Buddhist, Hindu and Jain rock-cut caves exist in:

Ajanta
Ellora
Elephanta
Nasik

The correct answer is (b), Ellora.

Ajanta and Ellora are both UNESCO World Heritage Sites located in the Indian state of Maharashtra. Ajanta is famous for its Buddhist caves, while Ellora is known for its Hindu and Jain caves. The caves at Ajanta were built between the 2nd century BCE and the 6th century CE, while the caves at Ellora were built between the 6th and 10th centuries CE.

The Buddhist caves at Ajanta are some of the finest examples of Buddhist art in the world. The caves are decorated with paintings and sculptures depicting scenes from the life of the Buddha. The Hindu caves at Ellora are also very impressive, and they include some of the largest rock-cut temples in the world. The Jain caves at Ellora are smaller than the Buddhist and Hindu caves, but they are still very beautiful.

Nashik is a city in the Indian state of Maharashtra. It is located on the banks of the Godavari River. Nasik is a holy city for Hindus, and it is home to many temples and shrines. The city is also known for its wine production.

In conclusion, the correct answer to the question “Buddhist, Hindu and Jain rock-cut caves exist in:” is (b), Ellora.