Bachelor of Science in Nursing or B.Sc Nursing is a 4-year undergraduate course, the minimum eligibility criterion for which is the successful completion of 10+2 level of education in Physics, Chemistry, and Biology. 

B.Sc. Nursing Entrance Exam syllabus

General Ability

English Language

General Knowledge

Biology

Living and Non-Living
Cell Structure and Function
Plant Physiology
Animal Physiology
Reproduction in Plant and Animal
Genetic Basis of Inheritance
Origin and Evolution of Life
Human Disorders
Ecology and Ecosystems

Physics

Units and Measurements
Mechanics
Heat Transfer
Vibration and Waves
Light and Sound
Electricity and magnetism
Modern Physics

Chemistry

The Atomic Structure
Chemical Bonding
States of Matter
Mixtures, solutions and Solubility
The Gas Laws
Elements and Compunds
The Periodic Table
Important Concepts in chemistry
Organic Chemistry
Water and Organic Compounds in the Environment

Hello.
Eligibility:
B.Sc (Basic) - Candidates should pass 10+2 in Physics, Chemistry and Biology and he/she should be medically fit.
B.Sc (Post-Basic) – Candidates should pass 10+2 in PCB. Those who have passed 10+1 are also eligible for admission. He/She must have obtained a certificate in General Nursing and Midwifery and registered as R.N.R.M (Registered Nurse Registered Midwife) with the State Nurses Registration Council. Also, a proof of training by Indian Nursing Council or equivalent is required in the following domain-

• O.T. Techniques
• Ophthalmic Nursing
• Leprosy Nursing
• TB Nursing
• Psychiatric Nursing
• Neurological and Neuro surgical Nursing
• Community Health Nursing
• Cancer Nursing
• Orthopedic Nursing

B.SC. (NURSING): ADMISSION PROCEDURE
B.Sc Nursing admission is purely based on entrance exams held in between April-June. Candidates can fill the application form in both online and offline mode.
For filling online, candidates need to go to the administrator website of the concerned entrance exam and fill the requirements. After that, a print out of the completed form is to be taken out. The print out along with the obligatory documents and DD of specified amount are needed to be sent to the relevant exam body. For offline application, candidates need to get the form along with the brochure from the exam conducting body or from the designated centers and can finish the formality.
There are many colleges that conduct entrance exams for admisssion to B.Sc. Nursing course. One must be well aware of the B.Sc. Nursing Entrance Exam syllabus to be well prepared for the same. 
Before listing the books, here is a quick gist of the exam pattern of BSc Nursing AIIMS entrance. The exam will comprise four sections with 30 questions each asked from Physics, Chemistry and Biology, and 10 questions asked from General Knowledge. The questions will be asked from PCB of Class 12 or equivalent.
Here are some popular books which are frequently used for the preparation of BSc Nursing:
Guide for Nursing Competitive Exam by Preeti Agarwal, RS Sharma and Vinod Gupta
BSc Nursing Entrance Test by Arihant
Nursing Entrance Test by R Gupta, among others.
Part I: Biology

• Living and Non-Living
• Cell Structure and Function
• Plant Physiology
• Animal Physiology
• Reproduction in Plant and Animal
• Genetic Basis of Inheritance
• Origin and Evolution of Life
• Human Disorders 
• Ecology and Ecosystems

• Part II: Physics
• Units and Measurements
• Mechanics
• Heat Transfer
• Vibration and Waves
• Light and Sound
• Electricity and magnetism
• Modern Physics
• Part III: Chemistry
• The Atomic Structure
• Chemical Bonding
• States of Matter
• Mixtures, solutions and Solubility
• The Gas Laws
• Elements and Compunds
• The Periodic Table
• Important Concepts in chemistry
• Organic Chemistry
• Water and Organic Compounds in the Environment
• Hope this is helpful.
• Good luck.