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Being a non domicile of Tamil Nadu if you still want to take admission in an agriculture institute in TN you can give all India exam (ICAR UET) conducted by Indian Council of Agriculture, New Delhi.  For more details you  can read the admission information brochure of TNAU by clicking on http://www.tnau.ac.in/wp-content/uploads/2020/05/UG_Admission_Brochure_2019.pdf