Botany

No, without entrance exam, it is not possible, but you can talk to officials because most of the colleges have management quota, you can get a seat through management quota.

There are over 140 M.Sc in Botany colleges in India. Please refer to the link provided below for a detailed list of these colleges. You should be able to navigate to a college of your choice using the filters on the web page. Download colleges brochure, read questions and student reviews. Compare colleges on fees, eligibility, placements and other details at this link.
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https://www.shiksha.com/science/colleges/m-sc-botany-colleges-india

In-order to get admission in Ranchi University for Post Graduate course in Botany, you have to clear the entrance exam organized by the university.
Admission Eligibility: B.Sc/ B.Sc (Hons.) with 55% aggregate marks.
For More Info please visit: http://www.ranchiuniversity.ac.in/2014-03-31-05-27-00/2014-04-02-06-49-40/botany.html

Please refer to the link provided below for eligibility criteria to pursue M.Sc in Petroleum Geology from The Maharaja Sayajirao University of Baroda.
https://www.shiksha.com/science/course/m-sc-in-petroleum-geology-the-maharaja-sayajirao-university-of-baroda-vadodara-179243

Yes, all biology, physics & chemistry portion of 11th & 12th CBSE board. You can expect many knowledge-based MCQ questions as well.

It depends on college to college. Yes, in prestigious colleges, they take an exam, and in some colleges, they offer you on the basis of your graduation percentage.

Yes, you can apply but you must have mathematics as a subject in your 10+2 course.
Thank you.