The correct option is 1 and 3 only.
Explanation
The Badami Cave temples in Karnataka, patronized by the early Chalukya dynasty in the 6th century CE, represent a significant extension of the Indian mural tradition. These paintings are primarily found in Cave No. 4, which is dedicated to Lord Vishnu.
Statement 1 is Correct:
The surviving murals in Cave No. 4 depict a palace scene. The central composition illustrates a royal figure seated on a throne, accompanied by his queen, attendants, and feudatories, witnessing a music and dance performance.
Statement 2 is Incorrect:
The paintings in Cave No. 4 are associated with the reign of the Chalukya king Mangalesha, who dedicated the cave in 578 CE. The royal figure depicted in the painting is identified as Kirtivarman I (Mangalesha's elder brother and the father of Pulakeshin II), not Pulakeshin II.
Statement 3 is Correct:
Badami Cave No. 4 is a Vaishnava cave. Its murals are recognized as the earliest surviving examples of Brahmanical (Hindu) wall paintings in South India. In contrast, earlier traditions like Ajanta are predominantly Buddhist, and Sittanavasal is Jain.
Key Takeaway:
Badami Cave 4 murals (Karnataka) are the earliest surviving Brahmanical paintings, patronized by Chalukya King Mangalesha, and depict King Kirtivarman I.