A precocious child, Rao completed BSc from Mysore University at age seventeen, and MSc from Banaras Hindu University at age nineteen. He earned a PhD from Purdue University at age twenty-four. He was the youngest lecturer when he joined the Indian Institute of Science in 1959. After a transfer to Indian Institute of Technology Kanpur, he returned to IISc, eventually becoming its Director from 1984 to 1994. He was Chair of the Scientific Advisory Council to the Prime Minister of India during 1985 to 1989 and 2005 to 2014. He found and works in Jawaharlal Nehru Centre for Advanced Scientific Research and International Centre for Materials Science.