Mathematics XII

Relations and Functions
8 Topics
Introduction to Relations
Reflexive, Symmetric and Transitive Relations
Introduction to Functions
Types of Functions
Composition of Functions
Invertible Functions
Introduction to Binary Operations
Properties Of Binary Operations
Inverse Trigonometric Functions
 18 Topics
Introduction to Inverse Trigonometric Functions
Basic Concepts
Inverse of Sine Function and its Graph
Inverse of Cosine Function and its Graph
Inverse of Tangent Function and its Graph
Inverse of Cotangent Function and its Graph
Inverse of Cosecant Function and its Graph
Inverse of Secant Function and its Graph
Properties of Inverse Trigonometric Functions-I
Properties of Inverse Trigonometric Functions-II
Properties of Inverse Trigonometric Functions-III
Properties of Inverse Trigonometric Functions-IV
Properties of Inverse Trigonometric Functions-V
Examples-I
Examples-II
Examples-III
Examples-IV
Examples-V
Matrices
 19 Topics
Introduction to Matrices
Representation of Vertices of Geometrical Figures
Types of Matrices
Equality of Matrices
Addition of Matrices
Multiplication of a Matrix by a Scalar
Difference of Matrices
Properties of Matrix Addition
Properties of Scalar Multiplication of a Matrix
Multiplication of Matrices
More about Multiplication of Matrices
Properties of Multiplication of Matrices-I
The Properties of Multiplication of Matrices-II
Transpose of a Matrix
Symmetric and Skew Symmetric Matrices
Theorems Relating Symmetric and Skew Symmetric Matrices
Elementary Operation (Transformation) of a Matrix
Invertible Matrices
Inverse of a Matrix by Elementary Operations
Determinants
 23 Topics
Introduction to Determinants
Determinants of Matrices of Orders 1 and 2
Determinant of a Matrix of order 3
Expansion along the First Row
Expansion along Second Row
Expansion along First Column
Some Rules Related to the Determinants
Properties of Determinants-I
Properties of Determinants-II
Properties of Determinants-III
Properties of Determinants-IV
Area of a Triangle
Properties of Determinants-V
Properties of Determinants-VI
Minors of Elements of Determinants
Cofactors of Elements of Determinants
Adjoint of a Matrix
Theorem Related to the Adjoint of a Matrix
More Theorems
Theorem on Invertible Matrices
1 of 2
Continuity and Differentiability
 22 Topics
Introduction To Continuity
Problems Based on Continuous Functions
Introduction To Differentiability
Basics Of Chain Rule
Problems Based On Chain Rule
Derivative of Implicit Functions
Derivative of Inverse Trigonometric Function
Problem Based on Derivative of Inverse Trigonometric Function
Exponential Functions
Features of Exponential Functions
Properties of Exponential Functions
Introduction to Logarithmic Function
Plot of Logarithmic Function
Properties of Logarithmic Function
Derivatives of Exponential and Logarithmic Functions
Logarithmic Differentiation
Derivatives of Functions in Parametric Forms
Introduction to Second Order Derivatives
Problems Based on Second Order Derivative
Rolle’s Theorem
1 of 2
Application of Derivatives
 17 Topics
Rate of Change of Quantities
Introduction To Increasing and Decreasing Functions
Derivative test for Increasing and Decreasing Functions
Finding intervals in which a given Polynomial Function is Increasing or Decreasing
Tangents
Equation of the Tangent
Normal
Equation of the Normal
Introduction to Approximations
Finding Approximate Value of Polynomials
Word Problem Involving Approximations
Introduction to Maxima and Minima
First Derivative Test
Second Derivative Test
Second Derivative Test: Example I
Second Derivative Test: Example II
Maximum and Minimum Values of a Function in a Closed Interval
Integrals
 24 Topics
Introduction to Integrals
Integrals of Important Functions-I
Integrals of Important Functions-II
Properties of Indefinite Integrals
Calculating Integrals
Integration by Substitution
Integrals of Trigonometric Functions
Example Based on Integration using Substitution
Integration Using Trigonometric Identities
Integration of Some Particular Functions-I
Integration of Some Particular Functions-II
Integrals of Some Particular Functions- III
Integration by Partial Functions-I
Integration by Partial Functions-II
Integration by Partial Functions-III
Integration by Parts
Integral of the Type
Integrals of Some More Types
Definite Integral as the Limit of a Sum
Fundamental Theorem of Calculus
1 of 2
Application of Integrals
 4 Topics
Finding area Under a Simple Curve
Problem Based on Finding the Area Under a Simple Curve
Area of the Region Bounded by a Curve and a Line
Area Between Two Curves
Differential Equations
 9 Topics
Basic Concepts of Differential Equation
General and Particular Solutions of a Differential Equation
Formation of a Differential Equation
Equations in Variable Separable Form
Problem Based on Variable Separable Form
Introduction to Homogenous Functions
Solving Homogeneous Differential Equations
Linear Differential Equations
Solving Linear Differential Equations
Vector Algebra
 13 Topics
Introduction to Vectors
Position Vector, Direction Cosines and Direction Ratios
Adding and Subtracting Vectors
Properties of Vector Addition
Components of a Vector
Scalar (or dot) Product of Two Vectors
Unit Vector in the Direction of a Given Vector
Section Formula-II
Scalar (or dot) Product of Two Vectors
Projection of a Vector on a Line and Another Vector
Vector Product of Two Vectors-I
Vector Product of Two Vectors-II
Vector Product of Two Vectors-III
Three Dimensional Geometry
 11 Topics
Direction Cosines and Direction Ratios of a Line
Introduction to Three Dimensional Geometry
Direction Cosines and Direction Ratios of a Line
Equation of a Line in Space
Angle Between Two Lines
Shortest Distance Between Two Lines
Plane
Coplanarity of Two Lines
Angle Between Two Planes
Distance of a Point from a Plane
Angle Between a Line and a Plane
Linear Programming
 14 Topics
Introduction to Linear Programming
Formulating Linear Programming Problems Mathematically
Rules of Solving the Linear Programming Problems Graphically
Solving LPP Graphically
Introduction to Linear Programming
Linear Programming Problem
Mathematical Formulation of the Linear Programming Problem
Graphical Method of Solving Linear Programming Problems
Different Types of Linear Programming Problems
Diet Problem Types of Linear Programming
Manufacturing Problems Types of Linear Programming
Allocation Problems Types of Linear Programming
Transportation Problems Types of Linear Programming
Corner Point Method of Solving linear Programming Problem
Probability
 10 Topics
Introduction to Probability
Conditional Probability
Properties of Conditional Probability
Multiplication Theorem on Probability
Multiplication Theorem on Probability
Baye’s Theorem
Probability Distribution of a Random variable
Random Variables and its Probability Distributions
Mean of a Random Variable
Variance of a Random Variable
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Properties Of Binary Operations

Mathematics XII Relations and Functions Properties Of Binary Operations
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[Binary Operations, Commutative Property, Associative Property, Identity Property, Inverse Property]

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