Exam

For accurate analysis please use Shiksha JEE Mains college predictor
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor
Good Luck.

Yes, colleges like IIM definitely expect its students to qualify CAT with 99+ percentile, then only you are eligible to take admission there.

Syllabus: Same as CBSE XI and XII standard physics, chemistry and mathematics. Section-I: Subject proficiency Test (SUPR), sample questions: https://drive.google.com/open?id=1PxYNsMpYo5eNEVZKzL08iUGs3gzQs8LS
Section-II: Research Aptitude Test REAP includes critical and creative thinking questions, Sa

All the government colleges in INDIA take admission on the basis of JEE score itself. Some state conducts their own JEE exam like West Bengal as WBJEE. So, most of the government colleges take admission based on JEE marks.

It is compulsory to give BITSAT exam for integrated M.Sc courses. You need to score above 265 to get into an integrated M.Sc course at Pilani campus.

Kindly visit the link:
https://www.shiksha.com/mba/mat-exam-cutoff
Good luck.

Kindly visit the link:
https://www.shiksha.com/mba/mat-exam-cutoff

Your son has got very good score. Your son stands a high chance in getting IIIT-Bangalore. Though, you should be aware that IIIT-Bangalore offer integrated M.Tech and not purely B.Tech which is B.Tech + M.Tech. You should also try for IIIT-Hyderabad which is top notch. Seeing the percentile, I hope

For MBA, the common entrance tests are CAT, MAT, XAT and CMAT. Institutes providing the course:
Indian Institute of Tourism and Travel Management
Christ University
Kerala Institute of Tourism and Travel Studies
VELS University
Rashmis Transworld Academy
The Global Open University
Central University of Jamm

MAT exam fees for 1 exam in Rs. 1,550. If you want to attempt 2 exams the fees will be Rs. 2,650.