The correct answer is option 'D', the Gurkha regiment, helped Colin Campbell to rescue the British holed up in the residency of Lucknow.

Below is a detailed explanation of the answer:

The context of the question lies in the events of the Indian Rebellion of 1857, also known as the Sepoy Mutiny. The rebellion erupted in several parts of India against the British East India Company's rule. One of the significant centers of the rebellion was Lucknow, where a large number of British residents, including women and children, were trapped in the residency.

1. The Siege of Lucknow:
- The British Residency in Lucknow was surrounded and besieged by rebel forces, including sepoys, local rebels, and elements of the Awadh nobility.
- The siege lasted for over 140 days, from June to November 1857, during which the British residents faced extreme hardships, including shortage of food, water, and medical supplies.

2. Sir Colin Campbell's Relief Force:
- Sir Colin Campbell, a British general, was appointed to lead a relief force to rescue the besieged residents in Lucknow.
- Campbell's force consisted of a variety of troops, including British, Indian, and Nepalese soldiers.

3. Role of the Gurkha Regiment:
- The Gurkha regiment, comprising soldiers from Nepal, played a crucial role in the relief of Lucknow.
- Gurkhas are known for their bravery, loyalty, and exceptional military skills.
- The Gurkhas fought alongside the British forces throughout the Indian Rebellion of 1857 and played a significant role in various operations.

4. The Battle for the Residency:
- Campbell's relief force fought their way through the rebel-held areas to reach the residency.
- The Gurkha regiment, known for their fierce combat skills, played a crucial role in several key battles during the relief operation.
- They engaged in close combat, fought off rebel attacks, and helped secure the path for the British forces to reach the residency.

5. Successful Rescue:
- With the help of the Gurkha regiment and other troops, Campbell's relief force successfully reached the residency and lifted the siege.
- The trapped British residents were evacuated and brought to safety.

In summary, the Gurkha regiment played a significant role in assisting Colin Campbell's relief force to rescue the British holed up in the residency of Lucknow during the Indian Rebellion of 1857. Their bravery and combat skills were instrumental in securing the path and defeating the rebel forces to reach the besieged residents.