The correct answer is (a) Godavari.
The Godavari is the largest river in India by discharge. It flows through the states of Maharashtra, Telangana, Andhra Pradesh, and Chhattisgarh. It originates in the Western Ghats near Nasik in Maharashtra and flows west and south before emptying into the Bay of Bengal.
The Periyar is a river in the Indian state of Kerala. It originates in the Western Ghats near the town of Thekkady and flows south before emptying into the Arabian Sea. The Periyar is a major source of water for irrigation and hydroelectric power in Kerala.
The Tungabhadra is a river in the Indian states of Karnataka and Andhra Pradesh. It is formed by the confluence of the Tunga and Bhadra rivers near Hampi. The Tungabhadra flows south before emptying into the Krishna River.
The Cauvery is a river in the Indian states of Karnataka, Tamil Nadu, Kerala, and Puducherry. It is the longest river in the Deccan Plateau. The Cauvery originates in the Western Ghats near the town of Talakaveri and flows east before emptying into the Bay of Bengal.
The Godavari is the only west-flowing river among the given options.