MBA Entrance Exam

Cut offs might vary every year depending on the number of applicants. A better answer can be obtained form the office of the institute. Previous year cutoffs might give you an indication

Common Admission Test (CAT) is national-level management entrance examination conducted by the Indian Institutes of Management (IIM). CAT scores are used for admission to various management courses across the country.
Common Entrance Test (CET) is a computer-based management entrance test. CET is conducted by the regional colleges eg. Maharashtra, Gujarat, Rajasthan, Tamil Nadu, etc and each have their own CET exams.

Below are some of the best bschools through NMAT:
TAPMI - Manipal
SIMSRE, Maharashtra
UPES Dehradun
XIME Kerala
IPE Hyderabad
BIMM Pune
All of these are good but if I've to choose the best then I would go with TAPMI & UPES. Both of these have good infrastructure, faculty, placements and industrial exposure.

You can refer this link for coaching centres in West Bengal:
https://testprep.shiksha.com/mba-entrance-exams-west-bengal-categorypage-14-47-1-0-0-1-127-2-0-none-1-0

The NMAT by GMAC exam has been, and will continue to be, a symbol of quality enabling test takers to access graduate management education and a career of choice, while providing schools access to top talent.

GMAT is basically for those who are interested in doing for MBA from foreign university mainly. GMAT is required for admission to most business schools.It is a computer-adaptive test.
Scores valid for 5 years.
Its cost is $250

The areas which you need to work on to excel in CAT are you logical reasoning skills, Vocabulary skills, Mathematical Skills ,Quantitative and Qualitative Analysis Skills and conversation skill.
I would recommend that you try out the study material from IMS / TIME / Career Launcher as your first resource.
Some of the Books recommended for CAT are-
How to prepare for Data Interpretation for the CAT TMH / Arun Sharma
Quantum CAT by Sarvesh Verma

For enhancing you Vocabulary go for Word Power Made Easy by Norman Lewis
It is brilliant book that helps you build a strong vocab. I would suggest you to buy this book and keep reading it again.
The book does not forces you to memorize any word, it explains the origin and history behind the word and hence making it easier to remember the words.
Know more on :
https://edudrona.com/questions/question/how-to-improve-my-vocabulary-and-spoken-english