 MATHEMATICS
నెల్లూరు: మనుబోలు మండలం బద్వేలు క్రాస్‌రోడ్డు దగ్గర కారు బోల్తా, ముగ్గురికి గాయాలు|కర్నూలు: 16 వ రోజు జగన్ ప్రజా సంకల్ప యాత్ర|రంగారెడ్డి: మైలార్‌దేవ్‌పల్లిలో కింగ్స్‌ కాలనీలో ముస్తఫా అనే వ్యక్తిపై దుండగుల కాల్పులు|కడప: జగన్ సీఎం అయితే తన ఆస్తులు పెరుగుతాయి..చంద్రబాబు సీఎంగా ఉంటే ప్రజల ఆస్తులు పెరుగుతాయి: మంత్రి సోమిరెడ్డి|సిరిసిల్ల: అన్ని గ్రామాల్లో కేసీఆర్ గ్రామీణ ప్రగతి ప్రాంగణాలు నిర్మిస్తాం: మంత్రి కేటీఆర్|హైదరాబాద్: బంజారాహిల్స్ పోలీస్‌ స్టేషన్‌లో యూసుఫ్‌గూడ కార్పొరేటర్ తమ్ముడిపై కేసు నమోదు|అమరావతి: చీఫ్‌విప్‌గా పల్లె రఘునాథరెడ్డి పేరు, శాసనమండలి చీఫ్‌ విప్‌గా పయ్యావుల కేశవ్‌ పేరు ఖరారు|అనంతపురం: జెట్ ఎయిర్‌వేస్‌లో ఉద్యోగాల పేరుతో మోసం, రూ.14 లక్షలు వసూలు చేసిన యువకుడు|ఢిల్లీ: సరి, బేసి విధానానికి ఎన్జీటీ గ్రీన్‌సిగ్నల్, కాలుష్యం పెరిగినప్పుడు అమలు చేసుకోవచ్చన్న ఎన్జీటీ|శ్రీకాకుళం: వైసీపీ ఎమ్మెల్యేల గొంతు నొక్కుతున్నారు.. నిరసనగా అసెంబ్లీని బహిష్కరించాం: వైసీపీ నేత ధర్మాన
CBSE XII > MATHEMATICS

# 13. Probability

 13.1. Introduction 13.2. Conditional Probability 13.2. Conditional Probability 13.2. Conditional Probability 13.2.1. Properties of Conditional Probability 13.2.1. Properties of Conditional Probability 13.2.1. Properties of Conditional Probability 13.3. Multiplication Theorem on Probability 13.4. Independent Events 13.4. Independent Events 13.4. Independent Events 13.5. Bayes' Theorem 13.5.1. Partition of a Sample Space 13.5.2. Theorem of Total Probability 13.6. Random Variables and its Probability Distributions 13.6. Random Variables and its Probability Distributions 13.6. Random Variables and its Probability Distributions 13.6.1. Probability Distribution of a Random Variable 13.6.2. Mean of a Random Variable 13.6.3. Variance of Random Variable 13.7. Bernoulli Trials and Binomial Distribution 13.7. Bernoulli Trials and Binomial Distribution 13.7. Bernoulli Trials and Binomial Distribution 13.7.1. Bernoulli Trials 13.7..2. Binomial Distribution

# 1. Relations and Functions

 1.1 Introduction 1.2. Types of Relations 1.2. Types of Relations 1.2. Types of Relations 1.2. Types of Relations 1.3. Types of Functions 1.3. Types of Functions 1.3. Types of Functions 1.4. Composition of Functions and Invariable Functions 1.4. Composition of Functions and Invariable Functions 1.4. Composition of Functions and Invariable Functions 1.5. Binary Operations

# 2. Inverse Trigonometric Functions

 2.1. Introduction 2.2. Basic Concepts 2.3. Properties of Inverse Trigonometric Functions 2.3. Properties of Inverse Trigonometric Functions 2.3. Properties of Inverse Trigonometric Functions 2.3. Properties of Inverse Trigonometric Functions 2.3. Properties of Inverse Trigonometric Functions 2.3. Properties of Inverse Trigonometric Functions

# 3.Matrices

 3.1. Introduction 3.2. Matrix 3.2. Matrix 3.2. Matrix 3.2.1. Order of Matrix 3.3. Types of Matrices 3.3. Types of Matrices 3.3. Types of Matrices 3.3.1. Equality of Matrices 3.3.1. Equality of Matrices 3.3.1. Equality of Matrices 3.4. Operations in Matrices 3.4.1. Addition of Matrices 3.4.2. Multiplication of Matrix by a Scalar 3.4.3. Properties of Matrix Addition 3.4.4. Properties of Scalar Multiplication of a Matrix 3.4.5. Multiplication of Matrices 3.4.5. Multiplication of Matrices 3.4.6. Properties of Multiplication of Matrices 3.5. Transpose of a Matrix 3.5.1. Properties of Transpose of the Matrix 3.6. Symmetric and Skew Symmetric Matrices 3.7. Elementary Operation (Transformation) of a Matrix 3.8. Invertible Matrices 3.8.1. Inverse of a Matrix by Elementary Operations 3.8.1. Inverse of a Matrix by Elementary Operations 3.8.1. Inverse of a Matrix by Elementary Operations

# 4. Determinants

 4.1. Introduction 4.2. Determinant 4.2.1. Determinant of a Matrix of Order One 4.2.2. Determinant of a Matrix of Order Two 4.2.3. Determinant of a Matrix of Order 3 x 3 4.3. Properties of Determinants 4.3. Properties of Determinants 4.3. Properties of Determinants 4.4. Area of Triangle 4.5. Minors and Co-Factors 4.6. Adjoint and Inverse of a Matrix 4.6.1. Adjoint of a Matrix 4.7. Applications of Determinants and Matrices 4.7.1. Solution of System of Linear Equations Using Inverse of a Matrix

# 5. Continuity and Differentiability

 5.1. Introduction 5.2. Continuity 5.2. Continuity 5.2. Continuity 5.2. Continuity 5.2. Continuity 5.2. Continuity 5.2. Continuity 5.2.1. Algebra of Continuous Functions 5.3. Differentiability 5.3. Differentiability 5.3. Differentiability 5.3. Differentiability 5.3. Differentiability 5.3. Differentiability 5.3. Differentiability 5.3.1. Derivatives of Composite Functions 5.3.1. Derivatives of Composite Functions 5.3.1. Derivatives of Composite Functions 5.3.2. Derivatives of Implicit Functions 5.3.3. Derivatives of Inverse Trigonometric Functions 5.4. Exponential and Logarithmic Functions 5.5. Logarithmic Differentiation 5.6. Derivatives of Functions in Parametric Forms 5.7. Second Order Derivative 5.7. Second Order Derivative 5.7. Second Order Derivative 5.8. Mean Value Theorem

# 6. Application of Derivatives

 6.1. Introduction 6.2. Rate of Change of Quantities 6.2. Rate of Change of Quantities 6.2. Rate of Change of Quantities 6.3. Increasing and Decreasing 6.3. Increasing and Decreasing 6.3. Increasing and Decreasing 6.3. Increasing and Decreasing 6.3. Increasing and Decreasing 6.4. Tangents and Normals 6.5. Approximations 6.5. Approximations 6.5. Approximations 6.5. Approximations 6.5. Approximations 6.5. Approximations 6.5. Approximations 6.6. Maxima and Minima 6.6. Maxima and Minima 6.6. Maxima and Minima 6.6.1. Maximum and Minimum Values of a Function in a Closed Interval

# 7. Integrals

 7.1. Introduction 7.1. Introduction 7.1. Introduction 7.2. Integration as an Inverse Process of Differentiation 7.2.1. Geometrical Interpretation of Indefinite Integral 7.2.2. Some Properties of Indefinite Integral 7.2.2. Some Properties of Indefinite Integral 7.2.3. Comparison between Differentiation and Integration 7.3. Methods of Integration 7.3.1. Integration by Substitution 7.3.1. Integration by Substitution 7.3.1. Integration by Substitution 7.3.2. Integration using Trigonometric Identities 7.4. Integrals of Some Particular Functions 7.5. Integration by Partial Fractions 7.5. Integration by Partial Fractions 7.5. Integration by Partial Fractions 7.6. Integration by Parts 7.6. Integration by Parts 7.6. Integration by Parts 7.6.1. Integral of the Type 7.6.2. Integrals of Some More Types 7.7. Definite Integral 7.7.1. Definite Integral as the Limit of a Sum 7.7.1. Definite Integral as the Limit of a Sum 7.7.1. Definite Integral as the Limit of a Sum 7.8. Fundamental Theorem of Calculus 7.8.1. Area of Function 7.8.2. First Fundamental Theorem of Integral Calculus 7.8.3. Second Fundamental Theorem of Integral Calculus 7.9 Evolution of Definite Integrals by Substitution 7.10. Some Properties of Definite Integrals 7.10. Some Properties of Definite Integrals 7.10. Some Properties of Definite Integrals

# 8. Application of Integrals

 8.1. Introduction 8.2. Area Under Simple Curves 8.2.1. The Area of the Region bounded by Curve and a Line 8.3. Area between Two Curves

# 9. Differential Equations

 9.1. Introduction 9.2. Basic Concepts 9.2.1. Order of Differential Equation 9.2.2. Degree of a Differential Equation 9.3. General and Particular Solutions of a Differential Equation 9.4. Formation of a Differential Equation Whose General Solution is Given 9.4.1. Procedure to form a Differential Equation that will represent a given Family of Curves 9.5. Methods of Solving First Order, First Degree Differential Equations 9.5.1. Differential Equations with Variables Separable 9.5.2. Homogeneous Differential Equations 9.5.3. Linear Differential Equations

# 10.Vector Algebra

 10.1. Introduction 10.2. Some Basic Concepts 10.2. Some Basic Concepts 10.2. Some Basic Concepts 10.2. Some Basic Concepts 10.2. Some Basic Concepts 10.3. Types of Vectors 10.4. Addition of Vectors 10.5. Multiplication of Vector by a Scalar 10.5. Multiplication of Vector by a Scalar 10.5.1. Components of a Vector 10.5.2. Vector Joining Two Points 10.5.3. Section Formula 10.6. Product of Two Vectors 10.6.1. Scalar (or dot) Product of Two Vectors 10.6.1. Scalar (or dot) Product of Two Vectors 10.6.1. Scalar (or dot) Product of Two Vectors 10.6.2. Projection of a Vector on a Line 10.6.3. Vector (or cross) Product of Two Vectors

# 11. Three Dimensional Geography

 11.1. Introduction 11.2. Direction Cosines Direction Ratios of a Line 11.2. Direction Cosines Direction Ratios of a Line 11.2. Direction Cosines Direction Ratios of a Line 11.2.1. Relation between the Direction Cosines of a Line 11.2.2. Direction Cosines of a Line Passing through Two Points 11.3. Equation of a Line in Space 11.3. Equation of a Line in Space 11.3. Equation of a Line in Space 11.3.1. Equation of a Line through a Given Point and Parallel to a Given Vector 11.3.2. Equation of a Line Passing through Two Given Points 11.4. Angle between Two Lines 11.4. Angle between Two Lines 11.4. Angle between Two Lines 11.5. Shortest Distance between Two Lines 11.5.1. Distance between Two Skew Lines 11.5.2. Distance between Parallel Lines 11.6. Plane 11.6.1. Equation of a Plane in a Normal Form 11.6.1. Equation of a Plane in a Normal Form 11.6.1. Equation of a Plane in a Normal Form 11.6.2. Equation of a Plane Perpendicular to a Given Vector and Passing through a Given Point 11.6.3. Equation of a Plane Passing through Three Non Collinear Points 11.6.4. Intercept Form of the Equation of a Plane 11.6.5. Plane Passing through the Intersection of Two Given Planes 11.7. Coplanarity of Two Lines 11.8. Angle between Two Planes 11.8. Angle between Two Planes 11.8. Angle between Two Planes 11.9. Distance of a Point from a Plane 11.10. Angle between a Line and a Plane 11.10. Angle between a Line and a Plane 11.10. Angle between a Line and a Plane 11.10. Angle between a Line and a Plane

# 12. Linear Programming

 12.1. Introduction 12.2. Linear Programming Problem and its Mathematical Formulation 12.2.1. Mathematical Formulation of the Problem 12.2.2. Graphical Method of solving Linear Programming Problems 12.3. Different Types of Linear Programming Problems