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Among the given options, option 3 - Dhaulagiri - is at the highest altitude.
To understand this, it is important to know that altitude refers to the height above sea level. Mountains are commonly ranked based on their altitude, with the highest ones being at the top of the list.
Annapurna, option 1, is one of the highest peaks in the world, but it is not the highest among the given options.
Badrinath, option 2, is a pilgrimage site located in the Himalayas but is not known to be at a very high altitude compared to the other options.
Dhaulagiri, option 3, is a mountain located in the Himalayas and is known for its extreme altitude. It stands at an elevation of 8,167 meters, making it one of the highest mountains in the world.
Nanda Devi, option 4, is also a mountain located in the Himalayas, known for its beauty and spiritual significance. However, it is not as high as Dhaulagiri.
Therefore, based on the given options, Dhaulagiri is at the highest altitude.