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First of all, let me tell you there are two types of universities:-
1) Autonomous under MU
2) Deemed Autonomous
The former university works according to their own rules but at end you get a degree certificate under Mumbai University while the latter one provides you a degree under their own university like Mukesh Patel or KJ Somaiya to name a few. Except VJTI and the deemed ones all other colleges provide BE degree only. The perks of autonomy are that there are no issues with Mumbai University. You get many holidays, papers get checked fast, exams get over as quick as possible. So I would recommend going for autonomous first then moving to non-autonomous. Hope this helps!
All the very best!

Raunit, yes it is possible. But most of the Govt. Polytechnics are done with their entrance tests are in last stage of their admission process. Better would be you try for admission in some good private university where admission process is still on.
Another thing is better option for you would be to join dual Diploma B.Tech course where you save yourself of the pressure of entrance tests after Diploma course.
After doing a diploma you get direct admission in the second year of B.Tech. There are many universities in India that are offering you these dual Diploma- B.Tech courses. Some of them are also offering you scholarships based on your percentage in your previous qualification.
So, I feel instead of simply doing a diploma and then again starting with the search for a college/ university for B.Tech,it is better to take admission in a dual Diploma-B.Tech course.
Here are some of the universities, you can visit their websites for more details:
MVN University, NH-2, Delhi-Agra Highway (NCR), Haryana
Lovely Professional University, get Road, Phagwara, Punjab
Maharishi Markandeshwar Engineering College, Ambala, Haryana
Best of luck!

Documents required at the time of admission in DU are following-
Documents required at the time of admission class 10 Board Examination certificate class 10 marks sheet class 12 marks sheet class 12 Provisional Certificate / Original certificate recent Character certificates/ST/PWD/CW/KM Certificate (in the name of the applicant) issued by the competent authority OBC (Non-creamy Layer) Certificate (in the name of the applicant) as in central list transfer certificate from school / college as well as migration certificate from board / university are required from those students who have passed senior secondary exam from outside Delhi two passport size self - attested photographs
Only self -attested copies of documents/papers will be accepted by the university.