can i get admission in government engineering college with my betterment result

Yes you can go to jntu,osmania if your eamcet rank is below 2000 for cse, And jntu sultanpur is also very good campus u can get admission with a rank below 8000 . I am talking about OC.
Or you can go to nit/iit/bits but you should have minimum of 75% in ipe to write the exam

Yes, you can take admission in government engineering exam by giving betterment result. You should get 75% marks in your boards exam or you should be in top 20 percentile to be eligible for NITs/IIITs/IITs and GFTIs.

Each Gov. college has different criteria to take the admission If you want to go for improvement exam for good result then according your score you can apply for any colleges whether IITs, NITs. IIITs, GFTIs or any other Gov. college. For further eligibility to apply for IIT JEE exam you can go through with given below link.

JEE main Eligibility criteria