and Guidance: They were later sent back to the Deccan region to quell local rebellions. Under the spiritual guidance and influence of the sage Vidyaranya, they returned to the Hindu fold and declared independence from the Delhi Sultanate.
3. Foundation of the Capital: They founded their capital city, Vijayanagara (meaning the 'City of Victory'), on the banks of the Tungabhadra River, marking the rise of one of the most powerful empires in southern India.

Why the other options are incorrect:
- Krishnadeva Raya was indeed the most famous ruler of the Vijayanagara Empire (belonging to the Tuluva dynasty), but he ruled much later, from 1509 to 1529 CE.
- Raja Raya (often referring to Rajaraja Chola I) and Rajendra II were prominent rulers of the Chola dynasty, which predated the Vijayanagara Empire.