The primary responsibility for school education in Tamil Nadu lies with the:

Department of School Education
Ministry of Education (previously HRD)
University Grants Commission (UGC)
National Council of Educational Research and Training (NCERT)

The correct answer is: Department of School Education.

The Department of School Education is the government department responsible for school education in Tamil Nadu. It is headed by the Minister for School Education, who is a member of the Tamil Nadu Legislative Assembly. The department is responsible for the planning, implementation, and monitoring of school education in the state. It also provides financial assistance to schools and colleges, and regulates the admission and examination procedures.

The Ministry of Education (previously HRD) is the central government department responsible for education in India. It is headed by the Minister of Education, who is a member of the Union Cabinet. The ministry is responsible for the planning, implementation, and monitoring of education at the national level. It also provides financial assistance to states and union territories for education, and regulates the admission and examination procedures.

The University Grants Commission (UGC) is a statutory body established by the Government of India to coordinate, maintain standards and promote the development of higher education in India. It is headed by the Chairman of the UGC, who is appointed by the President of India. The UGC is responsible for the funding of universities and colleges, and for the regulation of higher education in India.

The National Council of Educational Research and Training (NCERT) is an autonomous organization under the Ministry of Education, Government of India. It is responsible for the formulation and implementation of the national curriculum framework for school education in India. The NCERT also publishes textbooks and other educational material, and conducts research in education.