Hello aspirant,

You can easily apply for all the exams specified by you like IIT JEE, AIIMS and NEET.  Since you have completed your 10 and 12 from India. So you can easily apply for them. 
That is one of the basic eligibility criteria for the exams. 

Please visit this link for more info about eligibility criteria
https://www.google.com/url?sa=t&source=web&rct=j&url=https://engineering.careers360.com/articles/jee-main-eligibility-criteria/amp&ved=2ahUKEwjJwvzW89XjAhUDFHIKHVevAxsQFjAKegQIBxAB&usg=AOvVaw0Ddf__yVIUe0laa-JjEit-&ampcf=1

All the best
Prepare well and stay updated with the syllabus.