Explanation:

Statement 1 is incorrect-The Barabar Caves are the oldest surviving rock-cut caves in India. The Badami cave temples are a complex of four Hindu cave temples located in Badami, a town in the Bagalkot district in northern part of Karnataka, India. The caves are considered an example of Indian rock-cut architecture, especially Badami Chalukya architecture, which dates from the 6th century.

Statement 2 is incorrect- The Barabar rock-cut chambers date back to the 3rd century BC, Maurya period, of Ashoka (r. 273 BC to 232 BC.) and his son, Dasaratha. These caves were used by ascetics from the Ajivika sect, founded by Makkhali Gosala.

Statement 3 is correct- Ellora is a World Heritage Site The 12 Buddhist (caves 1–12), 17 Hindu (caves 13–29) and 5 Jain (caves 30–34) caves, built in proximity, demonstrate the religious harmony prevalent during this period of Indian history.