29 mm 8.5 X 11 inch IIT-JEE ADVANCED VOLUME I A t A bout he uthor Shashi Bhushan Tiwari is a distinguished academician and Physics guru. He graduated from IIT Kharagpur in year 1995 and has been mentoring students for IIT JEE for more than two decades. IIT-JEE ADVANCED VOLUME I Shashi Bhushan Tiwari McGraw Hill Education (India) Private Limited PREFACE In the past decade and a half, the entrance exam for IITs has seen many changes – in structure as well as in design of the question paper. No doubt, it has become more challenging. It requires high level of conceptual clarity and analytical skill, besides promptness and comprehension ability to excel in this exam. There are frequent surprises in terms of problems which require mathematical rigor or in depth understanding of physical conditions. This book is being presented with a very simple objective – it will test you and nurture you on all parameters which are required to excel in JEE exam. Every chapter in the book has been divided into three sections – LEVEL 1 – This section will test you on all basic fundamentals of the chapter. Problems are not very rigorous though they may be very conceptual. LEVEL 2 – This section will develop all necessary skills required to score a high rank in JEE exam. Few problems in this section may appear lengthy but they are the ones which test your confidence and patience. Don’t be scared of them. LEVEL 3 – This section contains problems that may require exceptional reasoning skill or mathematical ability. Since difficulty level is quite subjective and may vary from person to person — few problems may appear to you as misplaced in three sections described above. I have judged them to the best of my ability besides taking help from some very bright minds. I have not tried to include every other problem that is available in this universe. Most of the books available in market have this issue – in the name of being exhaustive, they have become repetitive. Believe me, while solving problems from this book you will not feel like wasting your time in doing similar problems again and again.. Most of the solutions are quite descriptive so that a serious student can understand on his/her own. Diagrams have been included wherever possible to make things lucid. JEE exam being objective, one may challenge the sanctity of a subjective book. Have no doubts in your mind — pattern of a question paper or type of question will never deter you if you have sound grasp of the subject and have developed right kind of temperament. Physics as a subject is notorious and can be learned only by subjecting yourself to the true rigor and complexity. While doing a subjective problem you cannot make a guess and bluff yourself! This collection of problems will appear to you as fresh and challenging. Start and enjoy learning physics! Suggestions are welcome. CONTENTS Preface v Chapter 1 Basic Maths 1.1 – 1.12 Chapter 2 Kinematics 2.1 – 2.101 Chapter 3 Newton's Laws 3.1 – 3.134 Chapter 4 Work - Power - Energy 4.1 – 4.69 Chapter 5 Momentum and Center Of Mass 5.1 – 5.87 Chapter 6 Rotational Motion 6.1 – 6.133 Chapter 7 Gravitation 7.1 – 7.40 Chapter 8 Fluids 8.1 – 8.52 Chapter 9 Surface Tension 9.1 – 9.19 Chapter 10 Viscosity 10.1 – 10.8 Chapter 11 Elasticity 11.1 – 11.9 Chapter 12 Simple Harmonic Motion 12.1 – 12.48 Chapter 13 Wave Motion 13.1 – 13.47