Closed Interval: Let a and b be two given real numbers such that a < b. Then the set of all real numbers x such that a ≤ x ≤ b is called a closed interval and is denoted by [a, b] i.e., [a, b] = {x ϵ R| a ≤ x ≤ b} Open Read more about Intervals[…]

Periodic Functions: A function f(x) is said to be a periodic function if there exists a positive real number T such that f (x+ T) = f (x) for all x ϵ R. We know that Sin (x + 2x) = sin (x + 4x) = … = sin x And, cos (x + 2x) Read more about Periodic Functions[…]

Definition: Let f: A → B and g: B → C be two functions. Then a function gof: A → C defined by (gof)(x) = g(f(x)), for all x ϵ A is called the composition of f and g.Note 1: It is evident from the definition that gof is defined only if for each x Read more about Composition of Functions[…]

CONSTANT FUNCTION: Let k be a fixed real number. Then a function f (x) given by f (x) = k for all x ϵ R is called a constant function. Sometimes we also call it the constant function k.IDENTITY FUNCTION: The function defined by I (x) = x for all x ϵ R is called the identity function on R.RECIPROCAL FUNCTION: The function that associates each non-zero real number x to its reciprocal 1/x Read more about Graphs of simple functions[…]

EQUALITY OF MATRICES DEFINITION: Two matrices A = [aij] mxn And B = [bij] mxn are said to be equal if 1. m = r, i.e., the number of rows in A equals the number of rows in B 2. n = s, i.e., the number of columns in A equals the number of columns in B 3. aI Read more about Algebra of Matrices of Order 2 and 3[…]

Definition: A set of mn numbers (real or imaginary) arranged in the form of a rectangular array of m rows and n columns is called an m x n matrix (to be read as ‘m’ by ‘n’ matrix). An m x n matrix is usually written as . In compact form the above matrix is Read more about Types of matrices[…]

Let A and B be two non-empty sets. Then a function ‘f’ from set A to set B is a rule or method or correspondence which associates elements of set A to elements of set B such that i) All elements of set A are associated to elements in set B. ii) An element of Read more about FUNCTIONS[…]

Hello MyRankers, Here is the explanation of Geometric Progression…… A sequence of non-zero numbers is called a geometric progression (abbreviated as G.P.). If the ratio of a term and the term preceding to it is always a constant quantity. The constant ratio is called the common ratio of the G.P. In other words, a sequence, a₁, a₂, Read more about GEOMETRIC PROGRESSION[…]

Introduction: Sequence: A sequence is a function whose domain is the set N of natural numbers. Real Sequence: A sequence whose range is a subset of R is called a real sequence. In other words, a real sequence is a function with domain N and the range a subset of the set R of real numbers. Read more about SEQUENCE AND SERIES[…]

Here goes the revision tips for a quick recollection of the important content in the chapter COMPLEX NUMBERS. Equation of perpendicular bisector: The equation of the perpendicular bisector of the line segment joining points z₁ and z₂ isz (z₁̅ – z₂̅) + z̅ (z₁ – z₂) = |z₁|² – |z₂|². Important results: If z₁, z₂, z₃ are Read more about Short cuts in COMPLEX NUMBERS[…]