Explanation:

- The Hirakud Dam is indeed built on the Mahanadi River in the state of Odisha, India. It is one of the longest earthen dams in the world.

- The Tapi River flows through central India, primarily through the states of Maharashtra, Gujarat, and Madhya Pradesh. It does not host the Hirakud Dam.

- The Godavari River is one of the major rivers in South India, often referred to as the "Dakshin Ganga." It flows through states like Maharashtra and Andhra Pradesh.

- The Kaveri River is another important river in Southern India, flowing through Karnataka and Tamil Nadu.