The correct answer is option 'A', the first five-year plan.

Explanation:
The Bhakra-Nangal, Kosi, and Damodar Valley projects were all planned during the first five-year plan in India. Let's understand more about these projects and their significance:

1. Bhakra-Nangal Project:
- The Bhakra-Nangal Project is a multipurpose river valley project located on the Sutlej River in the states of Himachal Pradesh and Punjab.
- It was planned during the first five-year plan (1951-1956) and completed in 1963.
- The main objectives of this project were irrigation, hydroelectric power generation, and flood control.
- The Bhakra-Nangal Dam is one of the highest gravity dams in the world and has a capacity of 9.34 billion cubic meters.
- It provides irrigation water to millions of acres of agricultural land, generates a significant amount of hydroelectric power, and helps in controlling floods in the region.

2. Kosi Project:
- The Kosi Project is a multipurpose river valley project located on the Kosi River in Bihar.
- It was also planned during the first five-year plan and completed in 1959.
- The main objective of this project was to control floods in the Kosi River, which is known as the "Sorrow of Bihar" due to its frequent devastating floods.
- The project involved the construction of the Kosi Barrage, which diverts excess water from the river into a channel called the Kosi Canal, thereby reducing the flood risk.

3. Damodar Valley Project:
- The Damodar Valley Project is a multipurpose river valley project located on the Damodar River in West Bengal and Jharkhand.
- It was planned during the first five-year plan and completed in 1953.
- The main objectives of this project were flood control, irrigation, and power generation.
- The project involved the construction of dams, reservoirs, canals, and power stations to harness the water resources of the Damodar River.
- It has helped in controlling floods, providing irrigation facilities, and generating hydroelectric power in the region.

These projects were significant in the early years of independent India as they aimed to address some of the key developmental challenges such as irrigation, power generation, and flood control. The first five-year plan laid the foundation for these projects, which played a crucial role in the economic and social development of the respective regions.