Description
Wiley Editorial Wiley'S Problems In Mathematics For Jee, Vol I by Wiley Editorial
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 of Contents
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
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 Questions