Hi,

According to your rank, you have very less chances for admission in core branches. You can try for your home state colleges. Also, For checking for your chances for admission, Certain other factors are also considered like your category, home state and preferred branches.

I would suggest you to check your best possibilities using College predictor tool. You can use the college predictor using the link - JEE Main College predictor

Hope this helps.

 Good Luck!!