CAT

You can apply in the below mentioned colleges:
1. TAPMI.
2. IFMR.
3. Great Lakes.
4. KJ Somaiya.
5. Welingkar.
6. Christ University.
7. ITM – Mumbai.
8. BIM – Trichy.
9. BIM – Noida.
10. XIME – Bangalore.
11. Jaipuria Institute – Noida.
You can check the below mentioned link:
https://www.shiksha.com/mba/resources/application-forms

If you are in general category, I would advise you to reappear for CAT because it is very difficult to get into any good institution with this score; especially IRMA.

First of all, you did not mention the name of department you want to take admission and your CAT score is quite low and may not get you a call for MBA (full time), but you can definitely try for other departments.

Below mentioned are the top colleges:
1. Great Lakes – Chennai.
2. Welingkar – Maharashtra.
3. IBS.

Can't surely say. Last year, the cut-off was 80 percentile. It may change this year. Anyway, you apply and let's see the rest.

KIAMS do profile based selection where they consider your academic records, competitive exam scores, performance in our interview process etc. With the cumulative score of all these KIAMS offers admission. So if you have 50 percentile and above with good academic records you can expect a call from KIAMS.

Do apply for Nirma Ahmedabad, Tapmi Manipal, FORE, KJ Somaiya Mumbai, IMI Delhi, IMT Ghaziabad, LBSIM, LIBA Chennai and IFMR. Prepare well for GDPI.
Best of luck.

You have got a good score with decent academic record and work experience. You stand a good chance to get admission in top 15 colleges.
All the best.