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
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MATHEMATICS
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
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
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
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