CAT

You can write CAT exam, if you are a final year graduate student or completed your graduation.

The eligibility criteria for CAT is any graduates or final year graduates.

I would suggest you to opt for a career aptitude test. This will help you to gain an insight about your personality. You will be able to figure out the careers, which you may opt suitable to your personality.
These tests are not always accurate but they definitely provide you with some sort of guidance, which is helpful on deciding your career path. And a word of advice, don't worry and stay relaxed. Everything will be fine. Just give some time to yourself.

Although IIMA didn't declare the cutoff of ABM, in my experience it was close to 93 percentile.

CAT is an objective type examination consisting of following sections:
Section I: Verbal Ability and Reading Comprehension;
Section II: Data Interpretation and Logical Reasoning; and
Section III: Quantitative Ability.

You can refer to link mentioned below:
https://iimcat.ac.in/per/g01/pub/756/ASM/WebPortal/1/index.html?756@1@1

IMT Nagpur gives weightage to your academics as well as your entrance exams. 10th score seems low so I would suggest you to score well in your graduation and CAT to get admission here. All the best!

Hi,
CAT 2016 takers need to be graduates in any discipline from a recognized institute or university with minimum 50% marks in aggregate or equivalent CGPA. For the reserved category candidates, the cutoff percentage is 45%. Final year graduation or Bachelor degree students will also be eligible to apply for CAT 2016. There is no age limit for appearing in CAT.

Dear Farhin,
Since, there are just few months to crack CAT 2016, you are advised to check the 10 tips, which will be beneficial for you.
You can check the below mentioned link:
https://www.shiksha.com/mba/articles/cat-preparation-blogId-20079

Dear Sumit Das,
As per last year, the fee of IIM was between Rs.9 lakh to Rs.19.5 lakh.
You can check here fee structure of MBA in top 20 B-schools:
http://goo.gl/fYI1w4