CUSAT

If any university is UGC and AICTE approved, it is best. Both the university are offering slimier course. Content and syllabus is important. KTU, I think is conducting theory exam, whereas MG is conducting online test. So, you have to check many other parameters i.e. supply of books, conducting special sessions to solve our doubt, when they provide degree certificate. And, main thing is any study center must be very transparent about fees.

No, it's not necessary to apply for CAT to get admission for 5 years integrated course in CUSAT, you can also get admission through CMAT and MAT scores.
Details are mentioned below:
https://www.shiksha.com/mba/exams/cusat-mba

The syllabus will have basic questions from all subjects you have in 12th.

Distance education should be your last option. Going for a regular course is safe.

How to Download Admit Card:
Candidates can download their admit card by following the procedure given below. Visit the official website link (https://cusat.nic.in/). On login page, enter your username, password and security code. Enter the security code and click on Sign In button. On logging, click on Admit Card tab. The admit card will appear on the computer screen. Check details printed on admit card and take a printout of it. Keep the printout of it and preserve it till the admission procedure. Regards.