It doesn't matter if you pass 12 from government school or private school. The only thing matters is that if you are eligible or not. There are numerous courses in the field of agriculture like-
B.E. / B.Tech in Agricultural Engineering, Dairy Technology, Agriculture and Dairy Technology, BSc in Agriculture, Dairy Science, plant science, Agricultural Biotechnology, Horticulture, Fishery sciences, BSc in Plant Pathology, Forestry, BSc in Crop Physiology etc.