Agriculture

Tamil Nadu Agricultural University (TNAU), Coimbatore is a STATE UNIVERSITY which provides B.Sc. (Agriculture) which is an n Under Graduate Degree program providing Full Time degree for a Duration of 4 years.
It is approved by ICAR and was established in 1971.
The University offers UG courses in 12 disciplines, Masters programme in 33 disciplines, regular Ph.D in 27 disciplines, integrated Ph.D in 4 disciplines and external Ph.D by research in 28 disciplines.
The candidate must have completed Class 12th in the relevant subjects for being eligible to apply for B.Sc and B.Tech.
Admission to UG courses is based on marks scored in 10+2 in the relevant subjects
Minimum eligibility for M.Sc, M.Tech and MBA is the candidate must have obtained B.Sc./B.Tech/BE in the respective field.
The University conducts an entrance test for admission to M.Sc ,M.Tech and MBA courses.

You are eligible for writing government exams like SSC CGL UPSC SBI and other government-related exams, but I don't think there is a need of studying agriculture for those jobs, a normal degree is enough for writing those exams. Moreover, the eligibility varies from state to state, do some research in your state regarding eligibility for government exams related to agriculture field. And one more thing, there is no government statutory body for agriculture unlike MCI for medicine, PCI for pharmacy, AICTE for engineering, in India it was governed by ICAR- a non-profit organisation and institute. Any rules can be made by ICAR without prior information to Non-ICAR colleges. There are some state universities which are not accredited by ICAR, there is no need of ICAR if you study in a state agriculture university.