Architecture Entrance Exam

For NATA, 12th should be passed by PCM Group. So, physics is necessary.

For IIT you must clear JEE Mains and Advance and then AAT.

You can appear for NATA but you can't get admission in architecture course as the eligibility criteria is 12th passed with maths and English for science students.
I hope it will help.

You only need a minimum of 55% in class 12th. Qualifying marks in NATA would be governed by the following rules. You must satisfy all three rules to qualify.
1. At least 25% must be secured in MCQ portion (30 out of 120)
2. At least 25% must be secured in drawing portion (20 out of 80)
3. Overall qualifying marks (out of 200) would be based on post-exam statistics and at the discretion of
the council.

If you have cleared NATA, everything should work out. You don't need to mention that you wrote a supplementary in Maths.