1. Cartesian product, relation as a subset of it, empty and universal relation 30min
2. Reflexive, Symmetric, Transitive and equivalence relations, ncert examples 24min
3. Equivalence relation_more ncert examples and equivalence class 31min
4. How to idenitify Reflexive, symmetric and transitive relations 12min
5. How to show a relation to be non-reflexive, non-symmetric or non-transitive, how to find out equivalence class 15min
6. Function as a special relation_various examples 30min
7.Various Definitions with examples of one-one,onto,many-one,into and bijective functions 22min
8. Various Questions to identify type of a function and also method to prove one-one and onto function 26min
9. A one-one function on a finite set is onto and vice-versa 8min
10. NCERT Exercise 1.2 Que No 1 to 7 16min
11. NCERT Exercise 1.2 Que. 8 to 12 14min
12. Composition of Functions through examples 26min
13. More Questions on composition of Functions and Summary 20min
14. Inverse Functions_to show a function to be invertible and to find its inverse 39min
15. Inverse of composite functions_NCERT Example 20min
16. Inverse of composite function_ A theorem 14min
17. Inverse of Quadratic Functions 25min
18. Uniqueness of Inverse of a function 7min
19. More Questions on Invertible Functions 21min
1. Inverse of Sine Function_Principal Value Branch, Domain and Range 35min
2. Inverse Trigonometric Functions_Principal Value Branch, Domain and Range, Questions 1 to 10 of Exercise 2.1 44min
3. Properties of Inverse Trigonometric Functions Part_1 8min
4. Properties of Inverse Trigonometric Functions Part_2 14min
5. Properties of Inverse Trigonometric Functions Part_3 15min
6. Properties of Inverse Trigonometric Functions Part_4 18min
7. Properties of Inverse Trigonometric Functions Part_5 14min
8. Proof of tan^-1 (x)+tan^-1(y) =tan^-1((x+y)/(1-xy)) ,when xy less than 1 16min
9. Proof of tan^-1 (x)+tan^-1(y) =? ,when xy>1 19min
10. Proof of tan^-1 (x)-tan^-1(y) =? 17min
11. Formula to convert [2 tan^-1(x)] in terms of sin^-1(x) 10min
12. Formula to convert [2 tan^-1(x)] in terms of cos^-1(x) 10min
13. Formula to convert [2 tan^-1(x)] in terms of tan^-1(x) 11min
1. Matrix: An Introduction 15min
2. Order of a Matrix and General form of a matrix 19min
3. Types of Matrices and Equality of Matrices 25min
4. Addition of Matrices and Multiplication by a scalar of a matrix, Properties of these operations on matrices 49min
5. Matrix Multiplication, Non Commutativity of matrix multiplication, Zero matrix as a product of two non-zero matrices 48min
6. The associative and the distributive law of matrix multiplication, the existence of multiplicative identity 29min
7. Transpose of a matrix, Properties of transpose of the matrices 26min
8. Symmetric and skew symmetric matrices, two related theorems 20min
9. To express given square matrix as the sum of a symmetric and a skew symmetric matrix 17min
10. To verify that a given matrix equation is satisfied by a given matrix equation 16min
11. Questions on Matrix Equations 20min
1. Determinants_Introduction and Expansion of determinants up to order 3 36min
2. Expanding a determinant along any row or column gives the same value 24min
3. If A = k B, then det A = k^n det B where A and B are square matrices of order n. 15min
4. Properties of Determinants 29min
5. Properties of Determinants ..Continued 26min
6. Finding value of Determinant using Properties of Determinants 17min
7. Area of a triangle using Determinant 28min
8. Expansion of a determinant in compact form using minors and cofactors 45min
9. Adjoint of a Matrix 33min
10. Theorem: A(adj A) = (adj A)A = (det A)I 31min
11. Theorem: det(AB) = (det A).(det B) 21min
12. Result: det (adj A) =(det A)^(n-1) 18min
13. Singular and non singular, Invertible and non invertible Matrices. If A and B are non singular, then AB and BA are also non-singular. A is invertible iff A is non singular. Also A^(-1)=(1/det A) adjA 30min
14. More Questions on Inverse of a matrix 30min
15. Solving system of equations by matrix method 24min
16. Solving More Questions by matrix method 29min
1.Meaning of continuity and Continuity of a function at a point 25min
2. Continuous function and continuous function on a close interval 33min
3. Concept of infinity and Continuity of a function 24min
4. Continuity of a polynomial function and points of discontinuity of the greatest integer function 29min
5. Algebra of continuous functions _ Two Theorems and Their Applications 46min
6. Differentiability of a function and every differentiable function is continuous but its converse is not true. 32min
7. Algebra of derivatives and Chain Rule for Derivatives of composite functions 34min
8. Explicit and Implicit functions and Derivatives of Implicit functions 29min
9. Derivatives of Inverse Trigonometric Functions 30min
10. Exponential and Logarithmic Functions 43min
11. Derivatives of expressions involving Exponential and Logarithmic functions 25min
