CBSE Class 12 Maths Notes Chapter 13 Probability 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…
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CBSE Class 12 Maths Notes Chapter 12 Linear Programming 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…
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CBSE Class 12 Maths Notes Chapter 11 Three Dimensional Geometry 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…
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CBSE Class 12 Maths Notes Chapter 10 Vector Algebra 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…
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CBSE Class 12 Maths Notes Chapter 9 Differential Equations 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…
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CBSE Class 12 Maths Notes Chapter 7 Integrals Integration is the inverse process of differentiation. In the differential calculus, we are given a function and we have to find the derivative or differential of this function, but in the integral calculus, we are to find a function whose differential is given. Thus, integration is a…
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Application of Derivatives Class 12 Notes Maths Chapter 6 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…
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Continuity and Differentiability Class 12 Notes Maths Chapter 5 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.…
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Determinants Class 12 Notes Maths Chapter 4 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|…
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Matrices Class 12 Notes Maths Chapter 3 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.…
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