The Mettur Dam, a major reservoir in Tamil Nadu, is built on the:

The correct answer is (a) Kaveri River.

The Mettur Dam is a masonry dam across the Kaveri River in the Indian state of Tamil Nadu. It is located in the Salem district, about 190 kilometres (120 mi) from the state capital Chennai. The dam was built between 1934 and 1939 and was inaugurated by the then Governor of Madras, Lord Erskine, on 24 October 1939.

The Mettur Dam is a major source of irrigation for the Cauvery Delta region in Tamil Nadu. It also provides drinking water to the city of Chennai and other towns and villages in the region. The dam is a popular tourist destination and offers a scenic view of the Kaveri River.

The other options are incorrect because:

• The Vaigai River is a river in the Indian state of Tamil Nadu. It is the second longest river in the state after the Kaveri River. The Vaigai River originates in the Western Ghats and flows through the Madurai district before joining the Bay of Bengal.
• The Palar River is a river in the Indian state of Tamil Nadu. It is the third longest river in the state after the Kaveri River and the Vaigai River. The Palar River originates in the Western Ghats and flows through the Vellore district before joining the Bay of Bengal.
• The Thamirabarani River is a river in the Indian state of Tamil Nadu. It is the fourth longest river in the state after the Kaveri River, the Vaigai River, and the Palar River. The Thamirabarani River originates in the Western Ghats and flows through the Tirunelveli district before joining the Bay of Bengal.