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Option 1: Gorakhpur - This district is not on the international border of India. It is a district in the state of Uttar Pradesh, located near the border with Nepal.
Option 2: Jaipur - This district is not on the international border of India. It is the capital city of the state of Rajasthan, located in the interior of India.
Option 3: Kinnaur - This district is on the international border of India. It is located in the state of Himachal Pradesh and shares its border with Tibet.
Option 4: Kullu - This district is not on the international border of India. It is located in the state of Himachal Pradesh, but it does not share a border with any other country.
Therefore, the correct answer is option 3, Kinnaur, as it is the only district listed that is located on the international border of India.