Nagaijunasagar Dam is located on the Krishna River. The Krishna River is one of the major rivers in southern India and is the fourth longest river in the country. It originates in the Western Ghats of Maharashtra and flows through the states of Karnataka, Telangana, and Andhra Pradesh before emptying into the Bay of Bengal.

Option 2, Tungabhadra, is not the correct answer. The Tungabhadra River is a tributary of the Krishna River, and the dam on the Tungabhadra River is known as the Tungabhadra Dam, not Nagaijunasagar Dam.

Option 3, Kaveri, is also incorrect. The Kaveri River is another major river in southern India, but it does not flow through the area where Nagaijunasagar Dam is located.

Option 4, Godavari, is also not the correct answer. The Godavari River is the second-longest river in India and flows through the states of Maharashtra, Telangana, Andhra Pradesh, and Odisha, but it does not pass through the area where Nagaijunasagar Dam is situated.

In conclusion, the correct answer is option 1, Krishna.