Economics

Yes you are eligible for B.A. (Hons. ). Economics. The eligibility criteria of DU's is given below for an idea. Eligibility criteria :
1. An aggregate of 45% marks in the qualifying examination I. e 10+2. The merit shall be determined on the basis of one language and three best academic/elective subjects.
3. The applicants must have studied and passed Mathematics at the qualifying exam for admission to B.A. (Hons) in Economics.

If your clear with goal I. e the field of career you want to expertise and aspire, it will be more easy to make decision. It is you who can make the better choice
If B.A. ( History) is the means by which you can achieve your final goal. I will suggest B.A. From either of the college with suitable combination in allignment with future goal. If B.A. Economics suit you, it is more job oriented.

You have not written about the college for better response. However the eligibility criteria of DU's is given below for an idea. B.Ed. Eligibility criteria of DU : Candidates with at least 50% marks in aggregate either in Bachelors Degree and / or in the Masters Degree in Science / Social Science /Humanities/ Commerce or any other qualification equivalent thereto are eligible for admission to the programme. Here M.Sc. Economics is falling under Social Science as per Table-1 of B.Ed. Prospectus 2020. Admission criteria : Admission test
So from above you are eligible for B.Ed. If meeting the aggregate percentage of eligibility criteria.

Both are good but it is more beneficial to choose subject combination according to future goal. With B.A. ( Eco +Maths) you have more opportunities. But I suggest you to be more clear with future goal so that you can make better choice.