With reference to the history of Indian rock-cut architecture, consider the following statements:<br/>1. The caves at Badami are the oldest surviving rock-cut caves in India.<br/>2. The Barabar rock-cut caves were originally made for Ajivikas by Emperor Chandragupta Maurya.<br/>3. At Ellora, caves were made for different faiths.<br/><br/>Which of the statements given above is/are correct?

1. Badami caves — Incorrect. The Badami caves are 6th century CE Chalukyan caves, not the oldest in India; earlier surviving rock-cut caves include the Barabar caves of the Mauryan period (3rd century BCE).

2. Barabar caves — Incorrect. These caves were indeed made for the Ajivikas, but they were mainly excavated under Emperor Ashoka and later his grandson Dasharatha, not Chandragupta Maurya.

3. Ellora caves — Correct. Ellora has rock-cut caves belonging to Buddhist, Hindu and Jain traditions, showing patronage to different faiths.

Therefore, only statement 3 is correct.