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 The Barabar rock-cut caves were originally made for Ajivikas by Emperor Chandragupta Maurya.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?
Statement 1 is incorrect: The caves at Badami (in Karnataka) were built during the 6th–7th centuries CE under the Chalukyas, but they are not the oldest. The oldest surviving rock-cut caves in India are the Barabar Caves in Bihar, dating to the 3rd century BCE (Mauryan period). Statement 2 is incorrect: The Barabar Caves were indeed made for the Ajivika sect, but they were constructed during the reign of Emperor Ashoka (and later his grandson Dasaratha), not Chandragupta Maurya. Statement 3 is correct: At Ellora, caves were excavated for three different faiths — Buddhism, Hinduism, and Jainism — reflecting religious harmony during the period (6th to 9th centuries CE).