The correct answer is option 'C' - The Kaveri River.

The Kaveri River is one of the major rivers in South India and is considered to be the lifeline of the region. It originates in the Western Ghats in Karnataka and flows through the states of Karnataka and Tamil Nadu before finally emptying into the Bay of Bengal. The river is known for its significance in agriculture, as it supports the cultivation of various crops in the region.

The Kaveri River has several tributaries that contribute to its flow and overall water resources. Some of the main tributaries of the Kaveri River include:

1. Amravati: The Amravati River is one of the major tributaries of the Kaveri River. It originates in the Yelandur taluk of Karnataka and joins the Kaveri River near Mysore. The river is known for its scenic beauty and provides water for irrigation purposes.

2. Bhavani: The Bhavani River is another important tributary of the Kaveri River. It originates in the Nilgiri Hills of Tamil Nadu and flows through the districts of Coimbatore and Erode before joining the Kaveri River. The Bhavani River is known for its dam, the Bhavanisagar Dam, which is one of the largest earthen dams in the world.

3. Hemavati: The Hemavati River is a tributary of the Kaveri River that originates in the Western Ghats of Karnataka. It flows through the districts of Hassan and Mandya before joining the Kaveri River near Krishnarajasagara. The Hemavati River is known for its reservoir, the Hemavati Dam, which is a major source of irrigation and drinking water supply in the region.

4. Kabini: The Kabini River, also known as the Kapila River, is a tributary of the Kaveri River. It originates in the Wayanad district of Kerala and flows through the districts of Mysore and Chamarajanagar in Karnataka before joining the Kaveri River. The Kabini River is famous for its wildlife sanctuary, which is home to a variety of flora and fauna.

These tributaries, along with several others, play a crucial role in maintaining the flow and water resources of the Kaveri River. They contribute to the overall water availability for agriculture, drinking water supply, and other purposes in the region. The Kaveri River and its tributaries are not only important for the states of Karnataka and Tamil Nadu but also have cultural and historical significance in South India.