11th Mathematics - TamilNadu State Board (English Medium)
Chapter 1 : Sets Relations and Functions
1. Sets, Relations and Functions: Introduction - Mathematics
2. Sets - Definition, Properties of Set Operations | Mathematics
3. Cartesian Product - Definition, Formula, Solved Example Problems, Exercise | Mathematics
4. Constants and Variables, Intervals and Neighbourhoods - Mathematics
5. Relations - Definition, Formula, Solved Example Problems, Exercise | Mathematics
6. Functions - Definition, Formula, Types, Some Special Functions, Solved Example Problems, Exercise | Mathematics
7. Graphing Functions using Transformations - Definition, Formula, Solved Example Problems, Exercise | Mathematics
8. Exercise 1.1: Cartesian Product - Problem Questions with Answer, Solution | Mathematics
9. Exercise 1.2: Relations - Problem Questions with Answer, Solution | Mathematics
10. Exercise 1.3: Functions - Problem Questions with Answer, Solution | Mathematics
11. Exercise 1.4: Graphing Functions using Transformations - Problem Questions with Answer, Solution | Mathematics
12. Exercise 1.5: Choose the correct or the most suitable answer - Sets, Relations and Functions | Mathematics
Chapter 2 : Basic Algebra
1. Basic Algebra: Introduction - Mathematics
2. Real Number System - Properties, Formula, Solved Example Problems, Exercise | Mathematics
3. Absolute Value - Definition, Properties, Equations Formula, Solved Example Problems, Exercise | Algebra | Mathematics
4. Linear Inequalities - Definition, Solved Example Problems, Exercise | Algebra | Mathematics
5. Quadratic Functions - Definition, Formula, Solved Example Problems, Exercise | Algebra | Mathematics
6. Polynomial Functions - Definition, Formula, Solved Example Problems, Exercise | Algebra | Mathematics
7. Rational Functions - Rational Inequalities, Partial Fractions, Graphical Representation | Definition, Formula, Solved Example Problems, Exercise | Algebra | Mathematics
8. Exponents and Radicals - Definition, Formula, Solved Example Problems, Exercise | Mathematics
9. Logarithm - Definition, Properties, Proof, Solved Example Problems, Exercise | Mathematics
10. Application of Algebra in Real Life
11. Exercise 2.1: Real Number System - Problem Questions with Answer, Solution | Mathematics
12. Exercise 2.2: Absolute Value - Problem Questions with Answer, Solution | Mathematics
13. Exercise 2.3: Linear Inequalities - Problem Questions with Answer, Solution | Basic Algebra | Mathematics
14. Exercise 2.4: Quadratic Functions - Problem Questions with Answer, Solution | Basic Algebra | Mathematics
15. Exercise 2.5: Quadratic Inequalities - Problem Questions with Answer, Solution | Basic Algebra | Mathematics
16. Exercise 2.6: Polynomial Functions - Problem Questions with Answer, Solution | Basic Algebra | Mathematics
17. Exercise 2.7: Method of Undetermined Coefficients - Problem Questions with Answer, Solution | Basic Algebra | Mathematics
18. Exercise 2.8: Rational Functions - Problem Questions with Answer, Solution | Basic Algebra | Mathematics
19. Exercise 2.9: Partial Fractions - Problem Questions with Answer, Solution | Basic Algebra | Mathematics
20. Exercise 2.10: Graphical Representation of Linear Inequalities - Problem Questions with Answer, Solution | Basic Algebra | Mathematics
21. Exercise 2.11: Exponents and Radicals - Problem Questions with Answer, Solution | Basic Algebra | Mathematics
22. Exercise 2.12: Logarithm - Problem Questions with Answer, Solution | Basic Algebra | Mathematics
23. Exercise 2.13: Choose the correct or the most suitable answer - Basic Algebra | Mathematics
Chapter 3 : Trigonometry
1. Trigonometry: Introduction - Mathematics
2. A recall of basic results - Solved Example Problems, Exercise | Trigonometry | Mathematics
3. Radian Measure - Definition, Formula, Solved Example Problems, Exercise | Trigonometry | Mathematics
4. Trigonometric functions and their properties - Mathematics
5. Trigonometric Identities - Definition, Formula, Solved Example Problems, Exercise | Mathematics
6. Trigonometric equations - Definition, Formula, Solved Example Problems, Exercise | Mathematics
7. Properties of Triangle - Trigonometry | Mathematics
8. The Law of Sines or Sine Formula - Definition, Formula, Solved Example Problems, Exercise | Mathematics
9. Area of a triangle (Heron�s Formula ) - Definition, Formula, Solved Example Problems, Exercise | Mathematics
10. Application to Triangle - Solved Example Problems, Exercise | Mathematics
11. Inverse Trigonometric Functions - Definition, Formula, Solved Example Problems, Exercise | Mathematics
12. Exercise 3.1: Basic results of Trigonometry - Problem Questions with Answer, Solution | Mathematics
13. Exercise 3.2: Radian Measure - Problem Questions with Answer, Solution | Trigonometry | Mathematics
14. Exercise 3.3: Trigonometric functions and their properties - Problem Questions with Answer, Solution | Mathematics
15. Exercise 3.4: Trigonometric Identities: Sum and difference identities or compound angles formulas - Problem Questions with Answer, Solution | Mathematics
16. Exercise 3.5: Trigonometric Identities: Multiple angle identities and submultiple angle identities - Problem Questions with Answer, Solution | Mathematics
17. Exercise 3.6: Trigonometric Identities: Product to Sum and Sum to Product Identities - Problem Questions with Answer, Solution | Mathematics
18. Exercise 3.7: Trigonometric Identities: Product to Sum and Sum to Product Identities - Problem Questions with Answer, Solution | Mathematics
19. Exercise 3.8: Trigonometric equations - Problem Questions with Answer, Solution | Mathematics
20. Exercise 3.9: Area of a triangle (Heron�s Formula) - Problem Questions with Answer, Solution | Trigonometry | Mathematics
21. Exercise 3.10: Trigonometry Application to Triangle - Problem Questions with Answer, Solution | Trigonometry | Mathematics
22. Exercise 3.11: Inverse Trigonometric Functions - Problem Questions with Answer, Solution | Mathematics
23. Exercise 3.12: Choose the correct or the most suitable answer - Trigonometry | Mathematics
Chapter 4 : Combinatorics and Mathematical Induction
1. Combinatorics and Mathematical Induction: Introduction - Mathematics
2. Fundamental principles of counting - Solved Example Problems, Exercise | Mathematics
3. Factorials - Definition, Formula, Solved Example Problems, Exercise | Mathematics
4. Permutations - Definition, Formula, Properties, Solved Example Problems, Exercise | Mathematics
5. Combinations - Definition, Formula, Solved Example Problems, Exercise | Mathematics
6. Mathematical induction - Definition, Solved Example Problems, Exercise | Mathematics
7. Exercise 4.1: Factorials - Problem Questions with Answer, Solution | Mathematics
8. Exercise 4.2: Permutations - Problem Questions with Answer, Solution | Mathematics
9. Exercise 4.3: Combinations - Problem Questions with Answer, Solution | Mathematics
10. Exercise 4.4: Mathematical induction - Problem Questions with Answer, Solution | Mathematics
11. Exercise 4.5: Choose the correct or the most suitable answer - Combinatorics and Mathematical Induction | Mathematics
Chapter 5 : Binomial Theorem Sequences and Series
1. Binomial Theorem, Sequences and Series: Introduction - Mathematics
2. Binomial Theorem - Binomial Coefficients | Definition, Formula, Solved Example Problems, Exercise | Mathematics
3. Particular cases of Binomial Theorem - Formula, Solved Example Problems, Exercise | Mathematics
4. Finite Sequences - Geometric Progression (GP), Arithmetic Progression (AP), Arithmetico-Geometric Progression (AGP), Harmonic Progression(HP), Arithmetic, Geometric and Harmonic Mean | Definition, Formula, Solved Exampl
5. Finite Series - Definition, Formula, Solved Example Problems, Exercise | Mathematics
6. Infinite Sequences and Series - Definition, Formula, Solved Example Problems, Exercise | Mathematics
7. Exercise 5.1: Binomial Theorem - Problem Questions with Answer, Solution | Mathematics
8. Exercise 5.2: Finite Sequences - Problem Questions with Answer, Solution | Mathematics
9. Exercise 5.3: Finite Series - Problem Questions with Answer, Solution | Mathematics
10. Exercise 5.4: Infinite Sequences and Series - Problem Questions with Answer, Solution | Mathematics
11. Exercise 5.5: Choose the correct answer - Binomial Theorem, Sequences and Series | Mathematics
Chapter 6 : Two Dimensional Analytical Geometry
1. Two Dimensional Analytical Geometry: Introduction - Mathematics
2. Locus of a point - Definition, Solved Example Problems, Exercise | Analytical Geometry | Mathematics
3. Straight Lines - Definition, Equations Formula, Solved Example Problems, Exercise | Analytical Geometry | Mathematics
4. Angle between two straight lines - Definition, Equation Formula, Solved Example Problems, Exercise | Analytical Geometry | Mathematics
5. Pair of Straight Lines - Definition, Equation Formula, Solved Example Problems, Exercise | Analytical Geometry | Mathematics
6. Exercise 6.1: Locus of a point - Problem Questions with Answer, Solution | Mathematics
7. Exercise 6.2: Straight Lines - Problem Questions with Answer, Solution | Mathematics
8. Exercise 6.3: Angle between two straight lines - Problem Questions with Answer, Solution | Mathematics
9. Exercise 6.4: Pair of Straight Lines - Problem Questions with Answer, Solution | Mathematics
10. Exercise 6.5: Choose the correct answer - Two Dimensional Analytical Geometry | Mathematics
Chapter 7 : Matrices and Determinants
1. Matrices and Determinants : Introduction
2. Matrices - Definition, General form, Properties, Theorem, Proof, Solved Example Problems, Exercise
3. General form of a matrix - Definition, Solved Example Problems
4. Types of Matrices - Definition
5. Equality of Matrices - Definition, Solved Example Problems
6. Algebraic Operations on Matrices - Solved Example Problems
7. Properties of Matrix Addition, Scalar Multiplication and Product of Matrices
8. Operation of Transpose of a Matrix and its Properties - Definition, Solved Example Problems
9. Symmetric and Skew-symmetric Matrices - Definition, Theorem, Solved Example Problems
10. Determinants of Matrices of different order - Definition, Solved Example Problems
11. Properties of Determinants
12. Application of Factor Theorem to Determinants - Definition, Theorem, Solved Example Problems
13. Product of Determinants - Definition, Solved Example Problems
14. Relation between a Determinant and its Cofactor Determinant
15. Determinants: Area of a Triangle - Definition, Solved Example Problems
16. Determinants: Singular and non-singular Matrices - Definition, Solved Example Problems
17. Exercise 7.1: Matrices - Problem Questions with Answer, Solution | Mathematics
18. Exercise 7.2: Determinants - Problem Questions with Answer, Solution | Mathematics
19. Exercise 7.3: Application of Factor Theorem to Determinants - Problem Questions with Answer, Solution | Mathematics
20. Exercise 7.4: Determinants: Area of a Triangle, Singular and non-singular Matrices - Problem Questions with Answer, Solution | Mathematics
21. Exercise 7.5: Choose the correct answer - Matrices and Determinants | Mathematics
Chapter 8 : Vector Algebra I
1. Vector Algebra: Introduction
2. Scalars and Vectors - Definition
3. Representation of a vector and types of vectors - Definition | Mathematics
4. Algebra of Vectors - Mathematics
5. Position vectors - Definition, Theorem, Solved Example Problems | Mathematics
6. Resolution of Vectors - Definition, Theorem, Solved Example Problems | Mathematics
7. Direction Cosines and Direction Ratios - Solved Example Problems, Exercise | Mathematics
8. Product of Vectors - Mathematics
9. Scalar product and Properties of Scalar Product
10. Vector Product and Properties of Vector Product
11. Exercise 8.1: Position vectors - Problem Questions with Answer, Solution | Mathematics
12. Exercise 8.2: Direction Cosines and Direction Ratios - Problem Questions with Answer, Solution | Mathematics
13. Exercise 8.3: Scalar product and Properties of Scalar Product - Problem Questions with Answer, Solution | Mathematics
14. Exercise 8.4: Vector Product and Properties of Vector Product - Problem Questions with Answer, Solution | Mathematics
15. Exercise 8.5: Choose the correct answer - Vector Algebra | Mathematics
Chapter 9 : Differential Calculus Limits and Continuity
1. Differential Calculus - Limits and Continuity - Introduction | Mathematics
2. The calculation of limits - Mathematics
3. One sided limits: left-hand limit and right-hand limit - Definition, Solved Example Problems | Mathematics
4. Theorems on limits - Mathematics
5. Infinite Limits - Definition, Solved Example Problems | Mathematics
6. Limits at infinity - Definition, Solved Example Problems | Mathematics
7. Limits of rational functions - Mathematics
8. Applications of limits - Solved Example Problems | Mathematics
9. Sandwich Theorem - Definition, Solved Example Problems | Mathematics
10. Two special Trigonometrical limits
11. Some important other limits - Mathematics
12. Continuity - Differential Calculus - Mathematics
13. Examples of functions Continuous at a point - Mathematics
14. Algebra of continuous functions - Mathematics
15. Removable and Jump Discontinuities - Differential Calculus - Definition, Solved Example Problems, Exercise | Mathematics
16. Exercise 9.1: One sided limits: left-hand limit and right-hand limit - Problem Questions with Answer, Solution | Mathematics
17. Exercise 9.2: Theorems on limits - Problem Questions with Answer, Solution | Mathematics
18. Exercise 9.3: Applications of limits - Problem Questions with Answer, Solution | Mathematics
19. Exercise 9.4: Some important limits - Problem Questions with Answer, Solution | Mathematics
20. Exercise 9.5: Algebra of continuous functions, Removable and Jump Discontinuities - Differential Calculus | Problem Questions with Answer, Solution | Mathematics
21. Exercise 9.6: Choose the correct answer - Differential Calculus - Limits and Continuity | Mathematics
Chapter 10 : Differential Calculus Differentiability and Methods of Differentiation
1. Differential Calculus- Differentiability and Methods of Differentiation
2. The concept of derivative - Mathematics
3. The tangent line problem - The concept of derivative - Mathematics
4. Velocity of Rectilinear motion - The concept of derivative - Mathematics
5. The derivative of a Function - The concept of derivative - Mathematics
6. One sided derivatives (left hand and right hand derivatives) - The concept of derivative - Mathematics
7. Differentiability and Continuity - Solved Example Problems, Exercise | Mathematics
8. Differentiation Rules
9. Derivatives of basic elementary functions - Differentiation Rules
10. Examples on Chain Rule (Differentiation Rules)
11. Implicit Differentiation - Solved Example Problems| Mathematics
12. Logarithmic Differentiation - Solved Example Problems| Mathematics
13. Substitution method - Differential Calculus - Solved Example Problems| Mathematics
14. Derivatives of variables defined by parametric equations - Solved Example Problems| Mathematics
15. Differentiation of one function with respect to another function - Solved Example Problems| Mathematics
16. Higher order Derivatives - Solved Example Problems| Mathematics
17. Exercise 10.1: Differentiability and Continuity - Problem Questions with Answer, Solution | Differential Calculus | Mathematics
18. Exercise 10.2: Derivatives of basic elementary functions - Differentiation Rules - Problem Questions with Answer, Solution | Differential Calculus | Mathematics
19. Exercise 10.3: Examples on Chain Rule (Differentiation Rules) - Problem Questions with Answer, Solution | Differential Calculus | Mathematics
20. Exercise 10.4: Higher order Derivatives - Problem Questions with Answer, Solution | Differential Calculus | Mathematics
21. Exercise 10.5: Choose the correct answer - Differentiability and Methods of Differentiation | Differential Calculus | Mathematics
Chapter 11 : Integral Calculus
1. Integral Calculus: Introduction
2. Newton Leibnitz Integral - Definition, Theorem
3. Basic Rules or Formula of Integration
4. Integrals of the Form (ax + b) - Equation, Solved Example Problems | Mathematics
5. Properties of Integrals
6. Simple applications of Integral Calculus - Solved Example Problems, Exercise | Mathematics
7. Methods of Integration
8. Decomposition Methods of Integration
9. Decomposition by Partial Fractions - Integration Method
10. Integration Method of substitution or change of variable
11. Important Results of Integral Calculus
12. Integration by parts - Equation, Solved Example Problems | Mathematics
13. Bernoulli�s formula for Integration by Parts
14. Integrals of the form e pow(ax) cos bx and e pow(ax) sin bx - Equation, Solved Example Problems | Mathematics
15. Integration of Rational Algebraic Functions - Types, Equation, Solved Example Problems | Mathematics
16. Exercise 11.1: Basic Rules or Formula of Integration - Problem Questions with Answer, Solution | Integral Calculus | Mathematics
17. Exercise 11.2: Integrals of the Form (ax + b) - Problem Questions with Answer, Solution | Mathematics
18. Exercise 11.3: Properties of Integrals - Problem Questions with Answer, Solution | Mathematics
19. Exercise 11.4: Simple applications of Integral Calculus - Problem Questions with Answer, Solution | Mathematics
20. Exercise 11.5: Decomposition by Partial Fractions - Integration Method - Problem Questions with Answer, Solution | Mathematics
21. Exercise 11.6: Important Results of Integral Calculus - Problem Questions with Answer, Solution | Mathematics
22. Exercise 11.7: Bernoulli�s formula for Integration by Parts - Problem Questions with Answer, Solution | Mathematics
23. Exercise 11.8: Integrals of the form e pow(ax) cos bx and e pow(ax) sin bx - Problem Questions with Answer, Solution | Mathematics
24. Exercise 11.9: Integrals of the form e pow(ax) cos bx and e pow(ax) sin bx - Problem Questions with Answer, Solution | Mathematics
25. Exercise 11.10: Integration of Rational Algebraic Functions (Type I,II) - Problem Questions with Answer, Solution | Mathematics
26. Exercise 11.11: Integration of Rational Algebraic Functions (Type III) - Problem Questions with Answer, Solution | Mathematics
27. Exercise 11.12: Integration of Rational Algebraic Functions (Type IV) - Problem Questions with Answer, Solution | Mathematics
28. Exercise 11.13: Choose the correct answer - Integral Calculus | Mathematics
Chapter 12 : Introduction to Probability Theory
1. Introduction to Probability Theory
2. Basic definitions for Probability Theory
3. Finite sample space - Probability Theory - Definition
4. Classical definition (A priori) of probability (Bernoulli�s principle of equally likely)
5. Axiomatic approach to Probability - Theorem, Solved Example Problems
6. Odds - Probability Theory
7. Some basic Theorems on Probability
8. Conditional Probability - Definition, Theorem, Solved Example Problems | Mathematics
9. Total Probability of an event - Theorem, Solved Example Problems | Probability Theory
10. Bayes� Theorem - Theorem, Proof, Solved Example Problems | Mathematics
11. Exercise 12.1: Odds - Probability Theory - Problem Questions with Answer, Solution | Mathematics
12. Exercise 12.2: Some basic Theorems on Probability - Problem Questions with Answer, Solution | Mathematics
13. Exercise 12.3: Conditional Probability - Problem Questions with Answer, Solution | Mathematics
14. Exercise 12.4: Bayes Theorem - Problem Questions with Answer, Solution | Mathematics
15. Exercise 12.5: Choose the correct answer - Introduction to Probability Theory | Mathematics
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