12th Maths - TamilNadu State Board (English Medium)
Volume I
Chapter 1: Applications of Matrices and Determinants
1. Introduction - Applications of Matrices and Determinants
2. Inverse of a Non-Singular Square Matrix - Applications of Matrices and Determinants
3. Adjoint of a Square Matrix - Definition, Theorem, Formulas, Solved Example Problems | Inverse of a Non-Singular Square Matrix
4. Definition of inverse matrix of a square matrix - Definition, Theorem, Formulas, Solved Example Problems | Inverse of a Non-Singular Square Matrix
5. Properties of inverses of matrices - Definition, Theorem, Formulas, Solved Example Problems | Inverse of a Non-Singular Square Matrix
6. Application of matrices to Geometry - Definition, Theorem, Formulas, Solved Example Problems | Inverse of a Non-Singular Square Matrix
7. Application of matrices to Cryptography - Definition, Theorem, Solved Example Problems | Inverse of a Non-Singular Square Matrix
8. Exercise 1.1: Inverse of a Non-Singular Square Matrix - Problem Questions with Answer, Solution
9. Inverse of a Non-Singular Square Matrix: Solved Example Problems
10. Elementary Transformations of a Matrix - Definition, Theorem | Elementary row and column operations
11. Row Echelon form - Definition, Theorem, Formulas, Solved Example Problems | Elementary Transformations of a Matrix
12. Rank of a Matrix - Definition, Theorem, Formulas, Solved Example Problems | Elementary Transformations of a Matrix
13. Gauss Jordan Method - Definition, Theorem, Formulas, Solved Example Problems | Elementary Transformations of a Matrix
14. Exercise 1.2: Elementary Transformations of a Matrix - Problem Questions with Answer, Solution
15. Elementary Transformations of a Matrix: Solved Example Problems - with Answers, Solution
16. Applications of Matrices: Solving System of Linear Equations
17. Formation of a System of Linear Equations - Applications of Matrices: Solving System of Linear Equations
18. System of Linear Equations in Matrix Form - Applications of Matrices: Solving System of Linear Equations
19. Solution to a System of Linear equations - Applications of Matrices: Solving System of Linear Equations
20. Matrix Inversion Method - Definition, Formulas, Solved Example Problems
21. Exercise 1.3: Matrices linear equations by matrix inversion method - Problem Questions with Answer, Solution
22. Matrices: Cramer�s Rule - Definition, Formulas, Solved Example Problems
23. Exercise 1.4: Matrices: Cramer�s Rule - Problem Questions with Answer, Solution
24. Matrix: Gaussian Elimination Method - Definition, Solved Example Problems
25. Exercise 1.5: Matrix: Gaussian Elimination Method - Problem Questions with Answer, Solution
26. Solved Example Problems on Applications of Matrices: Solving System of Linear Equations - Definition, Formulas, Solved Example Problems
27. Matrix: Non-homogeneous Linear Equations - Definition, Theorem, Formulas, Solved Example Problems | Applications of Matrices: Consistency of System of Linear Equations by Rank Method
28. Exercise 1.6: Matrix: Non-homogeneous Linear Equations - Problem Questions with Answer, Solution
29. Matrix: Homogeneous system of linear equations - Definition, Theorem, Formulas, Solved Example Problems | Applications of Matrices: Consistency of System of Linear Equations by Rank Method
30. Exercise 1.7: Matrix: Homogeneous system of linear equations - Problem Questions with Answer, Solution
31. Choose the Correct Answers - Applications of Matrices and Determinants
32. Summary - Applications of Matrices and Determinants
Chapter 2: Complex Numbers
1. Introduction - Complex Numbers
2. Introduction to Complex Numbers
3. Exercise 2.1: Introduction to Complex Numbers - Problem Questions with Answer, Solution
4. Complex Numbers - Definition, Illustration, Formulas, Solved Example Problems
5. Exercise 2.2: Complex Numbers - Problem Questions with Answer, Solution
6. Basic Algebraic Properties of Complex Numbers
7. Exercise 2.3: Properties of Complex Numbers - Problem Questions with Answer, Solution
8. Conjugate of a Complex Number - Definition, Geometrical representation, Properties, Proof, Solved Example Problems
9. Exercise 2.4: Conjugate of a Complex Number - Problem Questions with Answer, Solution
10. Modulus of a Complex Number - Definition, Formulas
11. Properties of Modulus of a complex number
12. Modulus of a Complex Number: Solved Example Problems - with Answers, Solution
13. Square roots of a complex number - Definition, Formulas, Solved Example Problems
14. Exercise 2.5: Modulus of a Complex Number - Problem Questions with Answer, Solution
15. Geometry and Locus of Complex Numbers - Definition, Illustration, Formulas, Solved Example Problems
16. Exercise 2.6: Geometry and Locus of Complex Numbers - Problem Questions with Answer, Solution
17. Polar form of a complex number - Definition, Illustration, Formulas
18. Euler�s Form of the complex number - Definition, Properties, Formulas, Solved Example Problems
19. Exercise 2.7: Polar and Euler form of a Complex Number - Problem Questions with Answer, Solution
20. de Moivre�s Theorem and its Applications - Definition, Formula, Solved Example Problems
21. de Moivre's Theorem - Definition, Formula, Solved Example Problems
22. Finding nth roots of a complex number - Definition, Formula
23. The nth roots of unity - Definition, Formula, Solved Example Problems
24. Exercise 2.8: de Moivre�s Theorem and its Applications - Problem Questions with Answer, Solution | Complex Numbers
25. Solved Example Problems on de Moivre�s Theorem
26. Choose the correct Answers - Complex Numbers
27. Summary - Complex Numbers
Chapter 3: Theory of Equations
1. Introduction - Theory of Equations
2. Basics and types of Polynomial Equations
3. Vieta�s formula for Quadratic Equations - Theory of Equations
4. Vieta�s formula for Polynomial Equations - Definition, Theorem, Formulas, Solved Example Problems | Theory of Equations
5. Exercise 3.1: Vieta�s Formulae and Formation of Polynomial Equations - Problem Questions with Answer, Solution
6. Nature of Roots and Nature of Coefficients of Polynomial Equations
7. Imaginary Roots - Complex Conjugate Root Theorem, Formulas, Solved Example Problems
8. Irrational Roots - Definition, Theorem, Formulas, Solved Example Problems | Theory of Equations
9. Rational Roots - Definition, Solved Example Problems | Theory of Equations
10. Applications of Polynomial Equation in Geometry
11. Exercise 3.2: Polynomial Equation in Geometry - Problem Questions with Answer, Solution
12. Roots of Higher Degree Polynomial Equations - Theory of Equations
13. Polynomials with Additional Information - Solved Example Problems | Theory of Equations
14. Exercise 3.3: Polynomials with Additional Information - Problem Questions with Answer, Solution
15. Partly Factored Polynomial - Solved Example Problems
16. Exercise 3.4: Partly Factored Polynomial - Problem Questions with Answer, Solution
17. Rational Root Theorem - Polynomial Equations with no Additional Information
18. Reciprocal Equations - Definition, Theorem, Formulas, Solved Example Problems
19. Non-polynomial Equations - Solved Example Problems | Theory of Equations
20. Exercise 3.5: Polynomial Equations with no Additional Information - Problem Questions with Answer, Solution
21. Descartes Rule - Definition, Theorem, Solved Example Problems | Theory of Equations
22. Exercise 3.6: Descartes Rule - Problem Questions with Answer, Solution
23. Choose the correct Answers - Theory of Equations
24. Summary - Theory of Equations
Chapter 4: Inverse Trigonometric Functions
1. Introduction - Inverse Trigonometric Functions
2. Some Fundamental Concepts of Inverse Trigonometric Functions
3. Sine Function and Inverse Sine Function - Definition, Graph, Properties, Solved Example Problems
4. Exercise 4.1: Sine Function and Inverse Sine Function - Problem Questions with Answer, Solution
5. The Cosine Function and Inverse Cosine Function - Definition, Graph, Properties, Solved Example Problems, Applications
6. Exercise 4.2: Cosine Function and Inverse Cosine Function - Problem Questions with Answer, Solution
7. The Tangent Function and the Inverse Tangent Function - Definition, Graph, Properties, Solved Example Problems
8. Exercise 4.3: Tangent Function and the Inverse Tangent Function - Problem Questions with Answer, Solution
9. Cosecant Function and the Inverse Cosecant Function - Definition, Graph, Properties
10. The Secant Function and Inverse Secant Function - Definition, Graph, Properties
11. The Cotangent Function and the Inverse Cotangent Function - Definition, Graph, Properties
12. Principal Value of Inverse Trigonometric Functions - Definition, Solved Example Problems
13. Exercise 4.4: Principal Value of Inverse Trigonometric Functions - Problem Questions with Answer, Solution
14. Properties of Inverse Trigonometric Functions
15. Solved Example Problems on Inverse Trigonometric Functions - with Answers, Solution
16. Exercise 4.5: Inverse Trigonometric Functions - Problem Questions with Answer, Solution
17. Choose the correct answers - Inverse Trigonometric Functions
18. Summary - Inverse Trigonometric Functions
Chapter 5: Two Dimensional Analytical Geometry II
1. Introduction - Two Dimensional Analytical Geometry II
2. Circle - Definition
3. Equation of a circle in standard form - Formula, Solved Example Problems
4. Equations of tangent and normal at a point P on a given circle
5. Condition for the line y = mx + c to be a tangent to the circle and finding the point of contact - Formula, Solved Example Problems
6. Circle: Solved Example Problems - with Answers, Solution
7. Exercise 5.1: Circle - Problem Questions with Answer, Solution
8. Conics - Definition
9. The general equation of a Conic
10. Parabola - Equation, Definition, Example, Solution, vertex
11. Ellipse - Equation, Definition, Theorem, Proof, Example, Solution, Types
12. Hyperbola - Equation, Definition, Theorem, Proof, Types, Solved Example Problems, Solution
13. Exercise 5.2: Conics - Problem Questions with Answer, Solution
14. Conic Sections
15. Exercise 5.3: Conic Sections - Problem Questions with Answer, Solution
16. Parametric form of Conics
17. Tangents and Normals to Conics - Equation, Definition, Theorem, Proof, Solved Example Problems
18. Exercise 5.4: Tangents and Normals to Conics - Problem Questions with Answer, Solution
19. Real life Applications of Conics
20. Exercise 5.5: Real life Applications of Conics - Problem Questions with Answer, Solution
21. Solved Example Problems on Real life Applications of Conics
22. Choose the correct Answer - Two Dimensional Analytical Geometry II
23. Summary - Equation, Formula | Two Dimensional Analytical Geometry II
Chapter 6: Applications of Vector Algebra
1. Introduction - Applications of Vector Algebra
2. Geometric introduction to vectors
3. Scalar Product and Vector Product - Definition, Theorem, Proof, Solved Example Problems, Solution
4. Exercise 6.1: Scalar Product and Vector Product - Problem Questions with Answer, Solution
5. Scalar triple product - Definition, Properties, Theorem, Proof, Solved Example Problems, Solution
6. Exercise 6.2: Scalar triple product - Problem Questions with Answer, Solution
7. Vector triple product - Definition, Theorem, Proof
8. Jacobi�s Identity and Lagrange�s Identity - Definition, Theorem, Proof, Solved Example Problems, Solution
9. Exercise 6.3: Vector triple product, Jacobi�s Identity and Lagrange�s Identity - Problem Questions with Answer, Solution
10. Application of Vectors to 3-Dimensional Geometry - Definition, Theorem, Proof, Solved Example Problems, Solution
11. Exercise 6.4: Application of Vectors to 3-Dimensional Geometry - Problem Questions with Answer, Solution
12. A point on the straight line and the direction of the straight line - Application of Vectors to 3-Dimensional Geometry
13. Straight Line passing through two given points - Definition, Theorem, Proof, Solved Example Problems, Solution
14. Angle between two straight lines - Definition, Theorem, Proof, Solved Example Problems, Solution
15. Point of intersection of two straight lines - Definition, Solved Example Problems, Solution
16. Shortest distance between two straight lines - Definition, Theorem, Proof, Solved Example Problems, Solution
17. Exercise 6.5: Point of intersection of two straight lines - Problem Questions with Answer, Solution
18. Different forms of Equation of a plane
19. Equation of a plane when a normal to the plane - Definition, Theorem, Proof
20. Equation of a plane perpendicular to a vector and passing through a given point
21. Intercept form of the equation of a plane
22. Exercise 6.6: Equation of a plane - Problem Questions with Answer, Solution
23. Equation of a plane passing through three given non-collinear points - Definition, Theorem, Proof
24. Equation of a plane passing through a given point and parallel to two given non-parallel vectors
25. Equation of a plane passing through two given distinct points and is parallel to a non-zero vector
26. Exercise 6.7: Equation of a plane - Problem Questions with Answer, Solution
27. Condition for a line to lie in a plane
28. Condition for coplanarity of two lines
29. Equation of plane containing two non-parallel coplanar lines
30. Exercise 6.8: Equation of a plane - Problem Questions with Answer, Solution
31. Angle between two planes - Definition, Theorem, Proof, Solved Example Problems, Solution
32. Angle between a line and a plane
33. Distance of a point from a plane - Definition, Theorem, Proof, Solved Example Problems, Solution
34. Distance between two parallel planes - Definition, Theorem, Proof, Solved Example Problems, Solution
35. Equation of line of intersection of two planes
36. Equation of a plane passing through the line of intersection of two given planes
37. Image of a Point in a Plane
38. Meeting Point of a Line and a Plane - Definition, Theorem, Proof, Solved Example Problems, Solution
39. Exercise 6.9: Equation of intersection of the planes - Problem Questions with Answer, Solution
40. Choose the correct answer - Applications of Vector Algebra
41. Summary - Applications of Vector Algebra
Volume II
Chapter 7: Applications of Differential Calculus
1. Applications of Differential Calculus - Mathematics
2. Derivative as slope - Meaning of Derivatives | Mathematics
3. Derivative as rate of change - Meaning of Derivatives | Mathematics
4. Related rates - Meaning of Derivatives | Mathematics
5. Exercise 7.1 : Meaning of Derivatives - Problem Questions with Answer, Solution
6. Equations of Tangent and Normal - Differential Calculus | Mathematics
7. Angle between two curves - Differential Calculus | Mathematics
8. Exercise 7.2 : Equations of Tangent and Normal, Angle between two curves - Problem Questions with Answer, Solution
9. Mean Value Theorem - Differential Calculus | Mathematics
10. Rolle�s Theorem - Mean Value Theorem | Mathematics
11. Lagrange�s Mean Value Theorem - Mean Value Theorem | Mathematics
12. Applications - Mean Value Theorem - Applications of Differential Calculus | Mathematics
13. Exercise 7.3: Mean Value Theorem - Problem Questions with Answer, Solution
14. Series Expansions: Maclaurin�s and Taylor�s Series - Differential Calculus | Mathematics
15. Exercise 7.4 : Series Expansions: Maclaurin�s and Taylor�s Series - Problem Questions with Answer, Solution
16. Indeterminate Forms - Applications of Differential Calculus | Mathematics
17. Exercise 7.5 : Indeterminate Forms - Problem Questions with Answer, Solution
18. Applications of First Derivative - Applications of Differential Calculus | Mathematics
19. Exercise 7.6 : Applications of First Derivative - Problem Questions with Answer, Solution
20. Applications of Second Derivative - Applications of Differential Calculus | Mathematics
21. Exercise 7.7: Applications of Second Derivative - Problem Questions with Answer, Solution
22. Applications in Optimization - Applications of Differential Calculus | Mathematics
23. Exercise 7.8: Applications in Optimization - Problem Questions with Answer, Solution
24. Symmetry and Asymptotes - Applications of Differential Calculus | Mathematics
25. Sketching of Curves - Applications of Differential Calculus | Mathematics
26. Exercise 7.9: Symmetry and Asymptotes, Sketching of Curves - Problem Questions with Answer, Solution
27. Exercise 7.10: Choose the correct or the most suitable answer - Applications of Differential Calculus | Mathematics
28. Summary - Applications of Differential Calculus | Mathematics
Chapter 8: Differentials and Partial Derivatives
1. Differentials and Partial Derivatives - Mathematics
2. Linear Approximation - Mathematics
3. Errors: Absolute Error, Relative Error, and Percentage Error - Linear Approximation | Mathematics
4. Exercise 8.1: Linear Approximation - Problem Questions with Answer, Solution
5. Differentials - Mathematics
6. Exercise 8.2: Differentials - Problem Questions with Answer, Solution
7. Functions of Several Variables - Differentials and Partial Derivatives | Mathematics
8. Recall of Limit and Continuity of Functions of One Variable - Functions of Several Variables | Mathematics
9. Limit and Continuity of Functions of Two Variables - Mathematics
10. Exercise 8.3: Functions of Several Variables - Problem Questions with Answer, Solution
11. Partial Derivatives - Mathematics
12. Exercise 8.4: Partial Derivatives - Problem Questions with Answer, Solution
13. Linear Approximation and Differential of a function of several variables - Mathematics
14. Exercise 8.5: Linear Approximation and Differential of a function of several variables - Problem Questions with Answer, Solution
15. Function of Function Rule - Mathematics
16. Exercise 8.6: Function of Function Rule - Problem Questions with Answer, Solution
17. Homogeneous Functions and Euler�s Theorem - Mathematics
18. Exercise 8.7: Homogeneous Functions and Euler�s Theorem - Problem Questions with Answer, Solution
19. Exercise 8.8: Choose the correct answer - Differentials and Partial Derivatives | Mathematics
20. Summary - Differentials and Partial Derivatives | Mathematics
Chapter 9: Applications of Integration
1. Applications of Integration - Mathematics
2. Definite Integral as the Limit of a Sum - Applications of Integration | Mathematics
3. Exercise 9.1: Definite Integral as the Limit of a Sum - Problem Questions with Answer, Solution
4. Limit Formula to Evaluate Definite Integral as the Limit of a Sum - Applications of Integration | Mathematics
5. Exercise 9.2: Limit Formula to Evaluate Definite Integral as the Limit of a Sum - Problem Questions with Answer, Solution
6. Fundamental Theorems of Integral Calculus and their Applications
7. Exercise 9.3: Fundamental Theorems of Integral Calculus and their Applications - Problem Questions with Answer, Solution
8. Bernoulli�s Formula - Applications of Integration
9. Exercise 9.4: Bernoulli�s Formula - Problem Questions with Answer, Solution
10. Improper Integrals - Applications of Integration | Mathematics
11. Exercise 9.5: Improper Integrals - Problem Questions with Answer, Solution
12. Reduction Formulae - Applications of Integration | Mathematics
13. Exercise 9.6: Reduction Formulae - Problem Questions with Answer, Solution
14. Gamma Integral - Applications of Integration | Mathematics
15. Exercise 9.7: Gamma Integral - Problem Questions with Answer, Solution
16. Evaluation of a Bounded Plane Area by Integration - Applications of Integration | Mathematics
17. Exercise 9.8: Evaluation of a Bounded Plane Area by Integration - Problem Questions with Answer, Solution
18. Volume of a solid obtained by revolving area about an axis - Applications of Integration | Mathematics
19. Exercise 9.9: Volume of a solid obtained by revolving area about an axis - Problem Questions with Answer, Solution
20. Exercise 9.10: Choose the correct answer - Applications of Integration | Mathematics
21. Summary - Applications of Integration | Mathematics
Chapter 10: Ordinary Differential Equations
1. Ordinary Differential Equations - Mathematics
2. Differential Equation, Order, and Degree - Ordinary Differential Equations | Mathematics
3. Exercise 10.1: Differential Equation, Order, and Degree - Problem Questions with Answer, Solution
4. Classification of Differential Equations - Mathematics
5. Formation of Differential equations from Physical Situations - Mathematics
6. Exercise 10.2: Formation of Differential equations from Physical Situations - Problem Questions with Answer, Solution
7. Formation of Differential Equations from Geometrical Problems - Mathematics
8. Exercise 10.3: Formation of Differential Equations from Geometrical Problems - Problem Questions with Answer, Solution
9. Solution of Ordinary Differential Equations - Mathematics
10. Exercise 10.4: Solution of Ordinary Differential Equations - Problem Questions with Answer, Solution
11. Variables Separable Method - Solution of First Order and First Degree Differential Equations | Mathematics
12. Substitution Method - Solution of First Order and First Degree Differential Equations | Mathematics
13. Exercise 10.5: Variables Separable Method, Substitution Method - Problem Questions with Answer, Solution
14. Homogeneous Form or Homogeneous Differential Equation - Solution of First Order and First Degree Differential Equations | Mathematics
15. Exercise 10.6: Homogeneous Form or Homogeneous Differential Equation - Problem Questions with Answer, Solution
16. First Order Linear Differential Equations - Mathematics
17. Exercise 10.7: First Order Linear Differential Equations - Problem Questions with Answer, Solution
18. Applications of First Order Ordinary Differential Equations - Mathematics
19. Exercise 10.8: Applications of First Order Ordinary Differential Equations - Problem Questions with Answer, Solution
20. Exercise 10.9: Choose the correct answer - Ordinary Differential Equations | Mathematics
21. Summary - Ordinary Differential Equations | Mathematics
Chapter 11: Probability Distributions
1. Probability Distributions - Mathematics
2. Random Variable - Probability Distributions | Mathematics
3. Exercise 11.1: Random Variable - Problem Questions with Answer, Solution
4. Types of Random Variable - Probability Distributions | Mathematics
5. Discrete random variables - Probability Distributions | Mathematics
6. Probability Mass Function - Probability Distributions | Mathematics
7. Cumulative Distribution Function or Distribution Function - Probability Distributions | Mathematics
8. Cumulative Distribution Function from Probability Mass function - Probability Distributions | Mathematics
9. Probability Mass Function from Cumulative Distribution Function - Probability Distributions | Mathematics
10. Exercise 11.2: Types of Random Variable - Problem Questions with Answer, Solution
11. Continuous Distributions - Definition, Properties | Probability Distributions | Mathematics
12. Exercise 11.3: Continuous Distributions - Problem Questions with Answer, Solution
13. Mathematical Expectation - Mean, Variance | Probability Distributions | Mathematics
14. Properties of Mathematical expectation and variance - Probability Distributions | Mathematics
15. Exercise 11.4: Mathematical Expectation - Problem Questions with Answer, Solution
16. Theoretical Distributions: Some Special Discrete Distributions - Probability Distributions | Mathematics
17. Exercise 11.5: Theoretical Distributions: Some Special Discrete Distributions - Problem Questions with Answer, Solution
18. Exercise 11.6: Choose the Correct answer - Probability Distributions | Mathematics
19. Summary - Probability Distributions | Mathematics
Chapter 12: Discrete Mathematics
1. Discrete Mathematics - Mathematics
2. Definitions of Binary Operations - Discrete Mathematics | Mathematics
3. Some more properties of a binary operation - Discrete Mathematics | Mathematics
4. Some binary operations on Boolean Matrices - Discrete Mathematics | Mathematics
5. Binary operations: Modular Arithmetic - Discrete Mathematics | Mathematics
6. Exercise 12.1: Binary operations - Problem Questions with Answer, Solution
7. Mathematical Logic - Discrete Mathematics | Mathematics
8. Mathematical Logic: Statement and its truth value - Discrete Mathematics | Mathematics
9. Mathematical Logic: Compound Statements, Logical Connectives, and Truth Tables - Discrete Mathematics | Mathematics
10. Mathematical Logic: Logical Connectives and their Truth Tables - Discrete Mathematics | Mathematics
11. Mathematical Logic: Tautology, Contradiction, and Contingency - Discrete Mathematics | Mathematics
12. Mathematical Logic: Duality - Discrete Mathematics | Mathematics
13. Some Laws of Logical Equivalence - Mathematical Logic | Discrete Mathematics | Mathematics
14. Exercise 12.2: Mathematical Logic - Problem Questions with Answer, Solution
15. Exercise 12.3: Choose the correct answer - Discrete Mathematics | Mathematics
16. Summary - Discrete Mathematics | Mathematics
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