Explanation: The Kaveri River, also known as Cauvery, is a significant river in southern India, particularly important for the states of Karnataka and Tamil Nadu. The river originates in the Western Ghats, specifically in the Brahmagiri Hills in the Kodagu district of Karnataka. It flows through Karnataka for a considerable distance before entering Tamil Nadu, where it continues its course and eventually empties into the Bay of Bengal.
The Kaveri River is not only a geographical feature but also a vital resource for both Karnataka and Tamil Nadu. It is a source of water for irrigation, drinking, and industrial use. The river's flow and management have been a subject of interstate disputes, particularly between Karnataka and Tamil Nadu, due to the reliance of both states on its waters.
The river's course through Karnataka and Tamil Nadu makes it a significant geographical feature that connects these two states. It is one of the major rivers in southern India and plays a crucial role in the agricultural and economic activities of the region. The Kaveri River is also culturally and religiously significant, with several important temples and pilgrimage sites located along its banks.
In contrast, the Mahamadi River is not a recognized river in the context of Karnataka or Tamil Nadu. This makes it an incorrect option in the context of the question. The Kaveri River, on the other hand, is a well-known and significant river that fits the description provided in the question.
Therefore, the correct answer is the Kaveri River, as it is the only river that originates in Karnataka and flows through both Karnataka and Tamil Nadu, making it a crucial geographical feature in the region.