The correct answer is: a) Tamil Nadu.
The Thamirabarani River is a perennial river that originates in the Western Ghats of Tamil Nadu, India. It flows through the districts of Theni, Madurai, Virudhunagar, and Tuticorin before emptying into the Bay of Bengal. The river is 576 kilometers long and has a drainage basin of 25,000 square kilometers. The Thamirabarani is a major source of irrigation and drinking water for the people of Tamil Nadu. It is also a popular tourist destination, with many temples and historical sites located along its banks.
The other options are incorrect because the Thamirabarani River does not originate or flow entirely within those states. The Periyar River originates in the Western Ghats of Kerala and flows through the states of Kerala and Tamil Nadu. The Kaveri River originates in the Western Ghats of Karnataka and flows through the states of Karnataka, Tamil Nadu, and Puducherry. The Godavari River originates in the Western Ghats of Maharashtra and flows through the states of Maharashtra, Telangana, Andhra Pradesh, Chhattisgarh, and Odisha.