The major river system flowing through Karnataka is the:

The correct answer is C) Kaveri (Cauvery).

The Kaveri is the longest river in the Indian state of Karnataka. It is also the third longest river in the Peninsular India, after the Godavari and the Krishna. The Kaveri originates in the Western Ghats near Talakaveri in the Kodagu district of Karnataka. It flows through the states of Karnataka, Tamil Nadu, and Kerala before draining into the Bay of Bengal.

The Kaveri is a major source of irrigation and drinking water for millions of people in the region. It is also a popular tourist destination, with many temples and historical sites located along its banks.

The other options are incorrect.

• The Krishna is a river in India that flows through the states of Maharashtra, Karnataka, Andhra Pradesh, and Telangana. It is the second longest river in the Peninsular India, after the Godavari.
• The Godavari is a river in India that flows through the states of Maharashtra, Telangana, Andhra Pradesh, Chhattisgarh, and Odisha. It is the longest river in the Peninsular India.
• The Mahanadi is a river in India that flows through the states of Chhattisgarh, Odisha, and Jharkhand. It is the fourth longest river in India.