IF you have completed your Diploma in Engineering after your 10th then you are eligible to go for any course of BTech through the later entry entrance. Through this examination, you will be provided admission directly to the 2nd year of the BTech. So yeah! if you have completed your Diploma then you can go for the BTech in Automobile Engineering.

The lateral entry examination is conducted by different states, so there are no all india examination for that, its a state level entrance.

To know more about Lateral Entry examination visit the link below:

https://engineering.careers360.com/articles/what-btech-lateral-entry-eligibility#:~:text=Tech%20lateral%20entry%20is%20the,first%20two%20semesters)%20of%20B.

To know more about Automobile engineering as a career visit the link below:

https://www.careers360.com/courses/automobile-engineering-course

I hope this answer helps. All the very best for your future endeavors!