Ofcourse.  Till last year TNAU was not accredited by the ICAR and thus TNAU had to conduct it's own entrance exam to enroll students.  

But this year it is accredited by ICAR. Thus a student can apply for any of the one. But as per my knowledge,  ICAR is enough for getting bsc ag. No need for TNAU entrance exam. 

Hello ABHISHEK , 

TNAU IS A DTATE LEVEL EXAM WHICH GIVES YOU ADMISSION IN A PARTICULAR REGION OF TAMIL NADU BUT BY GIVING ICAR THE GATES ARE OPEN FOR YOU ALL OVER INDIA TO GET ADMISSION IN AGR. SO YOU SHOULD GO FOR ICAR INSTEAD OF TNAU IF YOU WANT TO GET ADMISSION IN STATE OTHER THAN TAMIL NADU.

BEST IF LUCK.