WILEY PROBLEMS MATHEMATICS IN JEE FOR with Summarized Concepts VOLUME –I WILEY PROBLEMS INMATHEMATICS FO RJ EE VOLUME – I with Summarized Concepts Copyright © 2018 by Wiley India Pvt. Ltd., 4436/7, Ansari Road, Daryaganj, New Delhi-110002. Cover Image: Carlos_bcn/iStockphoto All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or scanning without the written permission of the publisher. Limits of Liability: While the publisher and the author have used their best efforts in preparing this book, Wiley and the author make no representation or warranties with respect to the accuracy or completeness of the contents of this book, and specifically disclaim any implied warranties of merchantability or fitness for any particular purpose. There are no warranties which extend beyond the descriptions contained in this paragraph. No warranty may be created or extended by sales representatives or written sales materials. Disclaimer: The contents of this book have been checked for accuracy. Since deviations cannot be precluded entirely, Wiley or its author cannot guarantee full agreement. As the book is intended for educational purpose, Wiley or its author shall not be responsible for any errors, omissions or damages arising out of the use of the information contained in the book. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered. It is sold on the understanding that the Publisher is not engaged in rendering professional services. Other Wiley Editorial Offices: John Wiley & Sons, Inc. 111 River Street, Hoboken, NJ 07030, USA Wiley-VCH Verlag GmbH, Pappellaee 3, D-69469 Weinheim, Germany John Wiley & Sons Australia Ltd, 42 McDougall Street, Milton, Queensland 4064, Australia John Wiley & Sons (Asia) Pte Ltd, 1 Fusionpolis Walk #07-01 Solaris, South Tower Singapore 138628 John Wiley & Sons Canada Ltd, 22 Worcester Road, Etobicoke, Ontario, Canada, M9W 1L1 First Edition: 2018 ISBN: 978-81-265-7629-6 ISBN: 978-81-265-8689-9 (ebk) www.wileyindia.com Printed at: Note to the Student Wiley Mathematics Problem Book is specifically designed to meet the needs of engineering (JEE) aspirants and give an edge to their preparation. The book offers complete coverage of the mathematics curriculum (of Class 11 syllabus) for JEE. It is enriched with unique elements and features that help students recapitulate the concepts, build problem-solving skills and apply them to solve all question-types asked in the engineering entrance examinations. The book is a valuable resource for both JEE (Main) and JEE (Advanced) aspirants. The chapter flow of the book is aligned with JEE Main syllabus and its coverage in the classroom. However, topics specific to JEE (Advanced) and advanced level questions are also covered both as solved examples and practice exercises. We will now walk you through the target examinations and some key features of the book that enhance the learning experience. TARGET EXAMINATION Admission to Undergraduate Engineering Programs at IITs, NITs and other Center and State (participating) funded Technical Institutions use the Joint Entrance Examination Main (JEE Main) score as eligibility/merit criteria. The JEE (Main) is also an eligibility test for the Joint Entrance Examination Advanced [JEE (Advanced)], which is mandatory for the candidate if he/she is aspiring for admission to the undergraduate program offered by the IITs. The JEE (Advanced) scores are used as an eligibility criteria for admission into IITs. An effective exam strategy for success in these examinations can be based on the detailed analysis of previous years question papers and planning your preparation accordingly. The Mathematics Question Paper of these examinations is a judicious mix of easy, moderate and tough questions. The analysis of question distribution over the units of mathematics syllabus for these examinations is given below. EXAM ANALYSIS OF PAPERS Mathematics question paper comes as an amalgamation of easy, moderate and tough questions. This section shows the unit-wise as well as chapter-wise analysis of previous 9 years (2010-2018) JEE Main and JEE Advanced papers. JEE Main Year Unit 2010 2011 2012 2013 2014 2015 2016 2017 2018 Algebra 14 13 13 12 12 11 12 13 12 Calculus 8 10 9 8 9 8 7 10 8 Trigonometry 2 1 1 3 2 3 3 2 3 Analytical Geometry 6 6 7 7 7 8 8 5 7 JEE Advanced Year Unit 2010 2011 2012 2013 2014 2015 2016 2017 2018 Algebra 16 17 12 14 12 6 12 10 8 Trigonometry 5 1 2 4 3 1 2 1 1 Analytical Geometry 13 8 9 10 7 3 9 7 9 Differential Calculus 2 7 6 2 11 5 7 8 12 Integral Calculus 8 7 10 7 5 4 5 7 4 Vector 3 3 2 3 2 1 1 3 2 Prelims_Volume I.indd 3 27-Jul-18 6:21:03 PM e) n n aiffli MO 1 1 1 2 1 1 3 1 1 2 1 1 2 1 1 3 5 2 JEE 18 ( 0 2 e) n n aiffli MO 1 2 3 1 3 1 2 2 2 2 2 1 1 2 3 2 JEE 17 ( 0 2 e) n n aiffli MO 2 1 1 2 1 1 2 1 1 1 2 1 1 2 2 1 5 3 ) JEE 16 ( 8 0 1 2 20 n ne) 0- aiffli 1 MO 2 2 2 1 2 1 1 2 3 2 1 2 1 4 4 20 JEE 15 ( ( 0 S 2 LYSI ain ffline) A MO 3 1 2 1 1 2 1 1 1 3 2 2 1 2 3 4 N JEE 14 ( A 0 2 S n R ai3 PE EE M201 3 1 1 1 1 1 2 1 1 1 2 1 3 1 2 1 3 4 A J P E 2 IN AIEE201 2 1 1 2 1 1 2 2 1 1 2 3 2 1 1 3 4 A M E 1 EE AIEE201 2 1 1 1 1 1 2 2 2 2 3 1 2 1 1 1 2 4 CS J AIEEE 2010 2 1 2 1 1 3 2 2 1 3 1 1 1 1 2 2 4 I T A s n M o MATHE Chapter Complex Numbers and Quadratic Equati Permutations and Combinations Binomial Theorem Sequences and Series Statistics Mathematical Reasoning Matrices and Determinants Vector Algebra Probability Sets, Relations and Functions Limits, Continuity and Differentiability Application of Derivatives Integrals Application of Integrals Differential Equations Trignometric Functions Inverse Trignometric Functions Conic Sections Three-Dimensional Geometry y Unit Algebra Calculus Trigonometr Analytical Geometry Prelims_Volume I.indd 4 27-Jul-18 6:21:03 PM 8 U 1 1 1 1 2 2 1 1 1 0 2 T d ce S 1 1 1 1 n va R 1 d E A Q 2 1 2 1 1 2 2 1 1 2 E J P 1 1 17 U 1 1 1 1 1 0 d 2 T e c S n a v R 2 3 d A E Q 1 1 1 1 2 1 4 E J P 1 1 1 1 1 6 U 1 1 1 1 1 0 2 T d ce S n va R 2 2 ) d 18 E A Q 1 1 2 4 3 1 2 0 JE P 1 1 2 1 1 1 1 2 - 5 U 1 1 1 1 1 1 0 1 1 20 T 0 d 2 ce S S ( dvan R 2 2 SI E A Q 1 1 2 1 Y JE P L A 4 U 1 1 1 1 1 1 1 1 N 0 2 T A d ce S 1 1 1 S n R va R 2 2 2 d PE EE A Q 1 2 1 1 2 2 A J P 1 1 2 1 2 1 P 3 U 1 2 1 D 201 T E d C nce S 1 1 1 N va R 2 2 2 d VA E A Q 1 1 1 2 1 1 2 1 1 D JE P 1 1 1 1 1 1 A U 1 1 E 2 T E 1 0 J 2 S E CS T-JE R 2 2 I II Q 1 2 1 1 1 2 T A P 1 1 1 2 1 1 1 1 2 2 1 1 M U 2 1 1 1 1 1 1 2 E 1 T H 1 0 T 2 S 1 A E M JE R 3 2 T- II Q 1 2 1 1 P 2 1 2 1 2 1 2 1 U 2 2 1 2 1 1 2 1 1 0 T 1 0 2 S 1 1 E JE R 3 3 2 T- II Q 1 1 1 P 1 1 1 1 1 2 2 1 Chapter Complex Numbers Quadratic Equations Permutations and Combinations Sequence and Series Binomial Theorem Logarithms Matrices and Determinants Probability Properties and Solution of Triangles (Heights and Distances) Trigonometric Equations Trigonometric Ratios and Identities Inverse Trigonometric Function (Principal Values Only) Rectangular Coordinate System Straight Lines and Pair of Lines Conics Circle Three-Dimensional Geometry Sets and Relations Limits Functions Continuity and Differentiability Differentiation nit arbeglA yrtemonogirT yrtemoeG lacitylanA suluclaC laitnereffiD U Prelims_Volume I.indd 5 27-Jul-18 6:21:03 PM 8 U 1 1 2 1 0 2 T d ce S n va R d E A Q E J P 7 U 1 0 d 2 T e c S n va R 3 2 e d p JEE A PQ 1 1 1 1 1 Type wer Ty 6 U 1 h ns d 201 T grap er A E Advance QRS 1 1 ParaR: : U Integ E J P 1 1 1 5 U 1 1 1 0 d 2 T ce S n va R JEE Ad PQ 1 1 1 ct Type 4 U 1 1 1 e d 201 T Corr ce S 1 n dvan R ptio EE A Q 1 e O J P 1 1 n O 2013 TU 1 han e d T p ce S 1 e Ty JEE Advan PQR 122 1 1 1 e or Mor asoning n e U 2 1 O R 12 T Q: T: 0 2 S E JE R 2 T- II Q 1 1 1 P 1 1 1 1 e U 1 1 1 p y T IIT-JEE 2011 PQRST 11 2 1 11 orrect Choice atch Type U 1 1 C M e x- 010 T ngl atri E 2 S Si M JE R 3 P: S: T- II Q 1 1 P 1 1 2 s n n o n o Chapter Application of Derivatives Indefinite Integrati Definite Integratio Area Under the Curve Differential Equati Vectors nit suluclaC largetnI ctor U e V Prelims_Volume I.indd 6 27-Jul-18 6:21:03 PM FEATURES OF THE BOOK A. Understand the Concepts 1. All the concepts as per the JEE curriculum are explained in simple steps to develop fundamental understanding of the subject. 2. Important points to remember about concepts highlighted as Key Points. B. Every Aspect of the Subject Covered In form of formulas, figures, graphs and tables to enhance problem-solving skills. C. Reinforce Concepts 1. Illustrations pose a specific problem using concepts already presented and then work through the solution. 2. Your Turn within each chapter is present to reinforce and check the understanding of the students. 3. Additional Solved Examples suitable for JEE exams are provided with in-depth solutions for the students to understand the logic behind and formula used. D. Understanding the Exam Pattern Through Previous Years' Solved JEE Main/AIEEE Questions and Previous Years' Solved JEE Advanced/IIT-JEE Questions. E. Practice to Complete Your Learning Through Practice Exercise 1 (JEE Main) and Practice Exercise 2 (JEE Advanced). All questions types as per JEE Main and Advanced covered.