The Ajanta Caves in Maharashtra are 30 rock-cut cave Buddhist temples. The Pallavas' buildings at Mahabalipuram were rock-cut. The tradition of rock-cut cave continued in the Deccan and they are found at Mahabalipuram under the patronage of the Pallavas. Both have rock-cut monuments - Statement 3 is correct. They were NOT built in the same period (Ajanta is from 2nd century BCE onwards, Mahabalipuram is from 7th-8th century CE) - Statement 1 is incorrect. They do NOT belong to the same religious denomination (Ajanta is Buddhist, Mahabalipuram is Hindu) - Statement 2 is incorrect.