CBSE 10th

Yes, you can join PINHMCT for a Bachelor's degree, Diploma or integrated course after class 10th . Visit PINHMCT official website for more information.

Courses you can pursue after clearing class 10th:
Art Teacher Diploma.
Commercial Art Diploma.
Diploma in Beauty Culture & Hairdressing.
Diploma in Garment Technology.
Diploma in Stenography.
Engineering Diploma.
Industrial Training Institutes.
Laboratory Technician Diploma.

Being honest, it's difficult because currently, Kirloskar has changed their admission criteria and as per you score it's difficult to get the admission.

You can't do MBA after your 12th. You need a suitable degree before doing any Masters. So, check for colleges to do your BBA or engineering or any other management degree if possible.

Yes there are Diploma courses available after 10th in management. But they are not as good as you would think of them to be. I would recommend you to complete high school and then go for BBA or BMS if management is the field you wish to choose.

Getting calls from IIMs not only depends on academic profile and CAT score but also on co-curricular profile and work profile also. IIMs try to keep diversity in the batch, so they may prefer students from non-engineering background with slightly lower academic profile but a good CAT score. A good score in CAT around 98-99 percentile will definitely enhance your chances to get calls.

Yes, definitely, you have a chance to get a call from IIMs, provided you do well in CAT. For a better idea, you can visit the website of IIM and can check out about the weightage each IIM gives to these components, as each IIM gives different weightage to your past academic record.

See, there are many criteria which IIM-A, B, and K will consider before giving out interview calls or final admission. Like your graduation stream, graduation percentage, quality of work experience, and extracurricular (though there is no separate weightage for this, but it helps you a lot during interviews) and the list goes on. So, if you can share some more details about your profile, I can give you more meaningful answer. Still, considering these two things for IIM-K, I think anything above 88-90 percentile may get you an interview call. I cannot comment on IIM A and B.

Anything above 8.5 or 85% is fine but above 9.0 or 90% is preferable. But you should remember one thing that even if you are scoring 100% it's still not necessary that you will get into IIM-C as there are many other criteria which they consider while giving interview calls or final admissions.

I would suggest you Lovely Professional University, because in this university they develops a student 3 dimensionally and not much eligibility is required.