M.Sc Zoology

No, the admission is through merit. You can find the details on college's website.

Yes, Institute of Engineering and Management Studies offers distance courses, and you may do your M.Sc. from here. For more information, you may please check this link too- https://www.shiksha.com/college/institute-of-engineering-and-management-studies-bhubaneswar-36313

The M.Sc. Zoology common entrance syllabus is as under.
1. Core Courses:
a. Bio systematic, Structure and Functions of Invertebrates
b. Tools and Techniques in Biology
c. Animal Physiology and Ethology
c. Genetics and Evolution
d. Structure and Function of Vertebrates
e. Environmental Biology
2. Elective Courses :
f. Biology of Parasitism
g. Chronobiology
h. Proteins- Structure, Functions and Evolution
I. Structure and Function of Genes
j. Animal Behavior
k. Comparative Endocrine Physiology.

Some of the top institutes for M.Sc Zoology in Karnataka are mentioned below:
Christ University, Bangalore
Yenepoya University, Mangalore
Jain University - [JU], Bangalore.

Hi Anjali,
Yes, there is an entrance exam for M.Sc Zoology and many universities such as Delhi University, Punjab University, JNU and many other universities. Entrance is conducted nearly in month of May and June and you can visit their site for further information and there is negative marking in these exams. Good luck.