Can I take admission for B.Sc agriculture in a private or a government college after 3 years of gap after 12th?

Yes you can. But one has to sit for an entrance exam. 

You are able to apply in a government or private college for a B.Sc. in agriculture once three years have passed since you finished high school. After completing their 12th grade in the Science stream, students who wish to pursue a career in agriculture should apply to the BSc Agriculture Courses. T