Indira Gandhi Centre for Atomic Research, established in 1971, is located at

Kolkata
Trombay, Maharashtra
Kalpakkam, Chennai
Indore

The correct answer is: C. Kalpakkam, Chennai.

Indira Gandhi Centre for Atomic Research (IGCAR) is an Indian government research institute located in Kalpakkam, Tamil Nadu. It was established in 1971 as the Bhabha Atomic Research Centre (BARC)’s second major facility, after Trombay. IGCAR is a major centre for research and development in nuclear science and technology. It is also involved in the production of nuclear fuel and the operation of nuclear power plants.

The other options are incorrect. Kolkata is the capital of West Bengal. Trombay is a suburb of Mumbai in Maharashtra. Indore is the capital of Madhya Pradesh.