Hello aspirint,
I am here for helping you...
as per your doubt I want to inform you that you definitely can go for IIT for doing your mtech degree and you definitely can have MNC but for that you will have to appear for GATE examination and will have to crack this examination as per the cutoff of any selected IIT and it doesn't matter that how much year back you got in your BTech examination yes but for having MNC you need to have good marks in your mtech and will have to move with determination will have to focus on your studies will have to  collect skills as much as you can.
I hope it will be beneficial for you....
For more queries you can  upvote my answer and can ask in the comment section below...

Best of luck...

Hello Midasala. 

I would like to tell you that if you clear the backlog then you can have your placements without any delay as you need to submit your gradereport and degree certificate. With back you would definitely not get the certificate and also your cgpa would reduce. It depends from company to company and interviewer to interviewer. 

If you have cleared your back paper then it would most probably get ignored but the interviewers but if not than certainly it won't leave a good impression to them. These companies mainly look for your coding skill so hopefully they should ignore the back part most probably. Also doing MTech from IIT Bombay after your BTech will help you alot in your placement for Job and you would have a great chance for getting job in companies like Google, Amazon, Diercti etc. Just focus on your studies and if possible contact your college and higher authorities to know more about it and such cases of previous year and their statys. 

Hope it helps.