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

Class 12 Mathematics Book Part-1    Chapter 1 – Relations and Functions  Chapter 2 – Inverse Trigonometric Functions  Chapter 3 – Matrices  Chapter 4 – Determinants  Chapter 5 – Continuity and Differentiability  Chapter 6 – Application of Derivatives   Class 12 Mathematics Book Part-2    Chapter 7 – Integrals  Chapter 8 – Application of Integrals […]

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 […]

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. […]

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 […]

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 […]

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 from […]

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 […]

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 […]

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, x = x0 represents the rate of change of y with respect to x at x = x0. If two variables x and y are varying with respect to another […]

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) […]

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. […]

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 […]

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 […]

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 […]

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

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