Veermata Jijabai Technological Institute - VJTI Mumbai

You'll have to appear in the MHT CET 2017. The application form is available online.

Hello Amey,
Admissions to VJTI are based in MH-CET and not on JEE Mains, as some people are thinking. Earlier once when MH CET was not conducted in that marks of JEE Mains and 12th marks were added in some ratio to form a merit list for admissions. However, since MH CET is going to be conducted this year, JEE Mains has no relevance.

Hello Harsh,
Unfortunately, VJTI admission is not on the basis of AIR in JEE Mains. But, it is based on the entrance exam conducted by Government of Maharashtra.

VJTI, Mumbai for sure. VJTI, being an autonomous, government college, always has the edge over PICT. This also ensures recognition throughout India.

According to me, it is from CET but I will suggest you to prepare for JEE because the news is that CET is going to be cancelled for all engineering and medical students. If you will prepare for JEE and then there will be CET, it will not be difficult for you because JEE has little higher level then CET.
All the best.

BITS Pilani is Tier I engineering college equivalent to legacy IITs. I will recommend that you opt for BITS Pilani for an excellent career and growth opportunities.