with a 89.2 percentile in JEE Main and rank of 114572, do i stand any chance of getting any engineering in government college. If yes, please let me know the options.

Hello,
With rank of more than 1 lakh in JEE Mains 2020, you have very less chances of getting a seat in any government engineering colleges like NITs IIITs and GFTIs.
If you are from general category, then you have almost no chances. If you are from reservation category, then. You might get non core branches like food technology, biomedical engineering,etc in some of the newer NITs like

• NIT Srinagar
• NIT Manipur
• NIT Mizoram
• NIT Arunachal

Please visit this link to use the JEE Mains college predictor to get to know the probable colleges according to your rank

hope it helps