The government engineering college in Banda is Rajkiya Engineering College.
The cut-off for this year has not been declared yet but we can get a rough idea of it from previous year's cut-off.
With a rank of 13001 in the general category, you will probably not be able to get admission here.
In 2018 cut-off, there were 3 rounds and the end ranks for various streams at the end of Round 3 were as follows-
- Information Technology- 6309
- Mechanical Engineering- 6844
- Electrical Engineering- 6916
The cut-off will most likely not reach upto 13000 rank this year so you do not have much chances of admission.
If you belonged to the SC/ST category then you could get admission here.
Don't be disappointed, you can try for other colleges as there are private colleges as well.
Use the below link to check the previous years' course-wise cut-off of Rajkiya Engineering College-
Hope this helps.