UPSC Prelims 2013 Art & Culture

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 The Barabar rock-cut caves were originally made for Ajivikas by Emperor Chandragupta Maurya.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?