Mastering Physics Volume II PDF
Preview Mastering Physics Volume II
MATH EMATICS JEE Advanced for the Manan Khurma Prakash Rajpurohit PEARSON ALWAYS LEARNING Mathematics for theJEE Advanced Manan Khurma Prakash Rajpurohit PEARSON Delhi • Chennai Copyright © 2013 Dorling Kinders lev (India) Pvt. Ltd. Licensees of Pearson Education in South Asia No part of this eBook may be used or reproduced in any manner whatsoever without the publisher’s prior written consent. This eBook may or may not include all assets that were part of the print version. The publisher reserves the right to remove any material in this eBook at any time. ISBN 9789332507975 elSBN 9789332520332 Head Office: A-8(A), Sector 62, Knowledge Boulevard, 7th Floor, NOIDA 201 309, India Registered Office: 11 Local Shopping Centre, Panchsheel Park, New Delhi 110 017, India S/a jbarenti an S/am^Jbamnt6 This page is intentionally left blank. Contents Preface ix Acknowledgemen ts X About the Authors xi Chapter 0 xii 1. General Algebra 1-76 PART-A: Summary of Important Concepts 1 PART-B: Illustrative Examples 22 PART-C: Advanced Problems 44 PART-D: Solutions to Advanced Problems 51 2. Complex Numbers 77-160 PART-A: Summary of Important Concepts 77 PART-B: Illustrative Examples 96 PART-C: Advanced Problems 134 PART-D: Solutions to Advanced Problems 140 3. Permutations and Combinations 161-204 PART-A: Summary of Important Concepts 161 PART-B: Illustrative Examples 170 PART-C: Advanced Problems 186 PART-D: Solutions to Advanced Problems 190 4. Probability 205-250 PART-A: Summary of Important Concepts 205 PART-B: Illustrative Examples 217 PART-C: Advanced Problems 233 PART-D: Solutions to Advanced Problems 238 vi Contents 5. Determinants and Matrices 251-294 PART-A: Summary of Important Concepts 251 PART-B: Illustrative Examples 267 PART-C: Advanced Problems 279 PART-D: Solutions to Advanced Problems 284 6. Vectors 295-348 PART-A: Summary of Important Concepts 295 PART-B: Illustrative Examples 314 PART-C: Advanced Problems 334 PART-D: Solutions to Advanced Problems 339 7. Trignometry 349-420 PART-A: Summary of Important Concepts 349 PART-B: Illustrative Examples 367 PART-C: Advanced Problems 387 PART-D: Solutions to Advanced Problems 395 8. Straight Lines 421-460 PART-A: Summary of Important Concepts 421 PART-B: Illustrative Examples 431 PART-C: Advanced Problems 441 PART-D: Solutions to Advanced Problems 445 9. Circles 461-518 PART-A: Summary of Important Concepts 461 PART-B: Illustrative Examples 474 PART-C: Illustrative Examples 498 PART-D: Solutions to Advanced Problems 504 Contents vii 10. Conic Section 519-632 PART-A: Summary of Important Concepts 519 PART-B: Illustrative Examples 541 PART-C: Advanced Problems 591 PART-D: Important Ideas and Tips 599 11.3-D Geometry 633-662 PART-A: Summary of Important Concepts 633 PART-B: Illustrative Examples 640 PART-C: Advanced Problems 649 PART-D: Solutions to Advanced Problems 653 12. Functions 663-710 PART-A: Summary of Important Concepts 663 PART-B: Illustrative Examples 686 PART-C: Advanced Problems 702 PART-D: Solutions to Advanced Problems 704 13. Limits, Continuity, Differentiability 711 -778 and Differentiation PART-A: Summary of Important Concepts 711 PART-B: Illustrative Examples 734 PART-C: Advanced Problems 762 PART-D: Solutions to Advanced Problems 766 14. Applications of Derivatives 779-830 PART-A: Summary of Important Concepts 779 PART-B: Illustrative Examples 786 PART-C: Advanced Problems 807 PART-D: Solutions to Advanced Problems 813 viii Contents 15. Integration 831-944 PART-A: Summary of Important Concepts 831 PART-B: Illustrative Examples 852 PART-C: Advanced Problems 891 PART-D: Solutions to Advanced Problems 902 16. Differential Equations 945-994 PART-A: Summary of Important Concepts 945 PART-B: Illustrative Examples 955 PART-C: Advanced Problems 966 PART-D: Solutions to Advanced Problems 972 Preface This book is essentially a book of good Mathematics problems, designed for students taking the JEE Mains and (especially) the JEE Advanced Mathematics test. There are 16 chapters in the book which cover all the topics as per the prescribed syllabus. The structure of each chapter is as follows: 1. Part A (Theory): Summary material containing the main highlights for the chapter and important facts and formulae. This sections ends with a very useful feature called Important Facts and Misconceptions. 2. Part B (Illustrative Examples): A lot of problems with detailed solutions, and a special emphasis on how to approach a problem. 3. Part C (Advanced Problems): Unsolved problems of both objective and subjective types. 4. Part D (Solutions): Solutions to the problems in Part C. Most of the solutions are fairly detailed. There is a lot of material in this book, designed to be covered over a period of two years. To get the most out of it, we recommend the following approach: 1. Once you have covered a chapter in your school (or elsewhere), read the corresponding Part A from this book. Clear any unresolved issues you might have at this stage. 2. Start Part B, but try to solve the problems on your own. In case you are able to solve a problem, compare your approach with the one in the book. In case a solution eludes you, analyze the provided solution to see where you faltered. 3. Each problem in Part C is very interesting and highlights the application of one or more concepts quite effectively. These problems are to be solved over an extended period of time, and not in one or two sittings. When you are unable to solve a problem, move to another and come back to the first problem later. Refer to the solutions only when you are convinced that you have made all the possible efforts. This book is a must-have Mathematics resource for the IIT-JEE and NEET aspirants. We are hopeful that if used as suggested, it will enable its readers to master the art of problem solving in Mathematics. Manan Khurma Prakash Rajpurohit
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