The Bhavani, Amaravati, and Noyyal are tributaries of the:

Palar River
Vaigai River
Kaveri River
Thamirabarani River

The correct answer is c) Kaveri River.

The Bhavani, Amaravati, and Noyyal are all tributaries of the Kaveri River. The Kaveri River is the longest river in the Indian state of Tamil Nadu and the second-longest river in the state of Karnataka. It is also one of the most important rivers in India, both for irrigation and for drinking water. The Kaveri River originates in the Western Ghats in Karnataka and flows through the states of Karnataka, Tamil Nadu, and Kerala. It empties into the Bay of Bengal near the city of Tuticorin in Tamil Nadu.

The Bhavani River is a tributary of the Kaveri River that originates in the Western Ghats in Karnataka. It flows through the states of Karnataka and Tamil Nadu before joining the Kaveri River near the town of Bhavani in Tamil Nadu. The Amaravati River is a tributary of the Kaveri River that originates in the Western Ghats in Karnataka. It flows through the states of Karnataka and Tamil Nadu before joining the Kaveri River near the town of Tiruchirapalli in Tamil Nadu. The Noyyal River is a tributary of the Kaveri River that originates in the Western Ghats in Tamil Nadu. It flows through the state of Tamil Nadu before joining the Kaveri River near the town of Coimbatore in Tamil Nadu.

The Bhavani, Amaravati, and Noyyal are all important rivers for irrigation and drinking water in the states of Karnataka and Tamil Nadu. The Kaveri River is also an important river for religious purposes.