Hello,
BMS college of engineering have courses where cutoff are in 4 digits.

• CSE  477
• EEE. 1439
• ECE 711
• Civil engineering 6093

It's is the civil engineering which has highest closing rank but your rank is a bit high.. still you can apply for it and wait for last round results. May you can get an admission.
Some of the college you can consider:-

• SKSJT INSTITUTE OF ENGINEERING
• DR. AMBEDKAR INSTITUTE OF TECHNOLOGY

FOR THE  abive you two college you can apply for civil engineering or EEE only.. it's  2019 cutoff but may change in different round of counselling.
Hope you will get one!
Good luck!

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