CAT

Good morning dear,
Look, colleges call students only when the students inquire about the same. Also, the colleges send emails in order to make you apply for it.
Thanks and all the best.

Yes, you are eligible to apply. The criteria is you need to have more than 50% aggregate in 10th, 12th and graduation. So if you get a call from them, you will get through if you clear their GD-PI process.

Yes, you are eligible for MBA entrance exam. You can clear the KT exam by the time your CAT entrance exam will be conducted and results will be announced. Just make sure you clear your KT exam. All clear results in all seems is preferred by institutes.

Yes, there are institutes for which applications remain opens after CAT results are announcesd. Just look for the application ads. Some of the institutes are - IFMR, ITM-Navi Mumbai, International School of Business & Media Pune / Bangalore/ Kolkata, IMI-Bhubaneswar, IMT-Nagpur and others.

Yes, you can apply for MBA program with this score at Manav Rachna International Institute of Research and Studies.

Hi,
You can try XAT (a tough exam, equal to or tougher than CAT entrance exam for XLRI and related institutes), MICAT (entrance exam for MICA), MAH-CET (Maharashtra CET), SNAP (for Symbiosis-Pune and related institutes), NMAT (for Narsee Monji - Mumbai and related institutes).

CAT Syllabus 2018:
CAT analyses the skills of the aspirant in four sections: Quantitative Aptitude, Verbal Ability, Logical & Analytical Reasoning and Data Interpretation. It is also a test of time management. Please refer to the link provided below for a detailed description of the syllabus for the CAT 2018:
https://www.shiksha.com/mba/exams/cat/syllabus

If you fall into CAT cut-off of IIMs then you will be getting calls automatically and for other colleges, you have to search according to your percentile and the college cut-off.

Yes, it's hard. You must be good in all aspects, right from English vocab to situational mathematics. I scored 92.3% only because of the dedication for one complete year.

You have to give at least one entrance exam. It doesn't need to be CAT only. Even MAT and several other such exams can get you through.