Indian Institute of Technology, IIT Bombay

The eligibility criteria of M.Des in Mobility and Vehicle Design from Industrial Design Centre - IIT Bombay is given below.
Eligibility criteria : Bachelors Degree in Design/Engineering/Architecture/ Interior Design: 10+2+4 years (minimum four year Bachelors course).
Note: B.Plan. considered equivalent to B.Arch. Four year B.Sc (Engg) course after HSC considered equivalent to BE/B.Tech.
OR Professional Diploma in Design: 10+2+4 years (minimum four year Diploma program).
OR BFA Sculpture (4 year professional program with entry after 10+2).
So from above B.Des is not mandatory for the asked course.

The admission in IIT Mumbai are based on ranks obtained in JEE Advanced. Last year's closing rank in B.Tech CSE at IIT-B for neutral gender general category was 63.

For every college KCET rank is required, So better to write KCET and however with respect to rank you can get the college. Government Colleges are also there.

The last year's closing rank at IIT-B in Chemical Engineering in General Neutral gender and PWD category was 123, which is equal (approximately) to 265 Marks.