Which is the highest Indian Peak entirely located within India:

Concept: "Highest Indian peak" conventionally means the tallest mountain located wholly within Indian-administered territory, not merely the tallest mountain over which India asserts a claim. A peak that straddles an international border, or that lies in territory administered by another country, is excluded from this reckoning even if it is geographically taller.

Application: Nanda Devi (7,816 m), in the Garhwal Himalayas of Uttarakhand, lies entirely within Indian-administered territory and is the tallest peak meeting this criterion. Kangchenjunga (8,586 m) is geographically taller, but it sits on the India-Nepal border in Sikkim, so it is not counted as being wholly within India. K2 (8,611 m), the world's second-highest mountain, lies in the Karakoram range on the Pakistan-administered Gilgit-Baltistan/China border and is not part of Indian-administered territory at all.

Cross-check: Comparing only the peaks offered here confirms the result -- Nanda Devi (7,816 m) is taller than Kamet (7,756 m), the next-tallest peak wholly within India, while K2 lies outside Indian-administered territory and Atlas is not a single peak in India but a mountain range across north-western Africa.