The headquarters of the East Sikkim district is:

Gangtok
Namchi
Geyzing
Mangan

The correct answer is: a) Gangtok.

Gangtok is the capital of the Indian state of Sikkim. It is located in the eastern part of the state, at an elevation of 1,650 meters (5,410 feet). The city has a population of about 100,000 people. Gangtok is a popular tourist destination, known for its beautiful scenery, temples, and monasteries.

Namchi is a town in the Indian state of Sikkim. It is located in the eastern part of the state, at an elevation of 1,780 meters (5,840 feet). The town has a population of about 20,000 people. Namchi is the headquarters of the South Sikkim district.

Geyzing is a town in the Indian state of Sikkim. It is located in the western part of the state, at an elevation of 1,750 meters (5,740 feet). The town has a population of about 15,000 people. Geyzing is the headquarters of the West Sikkim district.

Mangan is a town in the Indian state of Sikkim. It is located in the northern part of the state, at an elevation of 1,800 meters (5,900 feet). The town has a population of about 10,000 people. Mangan is the headquarters of the North Sikkim district.