MBA Private college

Dear student,
Universities with their own entrance other than those which you mentioned are:
Bhartiya Vidhyapeeth Pune
Jamia Millia Islamia
Narsimonji Mumbai
All the best.

There are many good colleges, which accept CMAT scores and application forms are still open.
1. Loyola College.
2. Jaipuria – Noida.
3. KIIT.
4. ITM.
5. IFMR.
6. KJ Somaiya.
7. Welingkar.
You can check the below mentioned link:
https://www.shiksha.com/mba/resources/application-forms.

Dear Subrata,
A year loss for MAT exam will affect because for clearing MAT exam it takes less than a month preparation, but if you are graduating this year and targeting admissions in next year I suggest you to prepare for CAT/XAT/SNAP/IIFT because these exams carries value.and if you manages to score anything above 85% then you will be getting in top 20' business schools.
All the very best.

In private you can look for colleges like SP Jain Mumbai, XLRI, Welingkar Mumbai, Alliance Bangalore, UPES Dehradun, ICFAI Hyderabad , IIFT and KJ Somaiya. The dates for GD/PI interviews are already out so if you are interested you can register and appear for GD/PI. Some of these have their own entrance too for candidates who do not have valid CAT/MAT/XAT/NMAT criteria.