Indian Institute of Technology, IIT Bombay

IDC IIT Mumbai is offering B. Des. Courses in the following specializations.
1. Industrial Design
2. Visual Communication
3. Animation Design
4. Interaction Design
5. Mobility and Vehicle Design
So from above IIT Mumbai does not offers B. Des. Course in Interior Design.

The closing cutoff ranks of IIT Mumbai for year 2020 are given below in asked category for an idea.
1. Aerospace Engineering: 591
2. Mechanical : 386.

You have to simply qualify the JEE Main exam in order to become eligible for JEE Advanced. As per the last year of trends, the closing ranks in asked courses are given below for general category Male candidates.
1. Mechanical : 999
2. Civil: 3005
So from above ranks below 1000 and 2500 in JEE Advanced are good enough for Mechanical and Civil respectively.