Wiley Problems in MATHEMATICS for JEE

Cover
Contents
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 cosp + b sinp
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 Permutation and Combination
7.1 Introduction
7.2 Fundamental Principles of Counting
7.3 Permutations (Arrangement of Objects)
7.4 Conditional Permutation
7.5 Circular Permutation (Arrangement of Object)
7.6 Combination (Selection of Object)
7.7 Divisors of a Given Natural Number
7.8 Division of Object into Groups
7.9 Method of Inclusion and Exclusion
7.10 Use of Multinomial
7.11 Some Important Points for Solving Geometrical Problems
7.12 Problems on Formation of Numbers
Chapter 8 Binomial Theorem
8.1 Binomial Expression
8.2 Binomial Theorem for Positive Integral Index
8.3 General Term
8.4 Independent Term or Constant Term
8.5 Middle Term in the Binomial Expansion
8.6 Greatest Binomial Coefficient
8.7 Numerically Greatest Term
8.8 Properties of Binomial Coefficient
8.9 Summation of Series Including Binomial Coefficient
8.10 An Important Theorem
8.11 Some Important Results
Chapter 9 Sequence and Series
9.1 Sequence
9.2 Progression
9.3 Different Means of Two Numbers
9.4 Relation between AM, GM and HM
9.5 Insertion of Means between Two Numbers
9.6 Weighted Means of Numbers
9.7 Arithmetico-Geometric Series
9.8 Sum of Miscellaneous Series
9.9 Sum of First n Natural Numbers
9.10 Inequalities
9.11 Exponential
9.12 Logarithm
9.13 Difference between the Exponential and Logarithmic Series
Chapter 10 Cartesian Coordinates and Straight Lines
10.1 Cartesian Coordinates
10.2 Slope of a Line
10.3 Intercepts of a Line
10.4 Slope of a Straight Line
10.5 Standard Forms of Equation of a Straight Line
10.6 Position of Two Points w.r.t. Straight Line
10.7 Angle between Two Straight Lines
10.8 Distance between Two Parallel Straight Lines
10.9 Perpendicular Distance of a Point From a Straight Line
10.10 Slope of Straight Line that Makes Angle ` with Line
10.11 Angle Bisectors
10.12 Family of Straight Lines
10.13 Locus of a Point
10.14 Shifting of Origin
Chapter 11 Pair of Straight Lines
11.1 Pair of Straight Lines − Fundamentals
11.2 Separation of Equations of Straight Lines from their Joint Equation
11.3 Combined Equation of Lines Joining Origin to Points of Intersections of a Line and a Curve
Chapter 12 Circle
12.1 Standard Equation of a Circle
12.2 General Equation of a Circle
12.3 General Equation of a Circle in Second Degree
12.4 Different Forms of Equations of Circle
Chapter 13 Parabola
13.1 Understanding Conic Section
13.2 Parabola: Definition and Its Terminologies
Chapter 14 Ellipse
14.1 Ellipse – Fundamentals
14.2 Position of Point Relative to Ellipse
14.3 Parametric Equation of Ellipse
14.4 Another Form of Ellipse (When b > a)
14.5 Tangent to Ellipse
14.6 Normal to Ellipse
14.7 Chords of Ellipse
14.8 Diameter of Ellipse
14.9 Geometric Properties of Ellipse
Chapter 15 Hyperbola
15.1 Hyperbola – Fundamentals
15.2 Position of Point Relative to Hyperbola
15.3 Parametric Equation of Hyperbola
15.4 Conjugation of Hyperbola
15.5 Tangent of Hyperbola
15.6 Normal to Hyperbola
15.7 Chords of Hyperbola
15.8 Asymptotes
15.9 Rectangular Hyperbola
Chapter 16 Statistics
16.1 Frequency Distribution
16.2 Measure of Central Tendency
16.3 Measure of Dispersion
16.4 Symmetric and Skew-Symmetric
Appendix: Chapterwise Solved JEE 2018 Questions