Indian Institute of Technology, IIT Bombay

First of all, many congratulations for your excellent performance in JEE Advanced. According to your marks, you will easily get admission in IIT-Mumbai for electrical engineering. On the basis of JEE Advanced score, there is no scholarship. Other scholarships are present inside the college. Do visit this website for more information:
http://www.indiaeducation.net/iit/bombay/fees-and-scholarship.aspx

Hey Nitesh,
I think that It's very difficult for you to take admission her with this score in IIT Bombay because your JEE Mains marks are very low.
I hope you understand well
You can check your rank based college here:-
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

Your marks are very low, you have just cleared the cutoff in JEE and your 12th percentage is very low, lower than the eligibility criteria. You are not eligible to get any NITs or IITs. But you can go for state level government colleges and private colleges across India.

Yes, IIT Bombay is best to do aerospace engineering. You will get a large amount of practical knowledge in IIT Bombay. The faculty and facilities of this college are simply world-class. Best of luck for your future and if any query, feel free to ask. If you like the answer, do upvote.

Specify the question.

In IITs, admissions are done only through JEE Advanced
JEE Mains exam is considered for admission into NITs and IIITs.

Well for M.Sc Degree at IIT Bombay, you need to give IIT JAM exam. I have given GATE exam (not JAM) for M.Tech, but my guess is that the admission procedure would be similar. Get a rank within top 150, after which are shortlisted for screening test+interview (sometimes only interview). Only after clearing those interview you are admitted. For an IITian the GATE/JAM exam is exempted but you need to clear a minimum GPA limit for this. And yes, maths is compulsory.

https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor
This is the college predictor link. Here, you will get that what college you will get.

To pursue B.Des from Industrial Design Centre - IIT Bombay (IDCIITB, one needs to have a qualifying mark in the UCEED (entrance test conducted by the institute).
For further details regarding this course please refer to the link provided below:
https://www.shiksha.com/design/fashion-design/course/b-des-industrial-design-centre-iit-bombay-idciitb-powai-mumbai-255094