MBA/PGDM

You have chances of getting into following Colleges:
CEG - College of Engineering Guindy, Anna University, Chennai
PSG College of Technology - PSGCT
UNOM - University of Madras
SSN School of Management
St. Joseph'S College of Engineering - SJCE
Thiagarajar School of Management

Since you have not mentioned your category so considering it as general. On such percentile and category you have good chances of getting some colleges through MHT CET counselling according to previous year's cut-off. As we go through previous year's cut-off then it shows that you can get following colleges-
1 - Kavi Kulguru Institute of Technology & Science, Ramtek - Civil Engineering
2 - Dr. D Y Patil Pratishthan's College of Engineering, Kolhapur - Computer Science and Engineering
3 - Shree L. R. Tiwari College of Engineering, Mira Road, Mumbai - Civil Engineering.

Yes, it is possible, it won't affect admissions for sure. There are students in top IIM who took time off for UPSC preparation. However, I can't say the same for placements.

Yes, there are some colleges such as Amity School of Distance Learning, IGNOU and Kotak Open University that offer a part-time Post Graduate Diploma in Human Resource Management programme. PGDM in HRM Highlights.

There are 5 reputed Universities that offer Free Online MBA Programmes
1- Kutztown University Of Pennsylvania Small Business Development Center This Kutztown University of Pennsylvania offers more than 90 online MBA free degree courses to those students who wanted to keep track of business and management career.
2- Open Learning Space.
3- University of Illinois.
4- Small Business Training Network.
5- University of Alaska. Hope That helps.

All IIMS have different criteria and weightage to the academia profile of a student. So, it is better if you go through the eligibility criteria of you specifically listed institutes. Good luck.

After completing the B.Com degree course, the two most common choices students have is to either pursue an MBA or an M.Com. Now, both courses have their advantages and rather than going for which one is popular, students should know what they want from their postgraduate education and choose accordingly. The MBA and M.Com are exceptional courses and can lead to some good careers. Both postgraduate courses are worth considering if you want to continue studying after your B.Com. In the following blog, there's a detailed comparison between both the courses that will help you decide which one is the course for you.

Graduation is necessary to be eligible for CAT.

It depends on your location.
1. In Bhopal, ACE CAT is the best.
2. In Indore, PT Education is the best.
3. In Pune, Career Launcher is the best.
4. In Delhi, TIME is the most popular.