The correct option is 3 only because the Ellora Caves are renowned for their remarkable representation of multiple faiths, including Buddhism, Hinduism, and Jainism, showcasing the cultural and religious diversity of India during the period of their construction (6th to 8th centuries CE). Statement 1 is inaccurate since the Badami caves, although significant, are not the oldest surviving rock-cut caves; that distinction typically goes to caves like the Barabar Caves. Statement 2 is also incorrect, as the Barabar Caves were commissioned by Emperor Ashoka for the Ajivikas, not Chandragupta Maurya. Understanding these points aligns with the study of Indian architectural evolution and religious syncretism, crucial for the UPSC Prelims.