Hello Bhavana. I hope you are doing well. You mentioned you have secured a rank of 37000 in KCET 2021. You didn't mention your caste in the question, so I assume you belong to General category and had Kannada Medium as Education Board. As per your rank, you have low chance to get admission at Mahatma Gandhi Mission's Jawaharlal Nehru Engineering College although you may get chance to grab a seat for various streams in other government and private engineering colleges which are not top-rated but good colleges. As per my opinion,  it would be better if you wait till the last round of seat allotment so that cutoff ranks get increased and the chances of getting a BE seat at better colleges get slightly high.

A good rank in KCET to get admission at top-rated colleges is from 1 - 10,000 for general candidates.

Nevertheless, based on this rank, you may get chance at few government institutes such as:

1. Janatha Education Trust's Vivekananda Institute of Technology (BE in CSE, ECE, ISE)
2. Government Engineering College, Chamarajanagar (BE in CSE, CE, ECE, ME)
3. University B.D.T College of Engineering, Visvesvaraya (BE in EIE, CE, ME)
4. MCE - Malnad College of Engineering (BE in Auto Engg, IPE)
5. Government Engineering College, Hassan (BE in CSE)

and more...

However, keep in mind that these assumptions are based on previous years' data and every year cutoff rank varies greatly.

To refer to the relation between marks and rank in KCET based on previous years' data, check out this article:

https://engineering.careers360.com/articles/kcet-marks-vs-rank

To know your college admission chances based on your Caste, Area Type, etc. & exam result and get your KCET personalised report with Top Predicted Colleges delivered on mail, I encourage you to use KCET 2021 College Predictor:

I hope you find this information helpful.

Thank you and all the best.