With reference to the history of Indian rock-cut 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 The Barabar rock-cut caves were originally made for Ajivikas by Emperor         Chandragupta Maurya.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?

[IAS (Pre) 2013]