Science

Yes, you can go for this with eligibility of graduation in mathematics with Statistics as a subject with 55% to 60% score.

That is not possible. You can take B.A. With economics and geography. Option of Economics in B.Sc. Is not available. B.A. Subject combination must be selected in such way that one have atleast 1 or 2 of these subjects ( History, Geography, Economics, Political Science). It is considered to be best subject combination if have any two of these subjects.
JADAVPUR UNIVERSITY offer B.sc in Geography/ Geological Science as a single subject.

Admission process will start very soon in the end of this month.

Yes, in AMU, M.Sc. Environmental Science is available you can join this year, forms are released, apply as soon as possible.

Yes many private colleges give admission without entrnace exams on basis of 10+2 marks or just on basis of first cone first serves Fees is comparatively higher.
Few of touch colleges are-
Vydehi Institute of Nursing.
MVJ Nursing College.
MS Ramiah Nursing College.
Krupanidhi Nursing College.
Manipal College of Nursing.
Navodaya College of Nursing.
Krupanidhi College of Nursing.
Aditya College of Nursing.

The fee structure at Bhai Ghanaiya Ekta College of Nursing for B.Sc. In Nursing is 25000 per year.