What is the third highest peak of India?

By the standard school/geography convention in India (which excludes K2), the third-highest peak is Kamet (7,756 m) in the Garhwal Himalaya, Uttarakhand. Kamet lies in the Zanskar range and is noted for long glacier approaches and severe winds. 

If you use the alternate convention that includes K2 from the Karakoram, the ranking shifts to: K2 (1st), Kangchenjunga (2nd), and Nanda Devi (7,816 m) as the 3rd highest entirely within India’s usual lists. For exams, follow your textbook’s convention; most boards expect Kamet as the correct answer. Elevation figures may vary slightly by source, but the values above are widely accepted.