Allahabad

Hi Sakshi!
These are the best coaching centers in Delhi for civil service exam preparation:
1. Rau's IAS Study Circle
2. MS Vajiram and Ravi
3. Unique Shiksha IAS Institute
4. Chanakya IAS Academy
5. Elite IAS Academy
In Allahabad, you can take coaching from the following institutes:
1. Krishna Coaching Institute
2. Centre for Excellence
3. Anand Academy.

Not very sure but you can check the cutoff as well as related information on:
http://www.mnnit.ac.in/index.php/admission#postgraduate

Please refer to the link below:
https://www.shiksha.com/university/university-of-Allahabad/exams/Allahabad-university-lat-exam/dates.

As a general category, you must score minimum off 275 + to get admission.

CSE is the very popular branch in mnnit and in order to get you have to secure under 5000 if you belong to OBC category.

The student must be a graduate in any discipline from a recognised university.

Hi Sarang,
Hope you are doing well. Well, being a student of mass communication who is pursuing from national capital, I do know some of the good institutes where you might find your future aspects ready, but no idea about the about cities you have mentioned. Some of the great institutes might be:
For Bachelors:-
National Institute of Mass Communication, DCAC (Delhi College of Arts and Commerce)
AAFT, IIMMI, Heritage, IAAN
For Masters:-
IIMC, Amity school of communication, Take one school.

Keep your self updated. Read newspapers, u need to have good vocabulary, books are available in the market for the preparation for CAT.
For more help, you can join any of the coaching classes which offers CAT preparations.