Sir! I secured GN 5932 , BCGL 851 rank in 2019 upsee what are my chances of getting a government college in up?

Yes, obviously you have good chance to get a good government College You have secured very good rank. Based on your rank you can get many government Colleges. As you  are in OBC category you will get some extra advantage. These are the Colleges where you can apply:

1. IET Lucknow

2. Chhatrapati Shahu Ji Maharaj University kanpur

3. Lucknow University

3. Bundelkhand Institute of Engineering and Technology

4. Rajkiya Engineering College Kannauj

You have chance to get government College in core branch.

These are the government Colleges where you can get admission easily. As cutoff vary from year to year. It depends on the level of paper whether it is easy, moderate or difficult. If you are interested in any private Colleges then you can get admission in these Colleges also. I have mentioning the top private Colleges of UPTU:

1. JSS Academy Noida

2. KIET Ghaziabad

3. Ajay Kumar Garg Ghaziabad

4. Galgotia engineering college Greater Noida

These are also Colleges where you can get admission. These Colleges are good in terms of placement. If your choice is CSE branch then you can get also this branch. If you have any other choice then go for it.you have good chance to get good College in other branch also like Electronics and communication engineering, Mechanical engineering,Civil Engineering etc.You can also predict your college according to your rank . You can visit sites of different Colleges and come to know about their fees, faculty and placement. Give your preference in the first round.