The correct answer is option 'D', Kaveri.

The Kaveri River, also known as the Cauvery, is one of the major rivers in South India and is considered the lifeline of the state of Karnataka and Tamil Nadu. It originates in the Western Ghats in Karnataka and flows through the states of Tamil Nadu and Puducherry before emptying into the Bay of Bengal.

The Kaveri River is fed by several tributaries, four of which are the Amravati, Bhavani, Hemavati, and Kabini. These tributaries play a crucial role in the overall flow and water availability of the Kaveri River.

Here is some information about each of these tributaries:

1. Amravati River:
- The Amravati River is a tributary of the Kaveri River and is located in the state of Karnataka.
- It originates in the Amravati hills of the Western Ghats near Chikkamagaluru district.
- The river flows through the districts of Hassan and Mandya before joining the Kaveri River near Srirangapatna.

2. Bhavani River:
- The Bhavani River is another important tributary of the Kaveri River and is located in the states of Tamil Nadu and Kerala.
- It originates in the Nilgiri Hills of Tamil Nadu and flows through the districts of Coimbatore and Erode.
- The Bhavani River joins the Kaveri River near the town of Bhavani in Tamil Nadu.

3. Hemavati River:
- The Hemavati River is a tributary of the Kaveri River and is located in the state of Karnataka.
- It originates in the Western Ghats near Ballala Rayana Durga in Chikkamagaluru district.
- The river flows through the districts of Hassan and Mandya before joining the Kaveri River near Krishnarajasagara Dam.

4. Kabini River:
- The Kabini River is a tributary of the Kaveri River and is located in the state of Karnataka.
- It originates in the Wayanad district of Kerala and flows through the districts of Mysore and Chamarajanagar.
- The Kabini River joins the Kaveri River near Tirumakudalu Narasipura.

These four tributaries significantly contribute to the water flow and overall water availability of the Kaveri River. They play a crucial role in supporting agriculture, providing drinking water, and sustaining ecosystems along the course of the river.