A UNESCO World Heritage Site in Karnataka known for its intricate carvings:

Hampi
Badami Caves
Pattadakal
Mahabalipuram

The correct answer is: A) Hampi

Hampi is a UNESCO World Heritage Site in Karnataka, India. It was the capital of the Vijayanagara Empire from the 14th to the 16th centuries. The city is known for its intricate carvings, which can be found on temples, palaces, and other buildings.

The Badami Caves are a group of Hindu and Jain rock-cut temples located in Badami, Karnataka, India. The caves date from the 6th century and are considered to be some of the finest examples of early Indian rock-cut architecture.

Pattadakal is a UNESCO World Heritage Site in Karnataka, India. It is a group of Hindu and Jain temples that were built between the 7th and 8th centuries. The temples are known for their intricate carvings and their fine state of preservation.

Mahabalipuram is a UNESCO World Heritage Site in Tamil Nadu, India. It is a group of Hindu temples that were built between the 7th and 8th centuries. The temples are known for their intricate carvings and their fine state of preservation.

In conclusion, the correct answer is: A) Hampi.