MBA/PGDM

Admissions for MBA are on the basis of entrance exams. So, you would not be able to study in any good college without writing one of the entrance exams like CAT/XAT/CMAT/MAT/MH-CET.

Definitely, BIMTECH is a better option if you get a call.

Some of the best colleges include:
North Eastern Regional Institute of Science and Technology, Nirjuli
Department of Business Administration, Assam University, Silchar

Admissions for MBA are on the basis of entrance exams. So you would not be able to study in any good college without writing one of the entrance exams.

For MBA, NIT-Silchar is not recommended since it's an average college.

You can apply. You can apply even without MAT. Below are the complete details regarding MBA admission at Alliance University.
Eligibility:-
1. Bachelor's degree with a minimum of 50% marks (45% for SC/ST) in aggregate from a recognized University.
2. A high score in GMAT/CAT/XAT/MAT/ATMA/CMAT/NMAT by G

Hi,
Amity University is a decent B-school for pursuing MBA. However, in terms of ROI, it's quite average: fees - 11L & average package - 5L. They offer a huge variety of courses and as mentioned on their official website, boast of experienced faculty. Some of the recruiting companies are Amazon.com,

As you say that it only accepts the CAT scores, I don't think there will be any chance for admission there still you can contact the admission cell of the college and also visit the college website for further assistance.

COCSIT is not a known college. You can refer the below link for some good hotel management colleges-
https://www.shiksha.com/top-10-hotel-management-colleges-in-india-article-10022-1

In PGDM, you will study general subjects in the 1st-year and you will get a chance to choose your favorite subjects for specialization in the 2nd-year. In MBA, you will study specific subjects related to your chosen stream of MBA.