Agriculture Science

No, you don't need to give ICAR examination for B.Sc agriculture. there are many private Universities which are giving direct admission on the basis of 12th marks.

Dolphin Colleges Of Science And Agriculture
Birsa Agricultural University
University Of Agricultural Sconce Bangalore
Indian Institute Of Agriculture
Indian Institute Of Agricultural Bio Technology

B.Sc agriculture is the best amongst all the branches mentioned as agriculture has more scope in future and is less crowded so you can get jobs easily here with better salary.

You may not be eligible for B.Sc agriculture as requirement for this in most of the universities is 10+2 with physics, chemistry, biology and mathematics. If you look into Dr Panjabrao Deshmukh Agricultural University, you need to study physics, chemistry, biology and mathematics and if you have not studied mathematics, you are still eligible but have to go for another additional course. However, you are eligible for B.Tech in agriculture as well as for B.Sc environmental science.