Sir, my UPSEE general rank is 31667, which trade can I get in government colleges?

No , it is quite difficult for you to get a good government college. But if you want to try then you can look for Lucknow University, Bundelkhand University . May be you will get chance in civil or mechanical branch. It depends on the cutoff list. The cutoff list depends on the number of students appeared in the exam and the level of paper whether it is easy , moderate or difficult. Do your counselling properly. You should go through counselling till last round . You may get seat in spot counselling. Otherwise you can look for private colleges:
1. Inderprastha Engineering College Ghaziabad
2. Krishna Engineering College
3. IIMT Engineering College Greater Noida
4. ITS Engineering College Greater Noida
5. Amity University Noida
6. Sharda University Greater Noida
So go through these Colleges if you can take admission in private College. Otherwise you should look for next year if you really want to take admission in a good government college. So go through these Colleges. You can come to know about these Colleges by visiting their respective websites.