Table Of ContentAlgebra Booster
with Problems & Solutions
for
JEE
Main and Advanced
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About the Author
REJAUL MAKSHUD (R M) Post Graduated from Calcutta University in PURE MATHEMATICS. Presently, he trains IIT
Aspirants at RACE IIT Academy, Jamshedpur.
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Algebra Booster
with Problems & Solutions
for
JEE
Main and Advanced
Rejaul Makshud
M. Sc. (Calcutta University, Kolkata)
McGraw Hill Education (India) Private Limited
CHENNAI
McGraw Hill Education Offices
Chennai NewYork St Louis SanFrancisco Auckland Bogotá Caracas
Kuala Lumpur Lisbon London Madrid Mexico City Milan Montreal
San Juan Santiago Singapore Sydney Tokyo Toronto
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McGraw Hill Education (India) Private Limited
Published by McGraw Hill Education (India) Private Limited
444/1, Sri Ekambara Naicker Industrial Estate, Alapakkam, Porur, Chennai - 600 116
Algebra Booster
Copyright © 2017, McGraw Hill Education (India) Private Limited.
No part of this publication may be reproduced or distributed in any form or by any means, electronic, mechanical,
photocopying, recording, or otherwise or stored in a database or retrieval system without the prior written permission
of the publishers. The program listings (if any) may be entered, stored and executed in a computer system, but they
may not be reproduced for publication.
This edition can be exported from India only by the publishers,
McGraw Hill Education (India) Private Limited
ISBN (13): 978-93-5260-250-6
ISBN (10): 93-5260-250-1
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reliable. However, neither McGraw Hill Education (India) nor its authors guarantee the accuracy or completeness
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for any errors, omissions, or damages arising out of use of this information. This work is published with the
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Cover Designer: Creative Designer
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Dedicated to
light of my life
(Rushda Manha, Daughter)
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Preface
ALGEBRA BOOSTER with Problems & Solutions for JEE Main and Advanced is meant for aspirants preparing for the entrance
examinations of different technical institutions, especially NIT/IIT/BITSAT/IISc. In writing this book, I have drawn heavily
from my long experience of teaching at National Level Institutes. After many years of teaching, I have realised the need of de-
signing a book that will help the readers to build their base, improve their level of mathematical concepts and enjoy the subject.
This book is designed keeping in view the new pattern of questions asked in JEE Main and Advanced Exams. It has eight
chapters. Each chapter has the concept booster followed by a large number of exercises with the exact solutions to the problems
as given below:
Level - I : Questions based on Fundamentals
Level - II : Mixed Problems (Objective Type Questions)
Level - III : Problems for JEE Advanced Exam
Level - IV : Tougher problems for JEE Advanced Exams
(0.......9) : Integer type Questions
Passages : Comprehensive link passages
Matching : Matrix Match
Reasoning : Assertion and Reasoning
Previous years’ papers : Questions asked in past IIT-JEE Exams
Remember friends, no problem in mathematics is difficult. Once you understand the concept, they will become easy. So
please don’t jump to exercise problems before you go through the Concept Booster and the Objectives. Once you are confident
in the theory part, attempt the exercises. The exercise problems are arranged in a manner that they gradually require advanced
thinking.
I hope this book will help you to build your base, enjoy the subject and improve your confidence to tackle any type of prob-
lem easily and skilfully.
My special thanks goes to Mr. M.P. Singh (IISc Bangalore), Mr. Manoj Kumar (IIT, Delhi), Mr. Nazre Hussain (B. Tech.),
Dr. Syed Kashan Ali (MBBS) and Mr. Shahid Iqbal, who have helped, inspired and motivated me to accomplish this task. As
a matter of fact, teaching being the best learning process, I must thank all my students who inspired me most for writing this
book.
I would like to convey my affectionate thanks to my wife, who helped me immensely and my children who bore with
patience my neglect during the period I remained devoted to this book.
I also convey my sincere thanks to Mr. Biswajit Das of McGraw Hill Education for publishing this book in such a beautiful
format.
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viii Preface
I owe a special debt of gratitude to my father and elder brother, who taught me the first lesson of Mathematics and to all my
learned teachers—Mr. Swapan Halder, Mr. Jadunandan Mishra, Mr. Mahadev Roy and Mr. Dilip Bhattacharya, who instilled
the value of quality teaching in me.
I have tried my best to keep this book error-free. I shall be grateful to the readers for their constructive suggestions toward
the improvement of the book.
Rejaul Makshud
M. Sc. (Calcutta University, Kolkata)
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Contents
Preface vii
Chapter 1 Sequence and Series 1.1–1.89
Introduction 1.1
Progression 1.1
Geometric Progression (GP) 1.2
Recognisation of AP, GP and HP 1.3
Means ( AM, GM and HM) 1.3
mth Powers Theorem 1.5
Cauchy-Schwartz Inequality 1.5
Maximum and Minimum Values of Positive Real Numbers 1.5
Arithmetico Geometric Progression 1.6
Summation of Series 1.6
Method of Differences 1.7
Exercises 1.7
Answers 1.25
Hints and Solutions 1.28
Chapter 2 Quadratic Equations and Expressions 2.1–2.76
Algebraic Expression 2.1
Polynomial 2.1
Equation 2.1
Identity 2.1
Types of Equations 2.1
Difference between an Equation and an Identity 2.1
Quadratic Formula 2.1
Nature of the Roots 2.2
Sum and Product of the Roots 2.2
Symmetic Functions of the Roots 2.2
Formation of an Equation 2.2
Common Roots of Quadratic Equations 2.2
Graph of a Quadratic Polynomial 2.3
Resolution of a Second Degree Expression in x and y 2.4
Location of the Roots 2.4
Some Special Types of Quadratic Equations 2.5
Transformation of Polynomial Equation 2.5
Intermediate Value Theorem 2.5
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