With reference to the history of Indian rock-cut architecture, consider the following statements:
1. The canves at Badami are the oldest surviving rock-cut caves in India.
2. The Barabar rock-cut caves wre originally made for Ajivikas by Emperor Chandragupta Maurya.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?