IIT Bombay - Indian Institute of Technology Mumbai Answered Questions

Yes, to appear in JEE (Advanced) a diploma holder can apply in JEE Main but his rank and score for JEE (Main) will not be declared as diploma holders cannot apply for admission in NITs and CFTIs through JEE (Main) channel. * The criteria of marks for diploma holders will be : If a Board gives aggregate marks considering the results of all three years of a 3-year diploma or courses of equivalent duration, then only the marks scored in the final year will be considered. Similarly, for Boards which follow a semester system, the marks scored in the final two semesters will be considered. * One of the criteria for admission to IITs and ISM is that the candidate should satisfy at least one of these two criteria: 1-He/she is within the category-wise top 20 percentile of successful candidates in his/her respective Class XII (or Diploma) Board examination. 2-He/she has secured 75% (for GEN or OBC-NCL) or 70% (SC, ST or PwD) of aggregate marks in the Class XII (or equivalent) Board examination. *All the rules listed above were followed in 2015.So keep checking if there are any changes.* In order to get admission in aerospace engineering at IIT Bombay your AIR should be less than 1500 more or less.

I personally relied on the study material provided by the coaching classes but still there are some nice texts like
For JEE Advanced
Physics - HC Verma(for Basics), Halliday Resnick Walker, if further you can go for I E Irodov (but personally i think it not required)
Chemistry- Morrison Boyd, Solomons Fryhle, M S Chouhan for question ( other books too from Balaji Publication on inorganic and physical are also good for questionsl like VK jaisawal) R C Mukherjee, JLee for Inorganic NCERT is quite nice
Maths- Hall and Knight , S L loney , also the whole arihant series topic wise books are nice, for questions Tata Mcgraw Hill , A Das Gupta
For JEE Mains
NCERT for all the 3 subjects especially for Chemistry
For physics NCERT + HC Verma
For maths NCERT+ arihant series will get the job done.

For Aerospace branch last year the closing rank was around 1500 and year before that was 1800 so you must have An AIR under 1500 to be on safe side. Regarding fees till this year the fees was around Rs.1,50,000/- for 1 year but from this year the fees is increasing and will most probably be around Rs.2,60,000/- for 1 year.