CBSE

Well, considering your class 12th percentage, you have good chances of getting admission into BBA.

Yes, it is possible to take admission in UP board after CBSE board.

Last year, all the seats of Hindu College for B.A.(Hons.) History got filled in the first round only with the closing percentage of 98.00.

You have not written about the College/ University name from where you wants to pursue the B.Sc. Economics course. The eligibility criteria may varies according to Universities. The eligibility criteria of Hindu Kanya College Kapurthala is 10+2 with minimum 40% of marks with Math. Hence Math is needed at 10+2 level for B.Sc. Economics.

Don't be dependent on JEE , as the seats are very less as compared to seats for CET students.
Talking of your CET marks , if you are a general category student then its somewhat difficult to get admission,but if you are a SC/ST then definitely there is a probable chance to get admission. Beside all this things there is another way of getting admission by management quota .
Also remember that if you have domicile of maharashtra then only your CET marks will be considered.
Wishing you best of luck.