The famous rock-cut temple of Kailasa is located in Ellora.

Option 1: Ajanta. The Ajanta caves are also rock-cut caves, but they primarily consist of Buddhist monastic buildings and paintings, not temples like Kailasa.

Option 2: Badami. Badami, located in Karnataka, is known for its rock-cut caves and temples, but the Kailasa temple is not situated there.

Option 3: Ellora. This is the correct answer. The Kailasa temple at Ellora is a remarkable example of rock-cut architecture. It is dedicated to Lord Shiva and was built in the 8th century AD. The temple is carved from a single massive rock and is considered one of the most impressive cave temples in India.

Option 4: Elephanta. The Elephanta caves, situated on Elephanta Island in Mumbai, also feature rock-cut caves and sculptures, but the Kailasa temple is not located there.

In summary, the correct answer is option 3, Ellora, as this is where the famous rock-cut temple of Kailasa is found.