The correct answer is: a) The Bahmani Sultanates.
The Battle of Talikota was fought on January 16, 1565, near the village of Talikota, Karnataka, India. The battle was fought between the Vijayanagara Empire and a coalition of four Deccan sultanates: the Adilshahi Sultanate of Bijapur, the Qutb Shahi Sultanate of Golconda, the Nizamshahi Sultanate of Ahmednagar, and the Berar Sultanate. The battle resulted in the defeat of the Vijayanagara Empire and the beginning of its decline.
The Vijayanagara Empire was a Hindu empire that ruled over much of southern India from the 14th to the 16th centuries. The empire was founded by Harihara I and Bukka Raya I, two brothers who were generals in the Hoysala Empire. The Vijayanagara Empire reached its peak under the rule of Krishnadevaraya (1509-1529), who expanded the empire’s territory and built many temples and palaces.
The Deccan sultanates were Muslim sultanates that ruled over the Deccan Plateau in southern India from the 14th to the 17th centuries. The sultanates were founded by Muslim invaders from Central Asia, who conquered the region from the Hindu kingdoms of the Deccan. The Deccan sultanates were often at war with each other, and they also fought against the Vijayanagara Empire.
The Battle of Talikota was a major turning point in South Indian history. The defeat of the Vijayanagara Empire led to the decline of the empire and the rise of the Deccan sultanates. The battle also marked the end of the Hindu golden age in southern India.
The other options are incorrect because they do not represent the correct historical period or the correct opponents of the Vijayanagara Empire. The Gajapatis of Odisha were a Hindu kingdom that ruled over eastern India from the 12th to the 16th centuries. The Portuguese were a European power that arrived in India in the 15th century. They established trading posts and forts along the Indian coast, and they also fought against the Vijayanagara Empire.