The correct answer is option 'C', New Delhi. The headquarters of the Border Security Force (BSF) is located in New Delhi, the capital city of India.

The Border Security Force is the primary border guarding force of India. It was formed on December 1, 1965, and is one of the five Central Armed Police Forces (CAPFs) of India. The primary responsibility of the BSF is to guard the borders of India and prevent any illegal activities such as smuggling, infiltration, and terrorist activities.

Here is a detailed explanation of the answer:

1. Introduction to BSF:
- The Border Security Force (BSF) is a paramilitary force under the Ministry of Home Affairs, Government of India.
- It is responsible for guarding India's land borders during peacetime and preventing transnational crime.
- The BSF is also involved in various internal security duties, including counter-terrorism operations.

2. Formation and Purpose:
- The BSF was established on December 1, 1965, in response to the 1965 Indo-Pak War.
- Its primary purpose is to ensure the security of India's borders and maintain peace in the border regions.
- The force is equipped with modern weapons, surveillance systems, and communication equipment to effectively carry out its duties.

3. Headquarters Location:
- The headquarters of the BSF is located in New Delhi, the capital city of India.
- The exact address of the headquarters is Block 10, CGO Complex, Lodhi Road, New Delhi.
- Being situated in the national capital, the headquarters allows for better coordination with the Ministry of Home Affairs and other government agencies.

4. Role and Responsibilities:
- The BSF has various roles and responsibilities, including border guarding, counter-insurgency operations, and disaster management.
- It is responsible for guarding the borders with Pakistan and Bangladesh, which are prone to infiltration and smuggling.
- The force also plays a crucial role in maintaining peace and security in Jammu and Kashmir, particularly along the Line of Control (LoC).

5. Organizational Structure:
- The BSF follows a hierarchical structure, with a Director General (DG) heading the force.
- The DG is assisted by Additional Directors General (ADGs) and other senior officers.
- The force is divided into various sectors, each headed by an Inspector General (IG).
- These sectors are further divided into battalions, companies, and platoons.

In conclusion, the headquarters of the BSF is located in New Delhi, India. It is responsible for guarding India's borders, maintaining peace, and preventing illegal activities. The force plays a crucial role in ensuring national security and protecting the sovereignty of the country.