# Wiley's Problems in Mathematics for JEE, Vol I

ISBN: 9788126541645

744 pages

## Description

Wiley Mathematics Problem Book covers the complete mathematics course for JEE. It is focused on the development of problem-solving skills in JEE aspirants. The chapter flow of the book is closely aligned with the JEE (Main) syllabus and its coverage in the classroom. However, the topics required for JEE (Advanced) are also covered. The problems presented saystematically cover all important concepts pertaining to the topic and the possible questions that can be framed on them.

Note to the Student

Chapter 1 Sets, Relations and Functions

1.1 Set Theory

1.2 Relation

1.3 Number Theory

1.4 Intervals

1.5 Basic Inequalities

1.6 Logarithm

1.7 Wavy Curve Method

1.8 Quadratic Expression

1.9 Absolute Value

1.10 Greatest Integer

1.11 Fractional Part

1.12 Basic Properties of Greatest Integer and Fractional Part

1.13 Functions, Domain, Co-Domain, Range

1.14 Algebra of Functions

1.15 Methods to Determine Range

1.16 Composition of Functions

1.17 Types of Functions

Chapter 2 Trigonometric Ratios and Identities

2.1 Introduction

2.2 Definitions

2.3 Measurement of Angles

2.4 Relation Between Three Systems of Measurement and Angle

2.5 Relation Between Arc and Angle

2.6 Trigonometric Ratio or Function

2.7 Formulae for Trigonometric Ratios of Sum and Differences of Two or More Angles

2.8 Formulae to Transform Product into Sum or Difference

2.9 Formulae to Transform Sum or Difference into Product

2.10 Trigonometric Ratio of Multiple of Angles

2.11 Trigonometric Ratio of Sub-Multiple of Angles

2.12 Maximum and Minimum Values of cos+ sin

2.13 Trigonometric Series

2.14 Conditional Trigonometrical Identities

2.15 Height and Distance

Chapter 3 Trigonometric Equation and Inequation

3.1 Introduction

3.2 Solution of a Trigonometric Equation

3.3 General Solution of the Standard Trigonometric Equation

3.4 System of Equations

3.5 Key Points to be Remembered for Solving the Trigonometric Equation

3.6 Trigonometric Inequation

3.7 Equations Containing Combination of Trigonometric and Non-Trigonometric Expressions

Chapter 4 Properties of Triangle

4.1 Introduction

4.2 Relation Between Sides and Angles of a Triangle

4.3 Theorem of the Medians (Apollonius Theorem)

4.4 Half-Angle Formulae

4.5 Area of a Triangle

4.6 Circle Connected with the Triangle

4.7 Orthocentre of a Triangle

4.8 Centroid of a Triangle

4.9 Pedal Triangle

4.10 Ex-Central Triangle

4.11 Cyclic Quadrilateral

4.12 Regular Polygon

4.13 Solution of a Triangle

Chapter 5 Complex Number

5.1 Introduction

5.2 Complex Numbers

5.3 Representation of a Complex Number

5.4 Conjugate of a Complex Number

5.5 Modulus of a Complex Number

5.6 Argument of a Complex Number

5.7 De Moivre’s Theorem

5.8 Roots of Unity

5.9 Rotation Theorem

5.10 Theory of Equations with Complex Coefficients

5.11 Logarithms of a Complex Number

5.12 Section Formula

5.13 Locus in an Argand Plane

Chapter 6 Quadratic Equations

6.1 Polynomial

6.2 Definition of a Quadratic Equation

6.3 Root of a Quadratic Equation

6.4 Discriminant of a Quadratic Equation

6.5 Nature of Roots

6.6 Identity

6.7 Formation of a Quadratic Equation

6.8 Condition for Common Root()

6.9 Quadratic Expression

6.10 Range of a Quadratic or Rational Expression

6.11 Location of Roots

6.12 Relation Between the Roots and Coefficients of Polynomial of Degree

6.13 Descartes’ Rule of Sign

6.14 Rolle’s Theorem

6.15 Transformation of Roots

6.16 Roots of Symmetric Equation

6.17 Wavy Curve Method (Sign Scheme)

6.18 Equation and Inequation Containing the Absolute Value

6.19 Equation Reducible to Quadratic Equation

Chapter 7 Sequence and Series

7.1 Sequence

7.2 Progression

7.3 Different Means of Two Numbers

7.4 Relation between AM, GM and HM

7.5 Insertion of Means between Two Numbers

7.6 Weighted Means of Numbers

7.7 Arithmetico-Geometric Series

7.8 Sum of Miscellaneous Series

7.9 Sum of First Natural Numbers

7.10 Inequalities

7.11 Exponential

7.12 Logarithm

7.13 Difference between the Exponential and Logarithmic Series

Chapter 8 Permutation and Combination

8.1 Introduction

8.2 Fundamental Principles of Counting

8.3 Permutations (Arrangement of Objects)

8.4 Conditional Permutation

8.5 Circular Permutation (Arrangement of Object)

8.6 Combination (Selection of Object)

8.7 Divisors of a Given Natural Number

8.8 Division of Object into Groups

8.9 Method of Inclusion and Exclusion

8.10 Use of Multinomial

8.11 Some Important Points for Solving Geometrical Problems

8.12 Problems on Formation of Numbers

Chapter 9 Binomial Theorem

9.1 Binomial Expression

9.2 Binomial Theorem for Positive Integral Index

9.3 General Term

9.4 Independent Term or Constant Term

9.5 Middle Term in the Binomial Expansion

9.6 Greatest Binomial Coefficient

9.7 Numerically Greatest Term

9.8 Properties of Binomial Coefficient

9.9 Summation of Series Including Binomial Coefficient

9.10 An Important Theorem

9.11 Some Important Results

Chapter 10 Matrices and Determinants

10.1 Definition of a Matrix

10.2 Order of a Matrix

10.3 Types of a Matrix

10.4 Equality of Matrices

10.5 Addition and Subtraction of Matrices

10.6 Multiplication of a Matrix by a Scalar

10.7 Multiplication of Two Matrices

10.8 Operations Regarding Matrices

10.9 Types of a Matrix on the Basis of Operations

10.10 Definition of a Determinant

10.11 Evaluation of Determinants

10.12 Minors

10.13 Cofactors

10.14 Adjoint of a Square Matrix

10.15 Inverse of a Matrix

10.16 Singular and Non-Singular Matrices

10.17 Elementary Operations or Elementary Transformations of a Matrix

10.18 Inverse of a Matrix by Elementary Operations (Elementary Operations on Matrix Equation)

10.19 Rank of a Matrix

10.20 Echelon Form of a Matrix

10.21 Homogeneous Linear Equations

10.22 System of Linear Non-Homogeneous Equations

10.23 Minor of Any Element of a Matrix

10.24 Cofactor of Any Element of a Matrix

10.25 Determinant of Any Matrix

10.26 Properties of Determinants

10.27 Sum of Determinants

10.28 Multiplication of Determinants

10.29 Differentiation of Determinants

10.30 Special Determinants

10.31 Solution of System of Linear Equations

Chapter 11 Cartesian Coordinates and Straight Lines

11.1 Cartesian Coordinates

11.2 Slope of a Line

11.3 Intercepts of a Line

11.4 Slope of a Straight Line

11.5 Standard Forms of Equation of a Straight Line

11.6 Position of Two Points w.r.t. Straight Line

11.7 Angle between Two Straight Lines

11.8 Distance between Two Parallel Straight Lines

11.9 Perpendicular Distance of a Point From a Straight Line

11.10 Slope of Straight Line that Makes Angle with Line

11.11 Angle Bisectors

11.12 Family of Straight Lines

11.13 Locus of a Point

11.14 Shifting of Origin

Chapter 12 Pair of Straight Lines

12.1 Pair of Straight Lines − Fundamentals

12.2 Separation of Equations of Straight Lines from their Joint Equation

12.3 Combined Equation of Lines Joining Origin to Points of Intersections of a Line and a Curve

Chapter 13 Circle

13.1 Standard Equation of a Circle

13.2 General Equation of a Circle

13.3 General Equation of a Circle in Second Degree

13.4 Different Forms of Equations of Circle

Chapter 14 Parabola

14.1 Understanding Conic Section

14.2 Parabola: Definition and Its Terminologies

Chapter 15 Ellipse

15.1 Ellipse – Fundamentals

15.2 Position of Point Relative to Ellipse

15.3 Parametric Equation of Ellipse

15.4 Another Form of Ellipse (When > )

15.5 Tangent to Ellipse

15.6 Normal to Ellipse

15.7 Chords of Ellipse

15.8 Diameter of Ellipse

15.9 Geometric Properties of Ellipse

Chapter 16 Hyperbola

16.1 Hyperbola – Fundamentals

16.2 Position of Point Relative to Hyperbola

16.3 Parametric Equation of Hyperbola

16.4 Conjugation of Hyperbola

16.5 Tangent of Hyperbola

16.6 Normal to Hyperbola

16.7 Chords of Hyperbola

16.8 Asymptotes

16.9 Rectangular Hyperbola

Additional Solved Examples

Previous Years’ Solved JEE Main/AIEEE Questions

Previous Years’ Solved JEE Advanced/IIT-JEE Questions

Practice Exercise 1

Practice Exercise 2

Answer Key

Solutions

Solved JEE 2017 Questions

Appendix: Chapterwise Solved JEE 2018 and JEE 2019 Questions