Exam

There are some colleges that take direct admissions;
-Shiv Nadar University
-UPES School of Business
-NDIM
-IMS Gaziabad
-IFIM College
-MIME Bangalore
-NSB Academy
-VBS
-Sri Balaji University
There are many more you can go for.

Top B Schools that do not necessarily require CAT Scores are:
ISB Hyderabad
XLRI Jamshedpur
IIFT Delhi and Kolkata
SPJIMR Mumbai
JBIMS Mumbai
SIBM Pune
NMIMS Mumbai
TISS Mumbai.

Visit the link given below for information.
https://www.shiksha.com/mba/articles/how-mat-score-and-percentile-are-calculated-blogId-14481

Here is the list of few colleges-
NSB Bangalore
AIMIT Bangalore
RV institute of Management
SIBM Bangalore
ITM Bangalore.

Please apply for the banking exam.

For taking admissions in top MBA colleges, a student is required to clear CAT exam first.

Apply for colleges that you are eligible for.

Yes, anybody can do any professional course at any age.

It completely depends on college and universities.

With your expected CMAT Score of 140 - 150, given below is the list of colleges where you have a good Probability of getting selected:
Prin. LN Welingkar Institute Of Management Development & Research, Mumbai
Institute of Management Technology Nagpur
K J Somaiya Institute of Management Mumbai
SIMSREE Mumbai
SIES Navi Mumbai.