Colleges in Pune

95 percentile is a general trend, but it can vary according to the quality of students every year.

For mechanical engineering :
https://www.shiksha.com/top-mechanical-engineering-colleges-in-pune-rankingpage-48-0-0-174-0
For automation engineering :
Planet Automation Systems
Chintamani Nagar, Kondhwa Khurd, Pune
09850396034
Prolific System ans Technologies pvt ltd
www.prolifictraining.com
Office No. 36, First Floor, Preet Chambers, Mumbai Pune Road, Wakde Wadi, Pune
020 25533691
PLC Automation Training
www.plctrg.com

Padmashree D Y Patil College of Architecture, Vidya Pratishthan's College of Engineering (VPCOE) and Bharati Vidyapeeth College of Architecture are the top colleges for B.Arch in Pune.

There is a Common Entrance Test (CET), only through CET the admission to such colleges shall will given, which is conducted by the Maharashtra Government. It's more like an entrance exam.
For more proper information, follow this link: https://ilslaw.edu/admissions-by-central-entrance-test/

ISB&M Nande is a much more better option than BIMM not only on the academic basis but for the further individual enhancement which leads to over all development of a candidate. Regarding the infrastructure of the campus, it is situated in one of the best location of the Pune with good accommodation and many other facilities within in the campus.
For the placement the average placement lies between Rs 6-7 lakhs while the highest went to Rs 17 lakhs. Brands like Credit Suisse, Asian Piants, Con Agra, Volvo, etc. come for the summer as well as finals recruitment.

Among these two, MITSOM is better option. You could also try Balaji group.

Following are the best colleges as per the brand value:
1) IIEBM
2) St.Francis
3) Indira

No , Mathematics is an important subject in BCA, so you are not eligible for it