Kangchenjunga, standing at 8,586 metres, is the correct answer, being both the world's third-highest mountain and the highest peak located entirely within Indian territory, situated in the state of Sikkim near the border with Nepal. Mount Everest, the first distractor at 8,849 metres, is unquestionably the world's highest peak, but it lies on the international border between Nepal and China (Tibet Autonomous Region), not within India, making it a frequent source of confusion since students often assume India's Himalayan presence automatically includes the world's tallest peak. K2, the second distractor, standing at 8,611 metres, is the world's second-highest mountain and lies in the Karakoram Range on the border of Pakistan-administered Gilgit-Baltistan and China, entirely outside Indian territory, and is notorious among mountaineers for being far more technically dangerous to climb than Everest. Nanda Devi, the third distractor, is significant as the highest peak located entirely within India without being on any international border, standing at 7,816 metres in Uttarakhand, but it ranks far behind Kangchenjunga in absolute height and is a commonly confused answer for 'highest peak fully inside India,' since Kangchenjunga technically sits very close to the Nepal border while Nanda Devi is wholly interior. The key exam distinction, therefore, is between 'highest point in Indian territory' (Kangchenjunga, on the Sikkim-Nepal border area) and 'highest peak entirely interior with no border proximity' (Nanda Devi).