Now as your rank is 31000 and you are really interested in cse, lemme break some facts..
1. Don't keep your hopes high for a very good college..No doubt it's your performance that matters finally.
2.If you choose to drop cse as your branch you probably might get a better college.

Now with your options I can suggest the below colleges.

1) Don Bosco Institute of Technology Bangalore

2) J N N college of Engineering Shimoga

3) Maharaja Institute of Technology Mysore

4) K S school of engineering and management Bangalore

5) A. C. S college of Engineering.