Description
McGraw Hill Algebra Booster With Problems & Solutions For Jee Main & Advanced 2Nd Edition by Makshud, Rejaul
Algebra Booster for IIT-JEE Main and Advanced has been conceptualised and produced for aspirants of various engineering entrance examinations. It renders complex concepts and problems of Algebra easy for the students and provides them as many opportunities for guided practice as needed. It covers all topics, and is imbued with a strong conceptual approach, with relevant theory being followed by plenty of solved exercise question, graded LODs and past years’ papers. The various levels of difficulties have numerous MCQs, integer type question, comprehensive link passage questions and matrix match questions for ample practice and thorough understanding. Step-by-step guidance in problem solving and alternative methods of approaching a problem are included to boost aspirants’ analytical and mathematical skills and are intended to teach them independent problem-solving techniques based upon the solutions.
SALIENT FEATURES
• Covers the latest JEE (Main & Advanced) syllabus as per the JEE Pattern
• Exercise questions graded into Level I, Level II, Level III and Level IV
• Level I questions based on Fundamentals
• Level II based on Mixed Problems
• Level III consist of Problems for JEE Advanced
• Level IV comprise of Tougher Problem
• Chapter-wise previous years’ questions with complete solution
• Solutions to questions have been provided in a step-by-step manner and alternate methods of solution have also been used wherever applicable
Preface vii
• Chapter 1 Sequence and Series 1.1–1.89
• Introduction 1.1
• Progression 1.1
• Geometric Progression (GP) 1.2
• Recognition of AP, GP and HP 1.3
• Means ( AM, GM and HM) 1.3
• m-th Powers Theorem 1.5
• Cauchy-Schwartz Inequality 1.5
• Maximum and Minimum Values of Positive Real Numbers 1.5
• Arithmetic 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
• Symmetric 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
• Descartes Rule of Signs 2.6
• Concept of solving Algebraic In-equation 2.6
• Equation Containing Absolute Values 2.6
• Irrational Equations 2.7
• Irrational In-equations 2.7
• Exponential Equations 2.7
• Exponential In-equations 2.8
Exercises 2.8
Answers 2.28
Hints and Solutions 2.31
• Chapter 3 Logarithm 3.1–3.31
• Introduction 3.1
• Basic Formulae on Logarithm 3.1
• Logarithmic Equation 3.2
• Logarithmic In-equation 3.2
• Conceptual Problem 3.2
• Conceptual Problem 3.4
• Conceptual Problem 3.6
Exercises 3.8
Answers 3.14
Hints and Solutions 3.15
• Chapter 4 Complex Numbers 4.1–4.89
• Introduction 4.1
• Algebra of Complex Numbers 4.1
• Equality of Complex Numbers 4.2
• Conjugate of Complex Numbers 4.2
• Modulus of a Complex Number 4.2
• Argument of a Complex Number 4.3
• Principal Value of Argument of a Complex Number z 4.3
• Representation of a Complex Number 4.4
• Square Root of a Complex Number 4.5
• Cube Roots of Unity 4.5
• Properties of Cube Roots of Unity 4.5
• Demoivre’s Theorem 4.6
• nth Roots of Unity 4.6
• Rotation 4.8
• Loci in a Complex Plane 4.11
• Ptolemy’s Theorem 4.14
Exercises 4.14
Answers 4.31
Hints and Solutions 4.34
• Chapter 5 Permutations and Combinations 5.1–5.53
• Factorial Notation 5.1
• Exponent of a Prime p in (n)! 5.1
• Fundamental Principle of Counting 5.1
• Permutations 5.1
• Sum of Numbers 5.1
• Permutation with Repetition 5.1
• Permutations of Alike Objects 5.1
• Restricted Permutations 5.2
• Rank of a Word in Dictionary 5.2
• Gap Method 5.2
• Circular Permutations 5.2
• Restricted Circular Permutations 5.2
• Combinations 5.2
• Some Important Results to Remember 5.2
• Restricted Combinations 5.2
• Combinations from Distinct Objects 5.3
• Combinations from Identical Objects 5.3
• Combinations when Identical and Distinct Objects are Present 5.3
• Divisor of a Given Natural Number 5.3
• Distribution into Group of Unequal Size among Sets (Groups) and Persons 5.3
• Distribution into Group of Equal Size among Sets (Groups) and Persons 5.3
• Arrangement into Groups 5.4
• De-arrangement 5.4
• Multinomial Theorem 5.4
• Solutions of the Equation with the Help of Multinomial Theorem 5.4
• Selection of Squares 5.5
• Geometrical Problems 5.5
Exercises 5.5
Answers 5.19
Hints and Solutions 5.23
• Chapter 6 Binomial Theorem 6.1–6.72
• Definition 6.1
• Factorial of a Natural Number, n. 6.1
• Binomial Coefficients 6.1
• Binomial Theorem (for positive integral index) 6.1
• Multinomial Theorem for Positive Integral Index 6.3
• Binomial Theorem for any Index 6.4
• Exponential Series 6.5
• Logarithmic Series 6.5
Exercises 6.6
Answers 6.21
Hints and Solutions 6.22
• Chapter 7 Matrices and Determinants 7.1–7.82
• Introduction 7.1
• Types of Matrices 7.1
• Addition of Matrices 7.2
• Multiplication of Matrices 7.2
• Transpose of a Matrix 7.3
• Determinant 7.4
• Cramers' Rule Statement 7.5
• Homogeneous System of Equations 7.6
• Multiplication of Two Determinants 7.6
• Differentiation of Determinant 7.6
• Integration of Determinant 7.7
• Summation of Determinants 7.7
• Adjoint of a Matrix 7.7
• Singular and Non-singular Matrices Singular Matrix 7.8
• Inverse of a Matrix 7.8
• Solutions of the System of Equations by Matrix (Inverse ) Method 7.8
• Elementary Transformations of a Matrix 7.9
• Advance Types of Matrices 7.9
Exercises 7.10
Answers 7.32
Hints and Solutions 7.32
• Chapter 8 Probability 8.1–8.77
• Introduction 8.1
• Sample Space 8.1
• Random Experiment 8.1
• Event Space 8.2
• Axioms of Probability 8.3
• Addition Theorem on Probability 8.3
• Inequalities in Probability 8.3
• Conditional Probability 8.4
• Independent Events 8.4
• Total Probability 8.4
• Baye’s Theorem 8.4
• Probability Distribution 8.4
• Binomial Distribution 8.5
• Geometrical Probability or Probability in Continuum 8.5
Exercises 8.5
Answers 8.26
Hints and Solutions 8.31•