Exam

Yes, of course, you can get admission.

Admission in NIT is based on JEE Mains score. You may use following link to predict in which college you can get admission based on JEE Advanced score: https://www.resonance.ac.in/reso/news/jee-advanced-branch-allotment.aspx

You are clear about your professional goal. You are advised to appear for CAT in final year of BMS. Why do you want to waste one year by appearing in CAT after BMS. It will be good idea to start your CAT preparations now.
All the best.

Hi Vansh,
Greetings from Shiksha.
Once you set your goal then nothing is impossible i am sure you will crack NDA exam just keep in mind these things regarding NDA
Applicants to the NDA are selected via a written exam conducted by the UPSC, followed by extensive interviews by the SSB covering general

Yes, you can get admission but that totally depends on whether the admission are open at that point of time.