Chapter 1 Relations and Functions Class 12 Notes Chapter 2 Inverse Trigonometric Functions Class 12 Notes Chapter 3 Matrices Class 12 Notes Chapter 4 Determinants Class 12 Notes Chapter 5 Continuity and Differentiability Class 12 Notes Chapter 6 Application of Derivatives Class 12 Notes Chapter 7 Integrals Class 12 Notes Chapter 9 Differential Equations Class 12 Notes Chapter 10 Vector Algebra Class 12 Notes […]

# CBSE Class 12th Mathematics, NCERT Solutions, Sample & Previous Year Papers

## CBSE Class 12 Maths Chapter 13 Probability Notes

Event: A subset of the sample space associated with a random experiment is called an event or a case. e.g. In tossing a coin, getting either head or tail is an event. Equally Likely Events: The given events are said to be equally likely if none of them is expected to occur in preference to the other. […]

## CBSE Class 12 Maths Chapter 12 Linear Programming Notes

Linear Programming Problem: A linear programming problem is one in which we have to find optimal value (maximum or minimum) of a linear function of several variables (called objective function) subject to certain conditions that the variables are non-negative and satisfying by a set of linear inequalities with variables, are sometimes called division variables. Terms related […]

## CBSE Class 12 Maths Chapter 11 Three Dimensional Geometry Notes

Direction Cosines of a Line: If the directed line OP makes angles α, β, and γ with positive X-axis, Y-axis and Z-axis respectively, then cos α, cos β, and cos γ, are called direction cosines of a line. They are denoted by l, m, and n. Therefore, l = cos α, m = cos β and […]

## CBSE Class 12 Maths Chapter 10 Vector Algebra Notes

Vector: Those quantities which have magnitude, as well as direction, are called vector quantities or vectors. Note: Those quantities which have only magnitude and no direction, are called scalar quantities. Representation of Vector: A directed line segment has magnitude as well as direction, so it is called vector denoted as or simply as . Here, the point A […]

## CBSE Class 12 Maths Chapter 9 Differential Equations Notes

Differential Equation: An equation involving independent variable, dependent variable, derivatives of dependent variable with respect to independent variable and constant is called a differential equation. e.g. Ordinary Differential Equation: An equation involving derivatives of the dependent variable with respect to only one independent variable is called an ordinary differential equation. e.g. From any given relationship between the […]

## CBSE Class 12 Maths Chapter 7 Integrals Notes

Properties of Indefinite Integral (i) ∫[f(x) + g(x)] dx = ∫f(x) dx + ∫g(x) dx (ii) For any real number k, ∫k f(x) dx = k∫f(x)dx. (iii) In general, if f1, f2,………, fn are functions and k1, k2,…, kn are real numbers, then ∫[k1f1(x) + k2 f2(x)+…+ knfn(x)] dx = k1 ∫f1(x) dx + k2 ∫ f2(x) dx+…+ kn ∫fn(x) dx […]

## CBSE Class 12 Maths Chapter 6 Application of Derivatives Notes

Rate of Change of Quantities: Let y = f(x) be a function of x. Then, represents the rate of change of y with respect to x. Also, [latex s=1]\frac { dy }{ dx }[/latex]x = x0 represents the rate of change of y with respect to x at x = x0. If two variables x and […]

## CBSE Class 12 Maths Chapter 5 Continuity and Differentiability Notes

Continuity at a Point: A function f(x) is said to be continuous at a point x = a, if Left hand limit of f(x) at(x = a) = Right hand limit of f(x) at (x = a) = Value of f(x) at (x = a) i.e. if at x = a, LHL = RHL = f(a) […]

## CBSE Class 12 Maths Chapter 4 Determinants Notes

Determinant: Determinant is the numerical value of the square matrix. So, to every square matrix A = [aij] of order n, we can associate a number (real or complex) called determinant of the square matrix A. It is denoted by det A or |A|. Note (i) Read |A| as determinant A not absolute value of A. […]

## CBSE Class 12 Maths Chapter 3 Matrices Notes

Matrix: A matrix is an ordered rectangular array of numbers or functions. The numbers or functions are called the elements or the entries of the matrix. Order of a Matrix: If a matrix has m rows and n columns, then its order is written as m × n. If a matrix has order m × n, then […]

## CBSE Class 12 Maths Chapter 2 Inverse Trigonometric Functions Notes

Inverse Trigonometric Functions: Trigonometric functions are many-one functions but we know that inverse of function exists if the function is bijective. If we restrict the domain of trigonometric functions, then these functions become bijective and the inverse of trigonometric functions are defined within the restricted domain. The inverse of f is denoted by ‘f-1‘. Let y […]

## CBSE Class 12 Maths Chapter 1 Relations and Functions Notes

Relation: A relation R from set X to a set Y is defined as a subset of the cartesian product X × Y. We can also write it as R ⊆ {(x, y) ∈ X × Y : xRy}. Note: If n(A) = p and n(B) = q from set A to set B, then n(A […]

## Class 12th Maths Formulas

Chapter-1 Relations and Functions Formula Chapter-2 Inverse Trigonometric Functions Formula Chapter-3 Matrices Formula Chapter-4 Determinants Formula Chapter-5 Continuity and Differentiability Formula Chapter-6 Application of Derivatives Formula Chapter-7 Integrals Formula Chapter-8 Application of Integrals Formula Chapter-9 Differential Equations Formula Chapter-10 Vector Algebra Formula Chapter-11 Three Dimensional Geometry Formula Chapter-12 Linear Programming Formula Chapter-13 Probability Formula

## Class 12 Mathematics NCERT Solutions

Continuity And Differentiability NCERT Solutions Application of Derivatives NCERT Solutions Integrals NCERT Solutions Differential Equations NCERT Solutions Probability NCERT Solutions

## Miscellaneous Exercises, Class 12 Mathematics NCERT Solutions

Misc Eg. 44, Continuity and Differentiability, NCERT Class 12th Maths Solutions https://www.youtube.com/watch?v=n0S_f8Cg6CoVideo can’t be loaded because JavaScript is disabled: Misc Eg. 44, Continuity and Differentiability, NCERT Class 12th Maths Solutions (https://www.youtube.com/watch?v=n0S_f8Cg6Co) Misc Eg. 45, Continuity and Differentiability, NCERT Class 12th Maths Solutions https://www.youtube.com/watch?v=YY2Yjz5qRIEVideo can’t be loaded because JavaScript is disabled: Misc Eg. 45, Continuity and […]

## Miscellaneous Exercises, Class 12 Mathematics NCERT Solutions

Misc Ex. 1 – “Matrices” Chapter 3 – NCERT Class 12th Maths Solutions https://www.youtube.com/watch?v=R7KUC1zT_rkVideo can’t be loaded because JavaScript is disabled: Misc Ex. 11 – “Matrices” Chapter 3 – NCERT Class 12th Maths Solutions (https://www.youtube.com/watch?v=R7KUC1zT_rk) Misc Ex. 2 – “Matrices” Chapter 3 – NCERT Class 12th Maths Solutions https://www.youtube.com/watch?v=hBGDhdzbI94Video can’t be loaded because JavaScript is […]

## Examples, Class 12 Mathematics NCERT Solutions

Example 2 – “Matrices” Chapter 3 – NCERT Class 12th Maths Solutions https://www.youtube.com/watch?v=jD6TzXtFdh4Video can’t be loaded because JavaScript is disabled: Example 2 – “Matrices” Chapter 3 – NCERT Class 12th Maths Solutions (https://www.youtube.com/watch?v=jD6TzXtFdh4) Example 6 – “Matrices” Chapter 3 – NCERT Class 12th Maths Solutions https://www.youtube.com/watch?v=qyI3M6sGCSoVideo can’t be loaded because JavaScript is disabled: Example 6 […]