Wiley Problems in MATHEMATICS for JEE

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Cover Contents 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 Matrices and Determinants 18.1 Definition of a Matrix 18.2 Order of a Matrix 18.3 Types of a Matrix 18.4 Equality of Matrices 18.5 Addition and Subtraction of Matrices 18.6 Multiplication of a Matrix by a Scalar 18.7 Multiplication of Two Matrices 18.8 Operations Regarding Matrices 18.9 Types of a Matrix on the Basis of Operations 18.10 Definition of a Determinant 18.11 Evaluation of Determinants 18.12 Minors 18.13 Cofactors 18.14 Adjoint of a Square Matrix 18.15 Inverse of a Matrix 18.16 Singular and Non-Singular Matrices 18.17 Elementary Operations or Elementary Transformations of a Matrix 18.18 Inverse of a Matrix by Elementary Operations (Elementary Operations on Matrix Equation) 18.19 Rank of a Matrix 18.20 Echelon Form of a Matrix 18.21 Homogeneous Linear Equations 18.22 System of Linear Non-Homogeneous Equations 18.23 Minor of Any Element of a Matrix 18.24 Cofactor of Any Element of a Matrix 18.25 Determinant of Any Matrix 18.26 Properties of Determinants 18.27 Sum of Determinants 18.28 Multiplication of Determinants 18.29 Differentiation of Determinants 18.30 Special Determinants 18.31 Solution of System of Linear Equations Chapter 19 Limit, Continuity and Differentiability 19.1 Limit of a Function 19.2 Definition 19.3 Algebra of Limits 19.4 Evaluation of Limits 19.5 Use of Standard Limits 19.6 Some More Standard Forms 19.7 Use of Expansion 19.8 L’Hospital’s Rule 19.9 Sandwich Theorem (Squeeze Play Theorem) 19.10 Continuity 19.11 Differentiability Chapter 20 Differentiation 20.1 Introduction 20.2 Differentiation from First Principle 20.3 Derivatives of Some of the Frequently Used Functions 20.4 Rules to Find Out Derivatives 20.5 Derivative of Second Order y″ or y2 20.6 Differentiation of a Function with Respect to Another Function Chapter 21 Applicationsof Derivatives 21.1 Geometrical Interpretation of Derivative 21.2 Tangent and Normal 21.3 Angles Between Two Curves 21.4 dy/dx as Rate Measures 21.5 Errors and Approximations 21.6 Monotonicity of Function 21.7 Maxima and Minima of Functions of a Single Variable 21.8 Mean Value Theorems 21.9 Geometrical Problems Chapter 22 Indefinite Integration 22.1 Primitive or Anti-Derivative of a Function 22.2 Indefinite Integral and Indefinite Integration 22.3 Methods of Integration 22.4 Integration by Partial Fractions Chapter 23 Definite Integration 23.1 Definition 23.2 Geometrical Meaning of Definite Integration 23.3 Definite Integration as the Limit of Sum 23.4 Properties of Definite Integration 23.5 Properties Based on Periodic Function 23.6 Properties Based on Inequality 23.7 Newton–Leibnitz Rule 23.8 Summation of Series by Integration 23.9 Reduction Formulae for Definite Integration 23.10 Wallis Formulae Chapter 24 Area Under the Curves 24.1 Curve Tracing 24.2 Steps to Draw Curve 24.3 Area of Bounded Region 24.4 Area Enclosed Between Two Curves Chapter 25 Differential Equations 25.1 Introduction 25.2 Basic Definition 25.3 Order of a Differential Equation 25.4 Degree of a Differential Equation 25.5 Formation of a Differential Equation 25.6 Solution of a Differential Equation 25.7 Differential Equations of First-Order and First-Degree 25.8 Solution of First-Order and First-Degree Differential Equations 25.9 Variable Separable Type Differential Equation 25.10 Equation Reducible to Variable Separable Type Differential Equation 25.11 Homogeneous Type Differential Equation 25.12 Non-Homogeneous Type Differential Equation 25.13 Exact Differential Equation 25.14 Linear Differential Equation 25.15 Solution of Differential Equation of the First Order but of Higher Degree 25.16 Applications of Differential Equation Chapter 26 Vector Algebra 26.1 Introduction 26.2 Representation of a Vector 26.3 Types of Vectors 26.4 Rectangular Resolution of Vectors (Orthogonal System of Vectors): Resolution of a Vector in Two Dimensions 26.5 Resolution of a Vector in Three Dimensions 26.6 Properties of Vectors 26.7 Fundamental Theorems of Vectors 26.8 Linear Combinations of Vectors 26.9 Linearly Dependent and Independent Vectors 26.10 Position Vector of a Dividing Point (Section Formulae) 26.11 Bisector of the Angle Between Two Vectors 26.12 Product of Two Vectors 26.13 Scalar or Dot Product of Two Vectors 26.14 Vector or Cross-Product of Two Vectors 26.15 Scalar Triple Product 26.16 Vector Triple Product 26.17 Scalar or Vector Product of Four Vectors 26.18 Method to Prove Collinearity 26.19 Vector Equation Chapter 27 Three-DimensionalGeometry 27.1 Rectangular Coordinate System in Space 27.2 Other Methods of Defining the Position of Any Point P in Space 27.3 Shifting the Origin 27.4 Distance Formula 27.5 Section Formula 27.6 Triangle and Tetrahedron 27.7 Direction Cosines of a Line 27.8 Direction Ratios 27.9 Projection of a Line 27.10 Equation of a Straight Line in Space 27.11 Angle Between Two Lines 27.12 Intersections of Two Lines 27.13 Shortest Distance Between Two Non-intersecting Lines 27.14 Point and Line 27.15 The Plane 27.16 Equation of Plane in Different Forms 27.17 Point and Plane 27.18 Angle Between Two Planes 27.19 Angle Bisectors of Two Planes 27.20 Family of Plane 27.21 Line and Plane 27.22 Sphere Chapter 28 Probability 28.1 Introduction 28.2 Concept of Probability in Set Theoretic Language 28.3 Definition of Probability with Discrete Sample Space 28.4 Axiomatic Definition 28.5 Basic Theories 28.6 Conditional Probability 28.7 Independent Events 28.8 Total Probability 28.9 Bayes’ Theorem or Inverse Probability 28.10 Random Variable and Probability Distribution 28.11 Binomial Distribution 28.12 Poisson Distribution 28.13 Probability of Events in Experiments with Countable Infinite Sample Space 28.14 Important Information Appendix: Chapterwise SolvedJEE 2018 Questions