Explanation:

Badami cave painting

1.Badami was the capital of the early Chalukyan dynasty which ruled the region from 543 to 598 CE. With the decline of the Vakataka rule, the Chalukyas established their power in the Deccan. The Chalukya king, Mangalesha, patronised the excavation of the Badami caves. He was the younger son of the Chalukya king, Pulakesi I, and the brother of Kirtivarman I. Hence statement 2 is incorrect. 2.Stylistically speaking, the painting represents extension of the tradition of mural painting from Ajanta to Badami in South India. Hence statement 1 is correct. 3.The inscription in Cave No.4 mentions the date 578–579 CE, describes the beauty of the cave and includes the dedication of the image of Vishnu. Thus it may be presumed that the cave was excavated in the same era and the patron records his Vaishnava affiliation.Therefore, the cave is popularly known as the Vishnu Cave. Hence statement 3 is correct.