Diploma

Yes you can take part in Lateral Entry for B.E. / B.Tech IN ANY OF THE FIELD
There shall be college level counseling for each branch and course selected by you in each college.
College basically can be inculcated in various heading qualities such as
Infrastructure
Fee
Academic
Co curricular
Placements
And coordination between teachers and students which helps you to select a good government college. Please specify the state in which you want the college then i can more betterly give you suggestions

Top Mechanical Engineering colleges in India:
Indian Institute of Technology Bombay- IIT Bombay
Indian Institute of Technology Delhi- IIT Delhi
Indian Institute of Technology Kanpur- IIT Kanpur
Indian Institute of Technology Madras- IIT Madras
Indian Institute of Technology Roorkee- IIT Roorkee
Birla Institute of Technology and Science (BITS-Pilani).

Dear Fazaludheen,
List of Examination Centres of this university are -
(i) Patna College
(ii) Science College
(iii) BN College
(iv) Vanijiya
(v) Magadah Mahila
(vi) Patna Law College
(vii) Patna Women College

Yes, the university is recognised by the government of India through UGC. The university can award Diploma to students.

Eligibility:
Candidates who have completed 10+2 or its equivalent from a recognized board/institute are eligible to apply.
Admission Process:
Register and Apply:
Interested candidates can apply online with the required information.
Merit Screening:
Admission is based on the marks obtained in 10+2.

Sorry to say, but they don't have automobile engineering Diploma. Other courses available are chemical engineering, mechanical engineering, electrical engineering, electronic engineering, civil engineering and civil engineering.

The course duration is of 18 months. And, for more details kindly check out the link mentioned below :
https://www.shiksha.com/hospitality-travel/culinary-arts/course/diploma-in-bakery-and-confectionery-institute-of-hotel-management-catering-and-nutrition-delhi-library-avenue-pusa-90919