The organization responsible for procuring and distributing food grains through the Public Distribution System (PDS):

Food Corporation of India
National Agricultural Cooperative Marketing Federation of India Ltd. (NAFED)
Ministry of Agriculture & Farmers Welfare
C) Ministry of Agriculture & Farmers Welfare D) Agricultural and Processed Food Products Export Development Authority (APEDA)

The correct answer is: A) Food Corporation of India (FCI).

The Food Corporation of India (FCI) is a statutory corporation of the Government of India under the Ministry of Consumer Affairs, Food and Public Distribution. It was established in 1965 to undertake procurement, storage, and distribution of food grains in India. The FCI is the largest food procurement agency in the world, and it plays a vital role in ensuring food security in India.

The FCI procures food grains from farmers at the minimum support price (MSP), which is a price that is guaranteed by the government. The FCI then stores the food grains in its warehouses and distributes them through the Public Distribution System (PDS). The PDS is a system of ration shops that provide food grains at subsidized prices to the poor and vulnerable sections of the population.

The FCI also exports food grains to other countries. In 2017-18, the FCI exported 10.5 million tonnes of food grains.

The National Agricultural Cooperative Marketing Federation of India Ltd. (NAFED) is a cooperative society that was established in 1958. NAFED is responsible for the procurement, processing, and marketing of agricultural produce. NAFED is not involved in the procurement and distribution of food grains through the Public Distribution System (PDS).

The Ministry of Agriculture & Farmers Welfare is a ministry of the Government of India that is responsible for the formulation and implementation of policies and programmes for the development of agriculture and farmers welfare. The Ministry is not directly involved in the procurement and distribution of food grains through the Public Distribution System (PDS).

The Agricultural and Processed Food Products Export Development Authority (APEDA) is an autonomous body under the Ministry of Commerce and Industry. APEDA is responsible for the promotion of export of agricultural and processed food products. APEDA is not involved in the procurement and distribution of food grains through the Public Distribution System (PDS).