Hello Aspirant 

Some of the good government Engineering Colleges in Kerala are:

1.Indian Institute of Space Science and Technology,Thiruvananthapuram

2.National Institute of Technology,Calicut

3.Cochin University of Science and Technology,Kochi

4.College of Engineering,Trivandrum

5.Government Engineering College,Thrissur

6.Government College of Engineering,Kannur

7.Government Engineering College,Barton Hill

8.Government Engineering College,Kozhikode

9.Government Engineering College,Stikrishnapuram

10.Government Model Engineering College,Thrikkakara

11.Indian Institute of Technology,Palakkad

12.Rajiv Gandhi Institute of Technology,Kottayam

13.Sree Chitra Thirunal College of Engineering,Thiruvananthapuram

You can visit this link to get more information:

https://engineering.careers360.com/colleges/ranking/top-government-engineering-colleges-in-kerala

So I hope you find this helpful

Thank you 

Good luck.