Hello,

Yes, you can become an engineer without any entrance exam. Here is how! However, government colleges do not take admission without entrance exams but, there are colleges that provide direct admission based on 12th marks. But you should score at least 45-50% in class 12th. some of the colleges are:

1. RV College Engineering, Bangalore.
2. PESU, Bangalore
3. VIT Vellore
4. SRMIST, Chennai
5. JNTUHCEH
6. Reva University
7. BITS Hyderabad
8. BIT Bangalore

These are few colleges that provide admission without any entrance exam. For more details, you can visit to :

https://engineering.careers360.com/articles/btech-college-in-india-without-entrance-exam-fees-structure-fsa#:~:text=Students%20don't%20have%20to,Btech%20direct%20admission%20in%20India.

Hope it helps.

All The Best