The National Food Security Act primarily aims to:

The correct answer is: Provide subsidized food grains.

Step-by-Step Explanation:

1. Understanding the National Food Security Act (NFSA):
The National Food Security Act (NFSA), enacted in India in 2013, marks a paradigm shift in the approach to food security from a welfare-based measure to a rights-based approach.

2. Key Objective:
The main objective of the act is to provide food and nutritional security in human life cycle approach, by ensuring access to an adequate quantity of quality food at affordable prices to people to live a life with dignity.

3. Targeted Coverage & Subsidy:
Under this act, up to 75% of the rural population and 50% of the urban population are entitled to receive heavily subsidized food grains (such as rice, wheat, and coarse grains) through the Targeted Public Distribution System (TPDS).

4. Evaluating the Options:
- Promote exports: The NFSA is focused on domestic food security, not agricultural trade export promotion.
- Provide subsidized food grains: This directly aligns with the legal entitlement created under NFSA to deliver food grains at subsidized rates to eligible households.
- Increase agricultural taxes: The act is a food support program and has no mandate to increase taxes on farmers.
- Encourage private farming: Private farming practices are outside the core scope of food grain distribution to targeted beneficiaries.

Therefore, the primary aim of the National Food Security Act is to provide subsidized food grains to ensure food security for vulnerable sections of the population.