Model

To become a male fashion model, the height requirements are between 6 feet and 6 feet 2 inches tall. Jacket should be a size 40 regular. Male models generally need a lean build; larger muscles in the arms and thighs are not desirable because they tend to pull the clothing. Clear skin and straight teeth are musts.

You can simultaneously try for the freelance modeling projects if you have got a good height and great looks.

Please ref.
http://urbansocialites.com/physical-requirements-to-become-a-model/
http://www.wikihow.com/Get-Into-Male-Modeling

The first and foremost thing to do is get your portfolio created by a good photographer. Then you will have to work on freelance projects to give your career a start and once starting it off, you may try to get into proper modelling after applying for various screen tests.

Auto mobile is a specific brach of mechanical engineering in many institute so the gate do not take specific exam on it now a day. You should appear in GATE exam and the GATE score will be valid to get admission in automobile engineering too.