Yes, definitely. There isn't any problem.
All the best.

Hi Jayakumar! Yes, you can definitely give both of these exams in the same year and the syllabus is also same for both of them. Also, both of the exam dates fall close so, it will be a benefit for you while preparing.
Prepare well and wish you luck!
Thank you!

Hii
Ya you can write both the exams at a time in the same year but you have more advantageous in NEET while in aiims as NEET is applicable for whole India
All the best

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