Here is a more detailed explanation of the correct matching of List I with List II:

I. Cauvery is matched with (B) Mettur. The Mettur Dam is located on the Cauvery River in Tamil Nadu, India. It is one of the largest dams in India and plays a crucial role in irrigation and hydroelectric power generation.

II. Krishna is matched with (A) Alamatti. The Alamatti Dam, also known as the Krishna Raja Sagara Dam, is located on the Krishna River in Karnataka, India. It is a multipurpose dam that serves irrigation, hydroelectric power generation, and drinking water supply purposes.

III. Narmada is matched with (D) Sardar Sarovar. The Sardar Sarovar Dam is located on the Narmada River in Gujarat, India. It is one of the largest dams in India and serves multiple purposes including irrigation, hydropower generation, and drinking water supply.

IV. Chambal is matched with (C) Gandhi Sagar. The Gandhi Sagar Dam is located on the Chambal River in Madhya Pradesh, India. It is a multipurpose dam that primarily serves irrigation and hydropower generation purposes.

Therefore, the correct matching of List I with List II is:

I-B, II-A, III-D, IV-C