College of Engineering, Pune

Yes, it is considered, but don't worry, if you want to do mechanical engineering, first pass your class 12th exam, then you will get a fine college.

Basically, cut-offs are not fixed every year. They keep changing every year depending on the highest score and the difficulty of the paper. But. usually, COEP has a very high cut-off i.e. around 175-180. So, if you are aiming for CSE in COEP keep a target of minimum score mentioned above.
All the best.
Hope this helps.

Check out the college reviews for both the colleges for details:
https://www.shiksha.com/college/bharati-vidyapeeth-college-of-engineering-lavale-lavale-pune-37220/reviews
https://www.shiksha.com/college/d-y-patil-college-of-engineering-akurdi-pune-20837/reviews

Cutoff required in JEE Mains to get CSE in COEP:
To get into CS-IT, EnTC 188+ score is required, for mechanical, electrical it's 176+ etc.

It would be around 50K.

Hello,
I think lateral entry into any engineering college in Maharashtra is restricted to those who have passed their diploma in Maharashtra. But perhaps window to study in Maharashtra is still open by way of admission to engineering colleges run by deemed to be university.