Correct Option
Statement 3 is correct. The Ellora cave complex is a significant example of Indian rock-cut architecture, featuring monuments and artworks associated with three major religions: Buddhism, Hinduism, and Jainism. These caves were excavated between the 6th and 10th centuries CE, reflecting a period of religious coexistence and artistic syncretism.
Incorrect Options
Statement 1 is incorrect. The Barabar caves in Bihar are considered the oldest surviving rock-cut caves in India, dating back to the 3rd century BCE during the Mauryan period, primarily under Emperor Ashoka. The caves at Badami, located in Karnataka, were excavated much later, predominantly between the 6th and 8th centuries CE under the Chalukya dynasty.
Statement 2 is incorrect. While the Barabar rock-cut caves were indeed originally made for the Ajivikas, a non-Vedic ascetic sect, they were commissioned and dedicated by Emperor Ashoka (reigned c. 268 to 232 BCE) and later by his grandson Dasharatha Maurya, not by Chandragupta Maurya.