Oldest Rock-cut Caves in India | Barabar and Badami

Barabar caves are the oldest in India, not Badami. Ellora is notable for having caves belonging to Buddhism, Hinduism, and Jainism.

ID: ART_ARC_2013_19 Ref: Standard Educational Reference

With reference to the history of Indian rockcut architecture, consider the following statements:
1. The caves at Badami are the oldest surviving rock-cut caves in India.
2. The Barabar rock-cut caves were originally made for Ajivikas by Emperor Chandragupta Maurya.
3. At Ellora, caves were made for different faiths.

Which of the statements given above is/are correct?