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 The Barabar rock-cut caves were originally made for Ajivikas by Emperor Chandragupta Maurya. 3.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?

1. Statement 1 is incorrect. The oldest surviving rock-cut caves in India are the Barabar caves in Bihar, dating back to the Mauryan period (3rd century BCE). The caves at Badami, attributed to the Chalukyas, belong to a later period (around 6th-7th century CE). 2. Statement 2 is incorrect. The Barabar rock-cut caves were indeed originally made for the Ajivika sect, but inscriptions indicate they were commissioned by Emperor Ashoka and his successor Dasharatha Maurya, not Emperor Chandragupta Maurya. 3. Statement 3 is correct. The caves at Ellora are renowned for representing different faiths. The site contains monasteries and temples dedicated to Buddhism (Caves 1-12), Hinduism (Caves 13-29), and Jainism (Caves 30-34), showcasing religious harmony and architectural evolution.