Indian Institute of Technology, IIT Bombay

Every year, the cut-off varies. 300-400 was the closing rank in 2017.
Hope this year it may vary slightly.

Hello Mayur,It is indeed heartening to know your dream of joining the premium institute of India. You have already won half the battle.
IITs do not give lateral admission. However, they accept Diploma as equivalent to class 12th. Hence, you need to score 75% marks or more in your Diploma, amd then clear JEE Mains followed by JEE Advanced.

Candidates are selected based on GATE score/IIT merit and performance in interview.
Exemptions:
Candidates having two years of relevant work experience are exempted from requirement of GATE score, provided their candidature is sponsored by the employer.
Candidate having an B.Tech. Degree from IITs and having a CGPA/CPI score of 8.00 (on 0-10 scale) and above are exempted from requirement of GATE qualification. They may be admitted to M.Tech. Program under TA/RA positions through written test and/or interview. Regards.

Getting into IIT Bombay- Admission
1) For all B.Tech programs- JEE Advanced
All the IIT aspirants have to sit for JEE Main and afterwards, JEE Advanced. Only the top 150,000 scores in JEE Main will become eligible to sit for JEE Advanced.
2) IIT Bombay Eligibility
JEE eligibility criteria apply to all the IITs for admissions to their undergraduate programs. Based upon their score and rank in the JEE Advanced exam, shortlisted candidates are called for counseling. Regards.

Dear Spatesh!
For Aerospace Engineering from IIT-B, you need to have your AIR Rank below than 250-300 in Jee Advance. As per the last year's trends.
Hope this helps.
Good Luck.

Hi Rohit!
Yes, Industrial Design Center which was set up by IIT Bombay does offer M.Des in Mobility and Vehicle Design. You can find a detailed information about the course on this page https://www.shiksha.com/design/industrial-product-design/course/m-des-in-mobility-and-vehicle-design-industrial-design-centre-iit-bombay-idciitb-powai-mumbai-255083.