Chetan, NCERT are the to go books for NEET preparation and 95% of the questions are asked from NCERT. So NCERT should help you in developing the necessary problem solving skills for Chemistry and Biology. But the other books give you an insight of how to solve them in a short cut given that time management is also of importance. To help you with your NEET preparation, we have NEET Knockout packages that you can check at: https://learn.careers360.com/knockout-neet-may/ . And also there are few books that might help you in your preparation:

Biology Best Books:

NCERT Biology Class XI and Class XII textbooks
Biology Vol 1 and Vol 2 by Trueman
Objective Biology by Dinesh
Objective Botany by Ansari
Pradeep Guide on Biology

GR Bathla publications for Biology

Chemistry Best Books:

NCERT Chemistry textbooks for Class XI and XII
Physical Chemistry by OP Tandon
ABC of Chemistry for Classes 11 and 12 by Modern
Concise Inorganic Chemistry by JD Lee
Dinesh Chemistry Guide
Practise books by VK Jaiswal, MS Chauhan and N Awasthi

Physics Best Books:

NCERT Physics Class XI & Class XII
Concepts of Physics by H. C. Verma
Objective Physics By DC Pandey
Fundamentals of Physics by Halliday, Resnick and Walker
Fundamental Physics by Pradeep
Problems in General Physics by IE Irodov

Hii Chetan!
Developing skills basically means clearing the basic concepts here. You need to clear all the basic concepts whether it is too small to be looked into or to big. Then, you need to read the question carefully and understand Its need. Then, think of all the ways to solve this problem based on the information provided. Basically, analyse the question. NCERT will definately help you develop the problem solving skill. Hence, the more you practice, the more you become good at it.
Hope this helps.
Good luck!

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