M.Sc

Yes, you can apply if you meet the eligibility criteria.

You need to select the same subject in the UGC NET exam in which you have done your PG.

You should check with authorities in your college if you are eligible to appear for back logs. I am sure there must be some provision for students who have failed to clear the subjects in their semester exams. You can ask faculty or consult with other students who have backlogs for the same. Regards.

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Hi, The syllabus can be described in the following table:
Core Courses:
Bio systematic, Structure and Functions of Invertebrates
Tools and Techniques in Biology
Animal Physiology and Ethology
Genetics and Evolution
Structure and Function of Vertebrates
Environmental Biology
Elective Courses:
Biology of Parasitism
Chronobiology
Proteins- Structure, Functions and Evolution
Structure and Function of Genes
Animal Behaviour
Comparative Endocrine Physiology.

Hi, Universities in India for M.Sc. Botany or M.Sc. Microbiology :
M.Sc botany: https://www.shiksha.com/science/colleges/m-sc-botany-colleges-india
M.Sc microbiology: https://www.shiksha.com/science/colleges/m-sc-microbiology-colleges-india.

Syllabus:
The syllabus consists of some core subjects and electives. At the end of each semester students has to submit an assignment which is the part of the internal assessment.The syllabus is made in such a way that it focuses deep into the analytics and methods to make a person function practically.
The subjects offered in almost all institutions are :
1) Real Analysis
2) Algebra
3) Number Theory
4) Topology
5) Probability Theory
6) Differential Geometry
7) Linear Programming
8) Complex Analysis
9) Geometry of Numbers
10) Elasticity
11) Vector Analysis
12) Field Theory

Please refer to the link provided below for important tips and tricks for preparation of top M.Sc entrance exams.
How to prepare for top M.Sc entrance exams:- https://www.shiksha.com/science/articles/how-to-prepare-for-top-msc-entrance-exams-blogId-13489