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Option 1: The Rath temple at Mamallapuram is a temple known for its magnificent rock-cut architecture. However, it does not display the most extensive and sumptuous rock-cut shrines in India, as there are other temples that surpass it in that regard.
Option 2: The Kailash temple at Ellora is the correct answer. It is known for its extensive and sumptuous rock-cut shrines, making it a marvel of architectural craftsmanship in India. The temple is dedicated to Lord Shiva and is renowned for its intricate carvings and larger-than-life sculptures.
Option 3: The Chaturbhuja-Vishnu temple at Khajuraho is a famous temple known for its intricate sculptures and erotic art. However, it is not primarily a rock-cut temple, so it does not match the criteria mentioned in the question.
Option 4: The Kailash temple at Kanchi does not exist. There is no such temple, so this option can be eliminated.
Therefore, the correct answer is option 2, the Kailash temple at Ellora, which displays the most extensive and sumptuous rock-cut shrines and is considered the most marvellous architectural freak in India.