Which Himalayan peak is the highest mountain entirely in India?

The Himalayan peak highest entirely within India is Nanda Devi.

Nanda Devi rises to 7,817 metres in Uttarakhand’s Garhwal Himalaya. It is India’s second-highest mountain overall, but it is the country’s highest summit located wholly within Indian territory. Kangchenjunga is higher, yet its summit lies on the India–Nepal border, which is why it does not fit the wording of this question.

The mountain is a two-peaked massif surrounded by a ring of high ridges known as the Nanda Devi Sanctuary. Its name means “Bliss-Giving Goddess,” and it has long been revered as a patron deity of the Garhwal and Kumaon Himalayas.

The first ascent was made in 1936 by Noel Odell and Bill Tilman. Because of its religious importance and fragile ecology, the inner sanctuary was closed to climbers in 1983. Nanda Devi National Park became part of a UNESCO World Heritage Site in 1988.