What Is Arithmetic ProgressionArithmetic Progression (A.P.)Arithmetic Progression is defined as a series in which difference between any two consecutive terms is constant throughout the series. This constant difference is called common difference. A seq…

Cross ProductVector or Cross product(1) Vector product of two vectors: Let a, b be two non-zero, non-parallel vectors. Then a × b = |a||b| sin θ \(\hat { n }\), and a × b = |a||b| sin θ where θ is the angle between a and b, \(\hat { n }\) is a unit vect…

Introduction to SetsA set is well defined class or collection of objects. A set is often described in the following two ways. Roster method or Listing method: In this method a set is described by listing elements, separated by commas, within braces { }.…

Point-Slope Equation of a LineEquations of straight line in different forms(1) Slope form: Equation of a line through the origin and having slope m is y = mx. (2) One point form or Point slope form: Equation of a line through the point (x1,  y1) and hav…

What is a Function?Definition of functionFunction can be easily defined with the help of the concept of mapping. Let X and Y be any two non-empty sets. “A function from X to Y is a rule or correspondence that assigns to each element of set X, one and onl…

Homogeneous Differential EquationsHomogeneous differential equationA function f(x,y) is called a homogeneous function of degree if f(λx, λy) = λn f(x, y). For example, f(x, y) = x2 – y2 + 3xy is a homogeneous function of degree 2. A homogenous function …

CorrelationThe relationship between two variables such that a change in one variable results in a positive or negative change in the other variable is known as correlation. Types of correlationPerfect correlation: If the two variables vary in such a mann…

Derivative RulesThe rate of change of one quantity with respect to some another quantity has a great importance. The rate of change of a quantity ‘y’ with respect to another quantity ‘x’ is called the derivative or differential coefficient of y with resp…

Inverse of a Matrix using Minors, Cofactors and AdjugateMinors and CofactorsMinor of an element: If we take the element of the determinant and delete (remove) the row and column containing that element, the determinant left is called the minor of that el…

Differentiable FunctionDifferentiability of a function at a pointThe function, f(x) is differentiable at point P, iff there exists a unique tangent at point P. In other words, f(x) is differentiable at a point P iff the curve does not have P as a corner…