To be very honest, considering your class 10th and 12th marks, your chances of making it into IIM Ahmedabad are very bleak especially if you are a general category student. 

IIM Ahmedabad has certain criteria pertaining to class 10th and 12th marks. Under this, it’s necessary for the average of 10th and 12th to be greater than 

• 80% in the Science stream
• 77% in the Commerce stream
• 75% in the Arts and Humanities stream

So, with your academic profile, even a 100 percentile in CAT will not fetch you a call from IIM Ahmedabad. However, you can go for top B Schools like FMS Delhi, SP Jain, MDI Gurugram, etc. that give more preference to CAT scores than par academic performance. 

No, IIM Calcutta does not usually reject you just because of a backlog in graduation provided that you have cleared it.

Majority of the batch consists of students from top colleges like IIT,NIT,BIT, DTU, etc. It's very common for a large number of students if these colleges have at least one backlog.

I have seen many cases where people receive calls from IIM Calcutta despite having repeated most of their courses. 

So no, a single backlog will not be a hindrance for your call from IIM Calcutta. 

You are eligible for IIM Ahmedabad. However, the question is whether you will get a call from IIM A or not. For IIM Ahmedabad, as per the 2021-23 shortlisting criteria, you need to be in the top 80% at each step of academics and CAT. But with your 12th score, you probably won’t be in the 80% as you are from the science stream. So you might not be shortlisted for IIM Ahmedabad.

Your chances of getting into IIM Ahmedabad or any of the BLACKI are quite thin. However, you should consider other top institutions like FMS and MDA that do not take into account past academic performance.

Despite the thin chances try to score 99.7+ in your CAT. Since you are from a non-Engineering background, you won’t face competition from among the engineering graduates. You’ll also get an advantage in the name of academic diversity. Make sure to get some work experience to make your chances of getting into IIM Ahmedabad better. 

Give your CAT all the effort. If not the top IIMs, you will get admission into the best MBA institutions in India.

My cousin recently got into IIM Amritsar with a profile of 8/7/7. She did not let her low grades discourage her and she strived hard to get a great CAT score. Don’t let your past affect your future prospects. Put your 100% effort and you will definitely get what you deserve. As far as her graduation score is concerned, not many scored above 8 GPA. So her 7 GPA wasn’t that bad. In class 12th also, most of the IIMs compare a score of 80 in the Assam board to an 80 in the Andhra board or CBSE. Engineers also face an academic diversity issue. So they need a higher percentile than other graduates. Nowadays IIMs are converting CAT percentiles to the percentage for the CAT weightage component. So, the gap between the 99 and 95 percentile stoops down to 2 points for 50 % CAT weightage. Had the CAT scores been taken, the gap would have been 10–12 points. Hence it makes candidates with low academic profiles difficult to get into IIM. Fortunately, my cousin was lucky enough to get admission as a GEM fresher with an average profile.

Full-time internships are often not possible when enrolled in the Fellow Program in Management (FPM) at SPJIMR Mumbai. 

FPM program is a full-time doctoral program in which students must complete coursework and research in order to graduate. Students in the FPM program are expected to spend the majority of their time on their studies and are not usually able to take on extracurricular activities such as internships. 

However, FPM students may be able to arrange for a part-time internship that does not interfere with their academic or research requirements. If you are an FPM student at SPJIMR Mumbai and want to do an internship, you should talk to your academic advisor or the program coordinator about your choices.

78% won’t be enough to get you into IIM Shillong. You need at least 80% in your 10 and 12 grades. So we can say that for the final selection you must have 98 percentile. Other criteria to be considered are:

• For engineers: Score of above 84 or 85 in 10th and 12th with min 8.0+ in undergraduate

• For non-engineers: Score of above 80 in 10th and 12th with min 7.5 in undergraduate 

This criterion is subject to change every year. Other factors that affect admissions are:

• Your performance in the interview 

• Gender

• Undergraduate stream

Both the IIMs will require above 85 to get admission. The eligibility criteria for IIM Kozhikode are a bit more strict than that of IIM Shillong. The minimum overall and sectional cutoff required for admission to IIM Kozhikode will remain 85 percentile and 75 percentile respectively for General category candidates.