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 systematically cover all important concepts pertaining to the topic and the possible questions that can be framed on them.
Table Content:
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 a cosq + b sinq
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(s)
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 n
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 n 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 a 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 b > a)
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
Chapter 17 Inverse Trigonometry
17.1 Introduction
17.2 Domain and Range of Inverse Trigonometric Functions
17.3 Properties of Inverse Trigonometric Functions
17.4 General Values of Inverse Circular Functions
Chapter 18 Limit, Continuity and Differentiability
18.1 Limit of a Function
18.2 Definition
18.3 Algebra of Limits
18.4 Evaluation of Limits
18.5 Use of Standard Limits
18.6 Some More Standard Forms
18.7 Use of Expansion
18.8 L’Hospital’s Rule
18.9 Sandwich Theorem (Squeeze Play Theorem)
18.10 Continuity
18.11 Differentiability
Chapter 19 Differentiation
19.1 Introduction
19.2 Differentiation from First Principle
19.3 Derivatives of Some of the Frequently Used Functions
19.4 Rules to Find Out Derivatives
19.5 Derivative of Second Order y’’ or y2
19.6 Differentiation of a Function with Respect to Another Function
Chapter 20 Applications of Derivatives
20.1 Geometrical Interpretation of Derivative
20.2 Tangent and Normal
20.3 Angles Between Two Curves
20.4 dy/dx as Rate Measures
20.5 Errors and Approximations
20.6 Monotonicity of Function
20.7 Maxima and Minima of Functions of a Single Variable
20.8 Mean Value Theorems
20.9 Geometrical Problems
Chapter 21 Indefinite Integration
21.1 Primitive or Anti-Derivative of a Function
21.2 Indefinite Integral and Indefinite Integration
21.3 Methods of Integration
21.4 Integration by Partial Fractions
Chapter 22 Definite Integration
22.1 Definition
22.2 Geometrical Meaning of Definite Integration
22.3 Definite Integration as the Limit of Sum
22.4 Properties of Definite Integration
22.5 Properties Based on Periodic Function
22.6 Properties Based on Inequality
22.7 Newton–Leibnitz Rule
22.8 Summation of Series by Integration
22.9 Reduction Formulae for Definite Integration
22.10 Wallis Formulae
Chapter 23 Area Under the Curves
23.1 Curve Tracing
23.2 Steps to Draw Curve
23.3 Area of Bounded Region
23.4 Area Enclosed Between Two Curves
Chapter 24 Differential Equations
24.1 Introduction
24.2 Basic Definition
24.3 Order of a Differential Equation
24.4 Degree of a Differential Equation
24.5 Formation of a Differential Equation
24.6 Solution of a Differential Equation
24.7 Differential Equations of First-Order and First-Degree
24.8 Solution of First-Order and First-Degree Differential Equations
24.9 Variable Separable Type Differential Equation
24.10 Equation Reducible to Variable Separable Type Differential Equation
24.11 Homogeneous Type Differential Equation
24.12 Non-Homogeneous Type Differential Equation
24.13 Exact Differential Equation
24.14 Linear Differential Equation
24.15 Solution of Differential Equation of the First Order but of Higher Degree
24.16 Applications of Differential Equation
Chapter 25 Vector Algebra
25.1 Introduction
25.2 Representation of a Vector
25.3 Types of Vectors
25.4 Rectangular Resolution of Vectors (Orthogonal System of Vectors): Resolution of a Vector in Two Dimensions
25.5 Resolution of a Vector in Three Dimensions
25.6 Properties of Vectors
25.7 Fundamental Theorems of Vectors
25.8 Linear Combinations of Vectors
25.9 Linearly Dependent and Independent Vectors
25.10 Position Vector of a Dividing Point (Section Formulae)
25.11 Bisector of the Angle Between Two Vectors
25.12 Product of Two Vectors
25.13 Scalar or Dot Product of Two Vectors
25.14 Vector or Cross-Product of Two Vectors
25.15 Scalar Triple Product
25.16 Vector Triple Product
25.17 Scalar or Vector Product of Four Vectors
25.18 Method to Prove Collinearity
25.19 Vector Equation
Chapter 26 Three-Dimensional Geometry
26.1 Rectangular Coordinate System in Space
26.2 Other Methods of Defining the Position of Any Point P in Space
26.3 Shifting the Origin
26.4 Distance Formula
26.5 Section Formula
26.6 Triangle and Tetrahedron
26.7 Direction Cosines of a Line
26.8 Direction Ratios
26.9 Projection of a Line
26.10 Equation of a Straight Line in Space
26.11 Angle Between Two Lines
26.12 Intersections of Two Lines
26.13 Shortest Distance Between Two Non-intersecting Lines
26.14 Point and Line
26.15 The Plane
26.16 Equation of Plane in Different Forms
26.17 Point and Plane
26.18 Angle Between Two Planes
26.19 Angle Bisectors of Two Planes
26.20 Family of Plane
26.21 Line and Plane
26.22 Sphere
Chapter 27 Probability
27.1 Introduction
27.2 Concept of Probability in Set Theoretic Language
27.3 Definition of Probability with Discrete Sample Space
27.4 Axiomatic Definition
27.5 Basic Theories
27.6 Conditional Probability
27.7 Independent Events
27.8 Total Probability
27.9 Bayes’ Theorem or Inverse Probability
27.10 Random Variable and Probability Distribution
27.11 Binomial Distribution
27.12 Poisson Distribution
27.13 Probability of Events in Experiments with Countable Infinite Sample Space
27.14 Important Information
Chapter 28 Statistics
28.1 Frequency Distribution
28.2 Measure of Central Tendency
28.3 Measure of Dispersion
28.4 Symmetric and Skew-Symmetric
Additional Solved Examples
Previous Years’ Solved JEE Main/AIEEE Questions
Practice Exercise 1
Practice Exercise 2
Answer Key
Solutions
Solved JEE 2017 Questions
