Variance Variance (σ2) in statistics is a measurement of the spread between numbers in a data set. That is, it measures how far each number in the set is from the mean and therefore from every other number in the set. In investing, the variance of the returns among assets in a portfolio is analyzed … Read more

Time & Work

 TIME AND WORK In these problems the number of persons, quantity of work done and time taken are important factors. Also time taken by a person depends on the efficiency of that person which comes into picture when different people do the work such as women, children do the work … Read more

Contribution Of Brahma Gupta

 Contribution of  Brahma gupta, in mathematics Brahmagupta was born in 598 Bhinmal city in the state of Rajasthan. He was a mathematician and astronomer, who wrote many important works on mathematics and astronomy. His best known work is the “Brahmasphuta‐siddhanta”, written in 628 AD in Bhinmal. He was the first to use … Read more


 Commercial mathematics Banking Banking can be defined literarily as the business activity of accepting and safeguarding money owned by individuals and entities and release of the money whenever the needs arise by the owner. It is the business of managing money and where money is involved everything must be carefully assessed, valued and … Read more


 Pie-chart A pie graph (or pie chart) is a specialized graph used in statistics. The independent variable is plotted around a circle in either a clockwise direction or a counterclockwise direction.The dependent variable (usually a percentage) is rendered as an arc whose measure is proportional to the magnitude of the quantity.Each arc is … Read more

Square Roots And Cube Roots

 Square Root & Cube Root   Step 1: First of all group the number in pairs of 2 starting from the right.   Step 2: To get the ten’s place digit, Find the nearest square (equivalent or greater than or less than) to the first grouped pair from left and put the square root of the … Read more

Concepts Of Geometry

 Concepts of geometry Points, Lines & Planes   The most fundamental geometric form is a point. It is represented as a dot with a capital alphabet which is its name. A line is a set of points and it extends in opposite directions up to infinity. It is represented by two points on … Read more

Number System

 Number system 1. Basic Formulae  (a + b)(a – b) = (a2 – b2) (a + b)2 = (a2 + b2 + 2ab) (a – b)2 = (a2 + b2 – 2ab) (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) (a3 + b3) = (a + b)(a2 – ab + b2) (a3 – b3) = (a – b)(a2 + ab + b2) (a3 + b3 + c3 – 3abc) = (a + b + c)(a2 + b2 + c2 – ab – bc – ac) When a + b + c = 0, then a3 + b3 + c3 = 3abc   2. Types of Numbers I. Natural Numbers Counting numbers 1,2,3,4,5,…1,2,3,4,5,… are called natural numbers   … Read more

Direction Test

 Direction test     Introduction: There are four main directions – East, West, North and South as shown below:         There are four cardinal directions – North-East (N-E), North-West (N-W), South-East (S-E), and South-West (S-W) as shown below:       Key points   At the time of sunrise if a man stands facing the east, his shadow will be towards … Read more


 Prepositions Prepositions are short words (on, in, to) that usually stand in front of nouns (sometimes also in front of gerund verbs). Even advanced learners of English find prepositions difficult, as a 1:1 translation is usually not possible. One preposition in your native language might have several translations depending on the situation. The … Read more

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