To answer this question, we need to know the location of the Mettur Dam.
The Mettur Dam is situated on the river Cauvery. Therefore, option A) Cauvery is the correct answer.
Option A) Cauvery - This option is correct because the Mettur Dam is indeed located on the Cauvery River.
Option B) Mahanadi - This option is incorrect because the Mettur Dam is not situated on the Mahanadi River.
Option C) Krishna - This option is incorrect because the Mettur Dam is not located on the Krishna River.
Option D) Godavari - This option is incorrect because the Mettur Dam is not situated on the Godavari River.
The correct answer is option A) Cauvery.