INS Arihant became India’s first nuclear-powered ballistic-missile submarine.
Arihant is the lead boat of India’s Arihant-class submarines and was built as part of the Advanced Technology Vessel programme. It was launched in 2009 and entered commissioned service in 2016. The submarine is powered by a pressurized-water reactor and is designed to carry submarine-launched ballistic missiles.
Its strategic role is connected with India’s stated nuclear triad, which places nuclear weapons on aircraft, land-based missiles, and sea-based platforms. A submarine offers concealment and can support a retaliatory capability because it is difficult for an opponent to locate while at sea.
INS Chakra, leased from Russia, was also nuclear-powered, but it was an attack submarine rather than an Indian-built ballistic-missile submarine. That distinction makes Arihant the specific answer to this question.