Wiley's Decoding Mathematics For JEE, Vol II
ISBN: 9789357469630
1000 pages
For more information write to us at: acadmktg@wiley.com
Description
Decoding Mathematics for JEE, Volume – II (as per Class 12 syllabus) offers a compelling solution for all CBSE students preparing for JEE and other engineering entrance examinations. The content has been organized to provide a more structured approach to meet the requirements of both JEE (Main and Advanced) and CBSE syllabi. The book offers multidimensional approach of the subject through clear and engaging explanation of concepts aided with interesting-colored figures. Also, the book deals with application-based approach through qualitative problem sets. This book empowers students' concept building and enhances critical thinking skills in mathematics and its fundamentals.
Note to the Teachers and Students
Preface
Chapter 1 Functions
1.1 Introduction
1.1.1 Function as a Machine
1.2 Defining a Function
1.2.1 Function – Definition
1.2.2 A Function as a Set of Ordered Pairs
1.3 Domain, Codomain and Range of a Function
1.3.1 Algebra of Domains
1.4 Some Useful Types of Functions
1.4.1 Polynomial Function
1.4.2 Algebraic Function
1.4.3 Exponential Function
1.4.4 Logarithmic Function
1.4.5 Absolute Value Function (Modulus)
1.4.6 Signum Function
1.4.7 Greatest Integer or Step-Up Function
1.4.8 Fractional Part Function
Solved Examples
Practice Questions
Answer with Explanation
1.5 Domain of a Function
1.5.1 Algebra of Domains of Functions
Solved Examples
Practice Questions
Answer with Explanation
1.6 Range of a Function
1.7 Finding Range of a Function
Solved Examples
Practice Questions
Answer with Explanation
1.8 Classification of Functions
1.9 One–One and Many–One Functions
1.9.1 One–One Function (Injective Mapping)
1.9.2 Many–One Function (Non-Injective)
1.9.3 Methods to Identify One–One or Many–One Functions
1.10 Onto and Into Functions
1.10.1 Methods to Identify Onto or Into Functions
Solved Examples
Practice Questions
Answer with Explanation
1.11 Nature of Functions
1.12 Odd and Even Nature of Function
1.13 Periodic Function
1.13.1 Rules for Finding the Period of A Periodic Function
Solved Examples
Practice Questions
Answer with Explanation
1.14 Inverse of a Function
1.14.1 Summary of Inverse Functions
1.15 Inverse Sine Function
1.15.1 Notes on the Graph of the Inverse Sine Function
1.16 Inverse Cosine Function
1.17 Some Standard Functions along with Their Inverse Functions
1.18 Properties of Inverse Function
Solved Examples
Practice Questions
Answer with Explanation
1.19 Composite Functions
1.20 Graphical Transformation
1.20.1 Graphs of Some Elementary Functions
1.20.2 Trigonometric or Circular Functions
1.20.3 The Inverse Circular (Trigonometric) Functions
1.21 Sequences of Transformations
Solved Examples
Practice Questions
Answer with Explanation
Important Formulas
Chapter Exercises
Previous Years’ JEE Main Questions (2008–2018)
Previous Years’ Advanced Questions (2008–2018)
Answer Key
Concept Map
Chapter 2 Limits, Continuity and Differentiability
2.1 Introduction
2.2 Defining Limits
2.2.1 Left-Handed Limit and Right-Handed Limit
2.2.2 Existence of Limit at a Point
2.3 Fundamental Theorems of Limits
2.4 Different Strategies to Evaluate Limits
2.4.1 Algebraic Methods
Solved Examples
Practice Questions
Answer with Explanation
2.4.2 Sandwich Theorem
Solved Examples
Practice Questions
Answer with Explanation
2.4.3 Expansion of a Function
Solved Examples
Practice Questions
Answer with Explanation
2.4.4 Theorem for 1∞ Indeterminate Form
Solved Examples
Practice Questions
Answer with Explanation
2.5 Continuity of a Function
2.5.1 Formulative Definition of Continuity
2.5.2 Continuity in an Interval
2.5.3 Reasons of Discontinuity
2.6 Types of Discontinuity
2.6.1 Removable Discontinuity
2.6.2 Non-Removable Discontinuity
2.6.3 Continuity of Functions Defined by Some Functional Rule
2.7 Theorems on Continuity
2.8 Properties of Function Continuous in [a, b]
Solved Examples
Practice Questions
Answer with Explanation
2.9 Differentiability of Functions
2.9.1 Existence of Derivative
2.9.2 Derivability over an Interval
2.9.3 Theorems on Differentiability
2.9.4 Finding Functions that are Differentiable and Satisfy Given Functional Rule
Solved Examples
Practice Questions
Answer with Explanation
Important Formulas
Chapter Exercises
Previous Years’ JEE Main Questions (2008–2018)
Previous Years’ JEE Advanced Questions (2008–2018)
Answer Key
Concept Map
Chapter 3 Application of Derivatives
3.1 Introduction
3.2 Derivative as Slope of Tangents
3.3 Derivative of a Function
3.3.1 Second Definition of Derivatives
3.3.2 Other Notations of Derivatives
3.4 Theorems of Differentiation
3.5 Chain Rule of Differentiation
3.6 Implicit Differentiation
3.7 Higher Order Derivatives
3.8 Tangent and Normal
3.8.1 Important Points to Remember
3.8.2 Some Common Parametric Coordinates on a Curve
3.9 Angle of Intersection of Two Curves
3.10 Length of Tangent, Normal, Subtangent and Subnormal
3.11 Approximation and Differentials
Solved Examples
Practice Questions
Answer with Explanation
3.12 Monotonicity of a Function
3.12.1 Monotonicity of a Function at a Point
3.12.2 Monotonicity in an Interval
3.12.3 Testing an Increasing and a Decreasing Function
3.13 Greatest Value and Least Value of a Function
3.14 Establishing Inequalities
Solved Examples
Practice Questions
Answer with Explanation
3.15 Maxima and Minima of a Function
3.15.1 How Maxima and Minima are Classified?
3.15.2 Necessary and Sufficient Conditions for a Local Maximum and Local Minimum
3.15.3 Use of Second-Order Derivative in Ascertaining the Maxima or Minima of a Differentiable Function
3.15.4 Concavity of Functions
3.15.5 Summary of Working Rules of Maxima and Minima
3.15.6 Sign of Second-Order Derivative and Points of Inflection
3.15.7 Different Graphs of Cubic Polynomials
Solved Examples
Practice Questions
Answer with Explanation
3.16 Rolle’s Theorem
3.17 Lagrange’s Mean Value Theorem (LMVT)
3.17.1 Alternative Form of LMVT
Solved Examples
Practice Questions
Answer with Explanation
Important Formulas
Chapter Exercises
Previous Years’ JEE Main Questions (2008–2018)
Previous Years’ JEE Advanced Questions (2008–2018)
Answer Key
Concept Map
Chapter 4 Indefinite Integrals
4.1 Introduction
4.1.1 Integration as Anti-Derivative
4.2 Anti-Derivatives
4.3 Some Standard Integration Formulas
4.4 Integration using Substitution
Solved Examples
Practice Questions
Answer with Explanation
4.5 Integration by Parts
4.5.1 Some Useful Results
4.6 Few Useful Trigonometric Formulas
4.7 Some Standard Substitutions Used in Integration
Solved Examples
Practice Questions
Answer with Explanation
4.8 Integration of Rational Functions
4.8.1 Different Methods of Breaking a Proper Fraction into Partial Fractions
4.9 Some Standard Forms of an Integral
4.10 Integration of Trigonometric Functions
Solved Examples
Practice Questions
Answer with Explanation
Important Formulas
Chapter Exercises
Previous Years’ JEE Main Questions (2008–2018)
Previous Years’ JEE Advanced Questions (2008–2018)
Answer Key
Concept Map
Chapter 5 Definite Integration
5.1 Introduction
5.1.1 Definite Integral as Infinitesimal Sum
5.1.2 Geometrical Meaning of Definite Integral
5.1.3 Integrals with Infinite Limits
5.2 Properties of Definite Integral
5.2.1 Basic Properties of Definite Integral
Solved Examples
Practice Questions
Answer with Explanation
5.3 Advanced Properties of Definite Integral
Solved Examples
Practice Questions
Answer with Explanation
5.4 Definite Integral as the Limit of a Sum
5.5 Method to Express the Infinite Series as Definite Integral
Solved Examples
Practice Questions
Answer with Explanation
Important Formulas
Chapter Exercises
Previous Years’ JEE Main Questions (2008–2018)
Previous Years’ JEE Advanced Questions (2008–2018)
Answer Key
Concept Map
Chapter 6 Area Under the Curve
6.1 Introduction
6.1.1 Curves
6.1.2 Types of Curves
6.2 Area Bounded by Single Curve
6.2.1 Steps to Find the Area Under the Curve
6.3 Area Bounded between Two Curves
6.3.1 Choosing Elementary Area and Limit of Integration
Solved Examples
Practice Questions
Answer with Explanation
Important Formulas
Chapter Exercises
Previous Years’ JEE Main Questions (2008–2018)
Previous Years’ JEE Advanced Questions (2008–2018)
Answer Key
Concept Map
Chapter 7 Differential Equations
7.1 Introduction
7.1.1 Differential Equation in Motion of a Spring
7.2 Introduction of a Differential Equation
7.3 Order and Degree of a Differential Equation
7.4 Formation of Differential Equation
Solved Examples
Practice Questions
Answer with Explanation
7.5 Solution of a Differential Equation
7.6 General Solution
7.6.1 Differential Equations Reducible to the Separable Variable Type
7.6.2 General Form of Variable Separation
7.6.3 Special Type of Second-Order Differential Equation
7.7 Particular Solution
7.8 Differential Equations in Variables Separable Form
7.9 Differential Equation Reducible to Variables Separable Form
Solved Examples
Practice Questions
Answer with Explanation
7.10 Homogeneous Differential Equation
7.11 Solution of Homogeneous Differential Equation
7.12 Linear and Non-Linear Differential Equations
7.12.1 First-Order Linear Differential Equation
7.12.2 Extended Form of Linear Differential Equations
Solved Examples
Practice Questions
Answer with Explanation
7.13 Orthogonal Trajectory of a Curve
7.13.1 Procedure to Find the Orthogonal Trajectory of a Curve
7.14 Solution by Inspection
7.15 First-Order Differential Equations – Real-Life Applications
7.15.1 Newton’s Cooling and Warming Law
7.15.2 Population Growth and Decay
7.15.3 Radioactive Decay
7.15.4 Mixture of Two-Salts Solution
Solved Examples
Practice Questions
Answer with Explanation
Important Formulas
Chapter Exercises
Previous Years’ JEE Main Questions (2008–2018)
Previous Years’ JEE Advanced Questions (2008–2018)
Answer Key
Concept Map
Chapter 8 Matrices
8.1 Introduction
8.2 Definition of Matrix
8.3 Types of Matrices
8.4 Operations on Matrices
8.5 Addition and Subtraction of Matrices
8.5.1 Properties of Addition and Subtraction of Matrices
8.6 Scalar Multiplication of Matrices
8.6.1 Properties of Scalar Multiplication
8.7 Multiplication of Two Matrices
8.7.1 Properties of Multiplication of Matrices
8.8 Types of Matrices Based on Operations
Solved Examples
Practice Questions
Answer with Explanation
8.9 Determinants of a Matrix
8.10 Minor, Cofactor and Adjoint of Matrices
8.11 Inverse of a Matrix
8.11.1 Properties of Inverse of a Matrix
Solved Examples
Practice Questions
Answer with Explanation
8.12 Consistent System of Equations
8.12.1 Solution of a 3 × 3 System of Linear Equations Using Inverse Matrix Method
8.12.2 Solution of a 2 × 2 System of Linear Equations Using Inverse Matrix Method
8.13 Homogeneous System of Equations
Solved Examples
Practice Questions
Answer with Explanation
Important Formulas
Chapter Exercises
Previous Years’ JEE Main Questions (2008–2018)
Previous Years’ JEE Advanced Questions (2008–2018)
Answer Key
Concept Map
Chapter 9 Determinants
9.1 Introduction
9.2 Determinants
9.2.1 Determinant of a Matrix of Order Two
9.2.2 Determinants of a Matrix of Order 3 × 3
9.3 Properties of Determinants
9.4 Area of a Triangle in Determinant Form
9.5 Product of Two Determinants
9.6 Differentiation of a Determinant
9.7 Summation of Determinants
9.8 Determinants Involving Integrations
9.9 Special Determinants
Solved Examples
Practice Questions
Answer with Explanation
9.10 Solution of Equations Using Determinant Method
9.10.1 System of Linear Equations
9.10.2 Cramer’s Rule
Solved Examples
Practice Questions
Answer with Explanation
Important Formulas
Chapter Exercises
Previous Year’s JEE Main Questions (2008–2018)
Previous Year’s JEE Advanced Questions (2008–2018)
Answer Key
Concept Map
Chapter 10 Vectors
10.1 Introduction
10.2 Geometric Description of Vectors
10.3 Types of Vectors
10.4 Properties of Vectors
10.4.1 Addition and Subtraction of Two Vectors
10.4.2 Parallelogram Law
10.4.3 Multiplication of Vectors with a Scalar
10.4.4 Vectors in the Coordinate Plane
10.4.5 Components of a Vector
10.4.6 Magnitude of a Vector
10.4.7 Addition of Vectors Using Components
10.5 Vectors in Three-Dimensions
10.6 Dot Product
10.6.1 Scalar Product of Two Vectors
10.6.2 Projection of a Vector
10.7 Cross Product of Vectors
10.7.1 Vector Product of Two Vectors (Cross Product)
10.7.2 Direction of Cross Product Vector
10.7.3 Angle Bisector of Two Vectors
Solved Examples
Practice Questions
Answer with Explanation
10.8 Scaler Triple Product
Solved Examples
Practice Questions
Answer with Explanation
10.9 Vector Triple Product
Solved Examples
Practice Questions
Answer with Explanation
10.10 Geometrical Applications
10.10.1 Angle Bisectors
10.11 Application of Vectors in Mechanics
10.12 Equations of Lines and Planes
10.12.1 Vector Equation of a Straight Line
10.12.2 Plane and Equation of Plane
10.12.3 Intersecting Planes
Solved Examples
Practice Questions
Answer with Explanation
Important Formulas
Chapter Exercises
Previous Years’ JEE Main Questions (2008–2018)
Previous Years’ JEE Advanced Questions (2008–2018)
Answer Key
Concept Map
Chapter 11 Three-Dimensional Geometry
11.1 Introduction to Three-Dimensional Rectangular Coordinate System
11.1.1 Plotting Points in Three-Dimensional Space
11.1.2 Distance Formula in Three-Dimensions
11.1.3 Section Formula
11.1.4 Shifting of Origin
11.2 Direction Cosines of a Straight Line
11.2.1 Relation between Direction Cosines
11.3 Direction Ratios
11.3.1 Parallel Lines
11.3.2 Direction Cosines of a Line Joining Two Points
11.3.3 Angle between Two Lines Whose Direction Ratios are Defined
11.4 Area of a Triangle
Solved Examples
Practice Questions
Answer with Explanation
11.5 Equations of Straight Lines
11.5.1 Equation of a Straight Line that Passes through a Point and Parallel to a Vector
11.5.2 Equation of a Straight Line that Passes through Two Points
11.5.3 Collinearity of Three Points
11.5.4 Projection of a Line Segment on Another Line
11.5.5 Perpendicular Distance of a Point from a Line
11.6 Angle between Two Lines
11.6.1 Cartesian Form
11.7 Shortest Distance between Two Lines
11.7.1 Skew Lines and Coplanar Lines
Solved Examples
Practice Questions
Answer with Explanation
11.8 The Plane
11.9 Equation of Plane in Different Forms
11.9.1 Equation of Planes in Various Form
11.10 Angle between Two Planes
11.10.1 Bisector Planes of Angle between Two Planes
11.11 Plane and Line
11.11.1 Intersection of a Line and Plane
11.11.2 Angle between a Line and a Plane
11.12 Point and Plane
11.12.1 Position of Two Points w.r.t. a Plane
11.12.2 Distance of a Point from a Plane
11.12.3 Perpendicular Distance between a Point and a Plane
11.13 Sphere
11.13.1 Equation of a Sphere whose Diameter is the Line Joining Two Points
Solved Examples
Practice Questions
Answer with Explanation
Important Formulas
Chapter Exercises
Previous Years’ JEE Main Questions (2008–2018)
Previous Years’ JEE Advanced Questions (2008–2018)
Answer Key
Concept Map
Chapter 12 Probability
12.1 Introduction
12.2 Basic Terminology
12.3 Probability Experiment
12.4 Classical Approach to Probability
12.5 Notation in Probability
12.6 Addition Rule
12.7 Dependent and Independent Events
Solved Examples
Practice Questions
Answer with Explanation
12.8 Conditional Probability
12.8.1 Conditional Probability and The Axioms of Probability
12.8.2 Properties of Conditional Probabilities
12.9 Multiplication Rule
12.10 Pairwise and Mutually Independent Events
Solved Examples
Practice Questions
Answer with Explanation
12.11 Law of Total Probability
12.11.1 Theorem of Total Probability
12.12 Bayes’ Theorem
Solved Examples
Practice Questions
Answer with Explanation
12.13 Probability Distribution of a Random Variable
12.13.1 True Randomness
12.13.2 Probability Distributions
12.13.3 Binomial Distribution
12.13.4 Binomial Distribution for Successive Events
Solved Examples
Practice Questions
Answer with Explanation
12.14 Geometrical Application and Mixed Approach Problems
Solved Examples
Practice Questions
Answer with Explanation
Important Formulas
Chapter Exercises
Previous Years’ JEE Main Questions (2008–2018)
Previous Years’ JEE Advanced Questions (2008–2018)
Answer Key
Concept Map
13 Principle of Mathematical Induction
13.1 Introduction
13.2 Principle of Mathematical Induction
Solved Examples
Practice Questions
Answer with Explanation
Important Formulas
Chapter Exercises
Answer Key
Concept Map
Chapter 14 Mathematical Reasoning
14.1 Introduction
14.2 Sentence
14.3 Statement
14.3.1 Types of Statements
14.4 Basic Logical Connectives or Logical Operators
14.4.1 Conjunction
14.4.2 Disjunction or Alternation
14.5 Negation
14.5.1 Negation of Compound Statements
14.6 Conditional or Implication Statements
14.6.1 Converse, Inverse and Contrapositive of an Implication
14.7 Bi-Conditional or Equivalence Statement
14.8 Negation of Conditional Statement
14.9 Special Types of Compound Statements
14.10 Logical Equivalence
14.11 Quantifiers
Solved Examples
Practice Questions
Answer with Explanation
Important Formulas
Chapter Exercise
Previous Years’ JEE Main Questions (2008–2018)
Answer Key
Concept Map
Chapter 15 Statistics
15.1 Introduction
15.2 Variables
15.3 Frequency Distribution
15.4 Statistical Terms
15.5 Average of Discrete Data
15.5.1 Arithmetic Mean
15.5.2 Weighted Arithmetic Mean
15.5.3 Geometric Mean
15.5.4 Harmonic Mean
15.5.5 Relation between Arithmetic Mean, Geometric Mean and Harmonic Mean
15.5.6 Mode
15.5.7 Median (Middle Observation)
15.6 Measure of Dispersion
15.6.1 Range
15.6.2 Mean Deviation
15.6.3 Standard Deviation
15.6.4 Quartile Deviation
15.7 Relative Frequency
15.8 Relation between Mean, Median and Mode
Solved Examples
Practice Questions
Answer with Explanation
Important Formulas
Chapter Exercise
Previous Years’ JEE Main Questions (2008–2018)
Answer Key
Concept Map
JEE Advanced Paper 2024 with Solutions