Which one of the following battles weakened the Vijaynagara kingdom?

Battle of Talikotta

The correct answer is Option 1 - Battle of Talikotta

The Battle of Talikota (26 January 1565) was a watershed battle fought between the Vijaynagara Empire and the Deccan sultanates. It ended in the defeat of Vijaynagara, resulting in its subsequent weakening.

Strain began to show within the imperial structure following Krishnadeva Raya’s death in 1529. His successors were troubled by rebellious nayakas or military chiefs. By 1542 control at the centre had shifted to another ruling lineage, that of the Aravidu, which remained in power till the end of the seventeenth century. During this period, as indeed earlier, the military ambitions of the rulers of Vijayanagara as well as those of the Deccan Sultanates resulted in shifting alignments. Eventually this led to an alliance of the Sultanates against Vijayanagara. In 1565 Rama Raya, the chief minister of Vijayanagara, led the army into battle at Rakshasi-Tangadi (also known as Talikota), where his forces were routed by the combined armies of Bijapur, Ahmadnagar and Golconda. The victorious armies sacked the city of Vijayanagara. The city was totally abandoned within a few years. Now the focus of the empire shifted to the east where the Aravidu dynasty ruled from Penukonda and later from Chandragiri (near Tirupati).