Class 12 Maths - Aspire Academy

Course Content

Class 12 Maths Video Lectures
The NCERT Class 12 Maths syllabus covers a wide range of topics in mathematics. Here is an overview of the syllabus: Unit 1: Relations and Functions - Types of relations and functions - Inverse trigonometric functions - Binary operations and compositions of functions Unit 2: Algebra - Matrices and determinants - Algebra of matrices - Determinants and their properties - Inverse of a matrix Unit 3: Calculus - Continuity and differentiability - Differentiation and its applications - Integrals and their applications Unit 4: Vectors and Three-Dimensional Geometry - Vectors and their properties - Scalar and vector products - Three-dimensional geometry Unit 5: Linear Programming - Introduction to linear programming - Mathematical formulation of linear programming problems - Graphical method of solving linear programming problems Unit 6: Probability - Conditional probability and independence - Random variables and probability distributions - Binomial distribution and its properties This syllabus is prescribed by the National Council of Educational Research and Training (NCERT) for Class 12 Mathematics. It is designed to provide a comprehensive understanding of various mathematical concepts and their applications.

Class 12_Chapter 1_Relation & function Hirok Lecture 1

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Class 12_Chapter 1_Relation & function Hirok Lecture 2

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Class 12_Chapter 1_Relation & function Hirok Lecture 3

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Class 12_Chapter 1_Relation & function Hirok Lecture 4

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Class 12 Chapter 1 Relation and function Hirok Lecture 5

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Class 12 Chapter 1 Relation and function Hirok Lecture 6

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Class 12 Chapter 1 Relation and function Hirok Lecture 7

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Class 12 Chapter 1 Relation and function Hirok Lecture 8

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Class 12 Chapter 1 Relation and function Hirok 9

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Class 12:Chapter 2 :Inverse trigonometric Function by Bhrigu Sir Lecture 1

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Class 12:Chapter 2 :Inverse trigonometric Function by Bhrigu Sir Lecture 2

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Class 12:Chapter 2 :Inverse trigonometric Function by Bhrigu Sir Lecture 3

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Class 12:Chapter 2 :Inverse trigonometric Function by Bhrigu Sir Lecture 4

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Class 12:Chapter 2 :Inverse trigonometric Function by Bhrigu Sir Lecture 5

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Class 12:Chapter 2 :Inverse trigonometric Function by Bhrigu Sir Lecture 6

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Class 12:Chapter 2 :Inverse trigonometric Function by Bhrigu Sir Lecture 7

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Class 12:Chapter 2 :Inverse trigonometric Function by Bhrigu Sir Lecture 8 & 9

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Class 12 Maths Chp10 Vector Algebra, Position vector by Ashrita ma’am Part 1

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Class 12 Maths Chp10 Vector Algebra, Position vector by Ashrita ma’am Part 2

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Class 12 Maths Chp10 Vector Algebra,Vector joining two points by Ashrita ma’am Part 3

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Class 12 Maths Chp10 Vector Algebra,Section Formula by Ashrita ma’am Part 4

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Class 12 Maths Chp10 Vector Algebra, Exercise 10 2 by Ashrita ma’am Part 5

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Class 12 Maths Chp10 Vector Algebra, Dot & Cross Product by Ashrita ma’am Part 6

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Class 12 Maths Chp10 Vector Algebra, Exercise 10 3 by Ashrita ma’am Part 7

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Class 12 Maths Chp10 Vector Algebra, Exercise 10 3 by Ashrita ma’am Part 8

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Class 12 Maths Chp10 Vector Algebra, Exercise 10 3 by Ashrita ma’am Part 9

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Class 12 Maths Chp10 Vector Algebra, Exercise 10 3 by Ashrita ma’am Part 10

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Class 12 Maths Chp10 Vector Algebra, Exercise 10 4 by Ashrita ma’am Part 10

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Class 12 Maths Chp10 Vector Algebra, Exercise 10 4 by Ashrita ma’am Part 11

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Class 12 Maths Chp10 Vector Algebra, Exercise 10 4 by Ashrita ma’am Part 12

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Class 12 Maths Chp2 Inverse Trigonometric Function by Sunmoni Sir Part 1

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Class 12 Maths Chp2 Inverse Trigonometric Function by Sunmoni Sir Part 2

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Class 12 Maths Chp2 Inverse Trigonometric Function by Sunmoni Sir Part 3

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Class 12 Maths Chp2 Inverse Trigonometric Function by Sunmoni Sir Part 4

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Class 12 Maths Chp3 Matrics by Ashrita ma’am Part 1

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Class 12 Maths Chp3 Matrics,EX 3 1 & 3 2 by Ashrita ma’am Part 2

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Class 12 Maths Chp3 Matrics,Operations of Matrices by Ashrita ma’am Part 4

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Class 12 Maths Chp3 Matrics,Operations of Matrices by Ashrita ma’am Part 5

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Class 12 Maths Chp3 Matrics,Operations of Matrices by Ashrita ma’am Part 6

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Class 12 Maths Chp3 Matrics,Ex 3 2 by Ashrita ma’am Part 7

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Class 12 Maths Chp3 Matrics,Ex 3 2 by Ashrita ma’am Part 8

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Class 12 Maths Chp3 Matrics,Ex 3 2 by Ashrita ma’am Part 9

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Class 12 Maths Chp3 Matrics,Ex 3 2 by Ashrita ma’am Part 10

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Class 12 Maths Chp3 Matrics,Ex 3 3 by Ashrita ma’am Part 11

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Class12 Maths Chp5 Continuity & Differentiability by Sunmoni sir Part 1

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Class12 Maths Chp5 Continuity & Differentiability by Sunmoni sir Part 2

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Class12 Maths Chp5 Continuity & Differentiability by Sunmoni sir Part 3

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Class12 Maths Chp5 Continuity & Differentiability,Exercise 5 1 by Sunmoni sir Part 4

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Class12 Maths Chp5 Continuity & Differentiability,Exercise 5 1 by Sunmoni sir Part 5

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Class 12 Maths Chp9 Differential Equations ONE SHOT by Sunmoni Sir

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Class12 Maths Chp5 Continuity & Differentiability,Exercise 5 1 by Sunmoni sir Part 6

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Class12 Maths Chp5 Continuity & Differentiability,Exercise 5 1 by Sunmoni sir Part 7

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Class12 Maths Chp5 Continuity & Differentiability, by Sunmoni sir Part 8

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Class12 Maths Chp1 Relation and Function by Bikash sir

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Class12 Maths Chp5 Continuity & Differentiability, by Sunmoni sir Part 9

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Class12 Maths Chp5 Continuity & Differentiability, by Sunmoni sir Part 10

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Class12 Maths Chp5 Continuity & Differentiability, by Sunmoni sir Part 11

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Class12 Maths Chp5 Continuity & Differentiability, by Sunmoni sir Part 12

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Class12 Maths Chp5 Continuity & Differentiability, by Sunmoni sir Part 13

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Class12 Maths CHP 6 Application of Derivatives by Sunmoni sir Part 1

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Class12 Maths CHP 6 Application of Derivatives by Sunmoni sir Part 2

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Class12 Maths CHP 6 Application of Derivatives by Sunmoni sir Part 3

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Class12 Maths CHP 6 Application of Derivatives by Sunmoni sir Part 4

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Class12 Maths CHP 6 Application of Derivatives by Sunmoni sir Part 5

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Class12 Maths CHP 6 Application of Derivatives by Sunmoni sir Part 6

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Class12 Maths CHP 6 Application of Derivatives,Maxima and Minima by Sunmoni sir Part 7

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Class12 Maths CHP 6 Application of Derivatives, Maxima by Sunmoni sir Part 8

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Class 12 Maths Chp4 Determinants by Ashrita ma’am Part 1

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Class 12 Maths Chp4 Determinants by Ashrita ma’am Part 2

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Class 12 Maths Chp4 Determinants by Ashrita ma’am Part 3

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Class 12 Maths Chp4 Determinants by Ashrita ma’am Part 4

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Class 12 Maths Chp4 Determinants, ex 4 2 by Ashrita ma’am Part 5

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Class 12 Maths Chp4 Determinants, ex 4 2 by Ashrita ma’am Part 6

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Class 12 Maths Chp4 Determinants, ex 4 3 by Ashrita ma’am Part 7

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Class 12 Maths Chp4 Determinants, ex 4 4 by Ashrita ma’am Part 8

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Class 12 Maths Chp4 Determinants, ex 4 5 by Ashrita ma’am Part 9

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Class12 Maths CHP 7 Integration by Sunmoni sir Part 1

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Class12 Maths CHP 7 Integration by Sunmoni sir Part 2

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Class12 Maths CHP 7 Integration by Sunmoni sir Part 3

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Class12 Maths CHP 7 Integration by Sunmoni sir Part 4

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Class12 Maths CHP 7 Integration by Sunmoni sir Part 5

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Class12 Maths CHP 7 Integration by Sunmoni sir Part 6

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Class12 Maths CHP 7 Integration by Sunmoni sir Part 7

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Class12 Maths CHP 7 Integration by Sunmoni sir Part 8

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Class12 Maths CHP 7 Integration by Sunmoni sir Part 9

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Class12 Maths CHP 7 Integration by Sunmoni sir Part 10

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Exam Notes on NCERT Class 12 Maths Chapter on Relations and Functions
The NCERT Class 12 Maths chapter on Relations and Functions covers several key concepts: Relations Definition: A relation R from set A to B is a subset of the cartesian product A × B A×B. It relates elements of two or more non-empty sets. Types of Relations: Empty Relation: In set A, if no element is related to any element in A, i.e., R = ϕ ⊂ A × A R=ϕ⊂A×A. Universal Relation: In set A, if each element is related to every element in A, i.e., R = A × A R=A×A. Reflexive Relation: If ( a , a ) ∈ R (a,a)∈R for every a ∈ A a∈A. Symmetric Relation: If ( a 1 , a 2 ) ∈ R (a 1 ,a 2 )∈R implies ( a 2 , a 1 ) ∈ R (a 2 ,a 1 )∈R for all a 1 , a 2 ∈ A a 1 ,a 2 ∈A. Transitive Relation: If ( a 1 , a 2 ) ∈ R (a 1 ,a 2 )∈R and ( a 2 , a 3 ) ∈ R (a 2 ,a 3 )∈R implies ( a 1 , a 3 ) ∈ R (a 1 ,a 3 )∈R for all a 1 , a 2 , a 3 ∈ A a 1 ,a 2 ,a 3 ∈A. Equivalence Relation: A relation that is reflexive, symmetric, and transitive. Functions Definition: A function f from set A to B is a relation where every element of A has one and only one image in B. Types of Functions: One to One Function (Injective): If distinct elements of set X have distinct images in set Y. Onto Function (Surjective): If every element of Y is the image of some element of X under f. One-One and Onto Function (Bijective): If the function is both one-one and onto. Composition of Functions: If f: A → B and g: B → C, the composition g ∘ f g∘f is defined as ( g ∘ f ) ( x ) = g ( f ( x ) ) (g∘f)(x)=g(f(x)) for all x ∈ A x∈A. Invertible Functions: A function f: X → Y is invertible if there exists a function g: Y → X such that g ∘ f = I X g∘f=I X and f ∘ g = I Y f∘g=I Y . Here, g is the inverse of f, denoted by f − 1 f −1 . For a function to be invertible, it must be bijective. These concepts form the foundation of understanding how different elements within a set or between different sets are related and how functions act as a special kind of relation with specific properties. The understanding of relations and functions is crucial for further studies in mathematics, especially in calculus, algebra, and discrete mathematics.

Exam notes on NCERT Class 12 Chapter Inverse Trigonometric Functions
The NCERT Class 12 Mathematics chapter on Inverse Trigonometric Functions covers several critical concepts essential for understanding the inversion of trigonometric ratios and their applications, not only in board exams but also in competitive exams like JEE. Here's a detailed summary of the chapter: Concepts Covered Introduction to Inverse Trigonometric Functions: This section explains the concept of finding the inverse of trigonometric functions by restricting their domain and range to make them bijective. The inverse of a function f f is denoted as f − 1 f −1 . Domain and Range of Inverse Trigonometric Functions: Each inverse trigonometric function has a specific domain and range: Arcsine (sin^{-1}x): Domain: [ − 1 , 1 ] [−1,1], Range: [ − π 2 , π 2 ] [− 2 π , 2 π ]. Arccosine (cos^{-1}x): Domain: [ − 1 , 1 ] [−1,1], Range: [ 0 , π ] [0,π]. Arctangent (tan^{-1}x): Domain: All real numbers, Range: ( − π 2 , π 2 ) (− 2 π , 2 π ). Arccotangent (cot^{-1}x): Domain: All real numbers, Range: ( 0 , π ) (0,π). Arcsecant (sec^{-1}x): Domain: ( − ∞ , − 1 ] ∪ [ 1 , ∞ ) (−∞,−1]∪[1,∞), Range: [ 0 , π 2 ) ∪ ( π 2 , π ] [0, 2 π )∪( 2 π ,π]. Arccosecant (csc^{-1}x): Domain: ( − ∞ , − 1 ] ∪ [ 1 , ∞ ) (−∞,−1]∪[1,∞), Range: [ − π 2 , 0 ) ∪ ( 0 , π 2 ] [− 2 π ,0)∪(0, 2 π ]. Properties of Inverse Trigonometric Functions: This section covers various properties that are crucial for solving problems involving inverse trigonometric functions. These properties simplify complex expressions and solve equations involving inverse trigonometric functions. Additional Points Inverse trigonometric functions are not the reciprocals of trigonometric functions. For example, sin ⁡ − 1 x sin −1 x is not equal to 1 sin ⁡ x sinx 1 . Principal Value Branch: The value of an inverse trigonometric function lying in the range of the principal value branch is called its principal value. Equations involving inverse trigonometric functions: This section includes solving equations and finding the values of inverse trigonometric functions given certain conditions. Practice and Problem Solving The chapter includes various problems and exercises to help students apply the concepts of inverse trigonometric functions in different contexts. Practicing these problems is crucial for a thorough understanding and application of the concepts. In summary, this chapter provides comprehensive insights into the inverse of trigonometric functions, their domains and ranges, and properties, along with problem-solving techniques essential for mastering this area of mathematics.

Course Content

Class 12_Chapter 1_Relation & function Hirok Lecture 1

Class 12_Chapter 1_Relation & function Hirok Lecture 2

Class 12_Chapter 1_Relation & function Hirok Lecture 3

Class 12_Chapter 1_Relation & function Hirok Lecture 4

Class 12 Chapter 1 Relation and function Hirok Lecture 5

Class 12 Chapter 1 Relation and function Hirok Lecture 6

Class 12 Chapter 1 Relation and function Hirok Lecture 7

Class 12 Chapter 1 Relation and function Hirok Lecture 8

Class 12 Chapter 1 Relation and function Hirok 9

Class 12:Chapter 2 :Inverse trigonometric Function by Bhrigu Sir Lecture 1

Class 12:Chapter 2 :Inverse trigonometric Function by Bhrigu Sir Lecture 2

Class 12:Chapter 2 :Inverse trigonometric Function by Bhrigu Sir Lecture 3

Class 12:Chapter 2 :Inverse trigonometric Function by Bhrigu Sir Lecture 4

Class 12:Chapter 2 :Inverse trigonometric Function by Bhrigu Sir Lecture 5

Class 12:Chapter 2 :Inverse trigonometric Function by Bhrigu Sir Lecture 6

Class 12:Chapter 2 :Inverse trigonometric Function by Bhrigu Sir Lecture 7

Class 12:Chapter 2 :Inverse trigonometric Function by Bhrigu Sir Lecture 8 & 9

Class 12 Maths Chp10 Vector Algebra, Position vector by Ashrita ma’am Part 1

Class 12 Maths Chp10 Vector Algebra, Position vector by Ashrita ma’am Part 2

Class 12 Maths Chp10 Vector Algebra,Vector joining two points by Ashrita ma’am Part 3

Class 12 Maths Chp10 Vector Algebra,Section Formula by Ashrita ma’am Part 4

Class 12 Maths Chp10 Vector Algebra, Exercise 10 2 by Ashrita ma’am Part 5

Class 12 Maths Chp10 Vector Algebra, Dot & Cross Product by Ashrita ma’am Part 6

Class 12 Maths Chp10 Vector Algebra, Exercise 10 3 by Ashrita ma’am Part 7

Class 12 Maths Chp10 Vector Algebra, Exercise 10 3 by Ashrita ma’am Part 8

Class 12 Maths Chp10 Vector Algebra, Exercise 10 3 by Ashrita ma’am Part 9

Class 12 Maths Chp10 Vector Algebra, Exercise 10 3 by Ashrita ma’am Part 10

Class 12 Maths Chp10 Vector Algebra, Exercise 10 4 by Ashrita ma’am Part 10

Class 12 Maths Chp10 Vector Algebra, Exercise 10 4 by Ashrita ma’am Part 11

Class 12 Maths Chp10 Vector Algebra, Exercise 10 4 by Ashrita ma’am Part 12

Class 12 Maths Chp2 Inverse Trigonometric Function by Sunmoni Sir Part 1

Class 12 Maths Chp2 Inverse Trigonometric Function by Sunmoni Sir Part 2

Class 12 Maths Chp2 Inverse Trigonometric Function by Sunmoni Sir Part 3

Class 12 Maths Chp2 Inverse Trigonometric Function by Sunmoni Sir Part 4

Class 12 Maths Chp3 Matrics by Ashrita ma’am Part 1

Class 12 Maths Chp3 Matrics,EX 3 1 & 3 2 by Ashrita ma’am Part 2

Class 12 Maths Chp3 Matrics,Operations of Matrices by Ashrita ma’am Part 4

Class 12 Maths Chp3 Matrics,Operations of Matrices by Ashrita ma’am Part 5

Class 12 Maths Chp3 Matrics,Operations of Matrices by Ashrita ma’am Part 6

Class 12 Maths Chp3 Matrics,Ex 3 2 by Ashrita ma’am Part 7

Class 12 Maths Chp3 Matrics,Ex 3 2 by Ashrita ma’am Part 8

Class 12 Maths Chp3 Matrics,Ex 3 2 by Ashrita ma’am Part 9

Class 12 Maths Chp3 Matrics,Ex 3 2 by Ashrita ma’am Part 10

Class 12 Maths Chp3 Matrics,Ex 3 3 by Ashrita ma’am Part 11

Class12 Maths Chp5 Continuity & Differentiability by Sunmoni sir Part 1

Class12 Maths Chp5 Continuity & Differentiability by Sunmoni sir Part 2

Class12 Maths Chp5 Continuity & Differentiability by Sunmoni sir Part 3

Class12 Maths Chp5 Continuity & Differentiability,Exercise 5 1 by Sunmoni sir Part 4

Class12 Maths Chp5 Continuity & Differentiability,Exercise 5 1 by Sunmoni sir Part 5

Class 12 Maths Chp9 Differential Equations ONE SHOT by Sunmoni Sir

Class12 Maths Chp5 Continuity & Differentiability,Exercise 5 1 by Sunmoni sir Part 6

Class12 Maths Chp5 Continuity & Differentiability,Exercise 5 1 by Sunmoni sir Part 7

Class12 Maths Chp5 Continuity & Differentiability, by Sunmoni sir Part 8

Class12 Maths Chp1 Relation and Function by Bikash sir

Class12 Maths Chp5 Continuity & Differentiability, by Sunmoni sir Part 9

Class12 Maths Chp5 Continuity & Differentiability, by Sunmoni sir Part 10

Class12 Maths Chp5 Continuity & Differentiability, by Sunmoni sir Part 11

Class12 Maths Chp5 Continuity & Differentiability, by Sunmoni sir Part 12

Class12 Maths Chp5 Continuity & Differentiability, by Sunmoni sir Part 13

Class12 Maths CHP 6 Application of Derivatives by Sunmoni sir Part 1

Class12 Maths CHP 6 Application of Derivatives by Sunmoni sir Part 2

Class12 Maths CHP 6 Application of Derivatives by Sunmoni sir Part 3

Class12 Maths CHP 6 Application of Derivatives by Sunmoni sir Part 4

Class12 Maths CHP 6 Application of Derivatives by Sunmoni sir Part 5

Class12 Maths CHP 6 Application of Derivatives by Sunmoni sir Part 6

Class12 Maths CHP 6 Application of Derivatives,Maxima and Minima by Sunmoni sir Part 7

Class12 Maths CHP 6 Application of Derivatives, Maxima by Sunmoni sir Part 8

Class 12 Maths Chp4 Determinants by Ashrita ma’am Part 1

Class 12 Maths Chp4 Determinants by Ashrita ma’am Part 2

Class 12 Maths Chp4 Determinants by Ashrita ma’am Part 3

Class 12 Maths Chp4 Determinants by Ashrita ma’am Part 4

Class 12 Maths Chp4 Determinants, ex 4 2 by Ashrita ma’am Part 5

Class 12 Maths Chp4 Determinants, ex 4 2 by Ashrita ma’am Part 6

Class 12 Maths Chp4 Determinants, ex 4 3 by Ashrita ma’am Part 7

Class 12 Maths Chp4 Determinants, ex 4 4 by Ashrita ma’am Part 8

Class 12 Maths Chp4 Determinants, ex 4 5 by Ashrita ma’am Part 9

Class12 Maths CHP 7 Integration by Sunmoni sir Part 1

Class12 Maths CHP 7 Integration by Sunmoni sir Part 2

Class12 Maths CHP 7 Integration by Sunmoni sir Part 3