Welcome to MSE!
First I explain What is CSIR-UGC NET ? It is a competitive exam for Awarding Junior Research Fellowship for doing Ph.D and Eligibility for Lecturership in India (The reason for mentioning this is to clarifying other users)
1) Structure of NET:
First of all, note that the syllabus of this test includes the following topics as you know:
Unit I: Real analysis, Linear Algebra
Unit II: Complex analysis, Abstract algebra, Topology
Unit III: Ode, Numerical analysis, Calculus of variations, Linear integral equations, Mechanics
Unit IV: Statistics
To Clear this Net Mathematical Science, you must familiar with atleast FOUR topics and personally I recommend the first two units.
2) Books recommended:
For Linear algebra, Axler book is fine but I also recommend Friedberg's Linear Algebra. Solve as my problems as you can from this books. I also mention two familiar problem books in linear algebra
Paul Halmos: Linear algebra problem book
Fuzhen Zhang: Linear algebra: Challenging problems for students
For real analysis, first work through Abbott's analysis or A basic course in real analysis by Kumereasan and then move on to Rudin. Baby Rudin book contains lot of challenging problems comparing to Abbott. For Problem Books, I recommend,
AMS Problems in Mathematical Analysis Book Series(3 books)
Asuman G.Aksoy, M.A. Khamsi: A problem book in real analysis
For Abstract algebra, I think Gallian is enough for CSIR NET. Anyhow, work first Gallian and then move on to Herstein or Artin. Solve as many problems as you can in these books. Also Gallian web page contains lot of resources for algebra.
3) Others:
At each time CSIR asks repeated type of questions like irreducibility, uniform continuity, use of identity theorem,diagonalizability, etc. (not many and not too little)
So solving previous years questions is necessary not sufficient!
From my point of view, trying to answer from Part A is just a waste of time. For preparing this exam, I advice you that do not try to buy a previous years solved books from online. Think and solve your own. Of course, this take lot of time, but that is not the problem. For solving exercise problems, remember, hints and answers in the book back should be consulted only after serious attempts have been made to solve the problems. If you ignore this
advice(not mine, actually Kenneth Ross from Elementary analysis), you will only cheat yourself!. Do not try to learn the different topics in isolation.
Last, Don't forgot the following two quotes for learning concept and solving problems:
From Axler:
You Cannot expect to read a mathematics the way you read a novel. If you zip through a page less than an hour, you are probably going too fast
From Polya:
There is a grain of discovery in every solution of the problem.
Good Luck!
Best Answer
For a book which contains lots of information with respect to probability and statistics, try Probability and Statistical Inference by Hogg and Tanis. I'm not sure how its price is in India, but it contains loads of information on multifarious topics, as well as no shortage of exercises. I used it for two classes in probability and statistics, and found it quite handy, so I think it is a fine starting point. If I remember correctly, it's also suggested in the syllabus for the actuarial exam in probability in the USA.
On other, more specialized topics that I saw in your syllabus, I'm not too sure. It seems like one could study an entire degree (or more!) on the material mentioned.
In particular, if you're interested in surveys and sampling, Statistics Canada has suggested reading for its candidates for employment in mathematical statistics positions. http://www.statcan.gc.ca/employment-emploi/recruit-recrue/ma/readings-lectures-eng.htm