EXERCISE 5.1( 6TH STD)

EXERCISE 5.1

3RD SUM
 

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Pascal's Triangle Pascal’s Triangle  is a kind of number pattern.  Pascal’s Triangle is the triangular arrangement of numbers that gives the coefficients in the expansion of any binomial expression.  The numbers are so arranged that they reflect as a triangle. Firstly, 1 is placed at the top, and then we start putting the numbers in a triangular pattern. The numbers which we get in each step are the addition of the above two numbers. It is similar to the concept of  triangular numbers .  In this article, we are going to learn Pascal’s triangle history, definition, properties, patterns, formulas and examples with complete explanation. Table of contents: History Definition Construction How to use Patterns Properties Formula Expansion FAQs Pascal’s Triangle History Blaise Pascal was born at Clermont-Ferrand, in the Auvergne region of France on June 19, 1623. In 1653 he wrote the Treatise on the Arithmetical Triangle which today is known as the  Pascal’s Triang...
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BODMAS RULE IN MATHEMATICS

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  What is BODMAS ? The evaluation of an expression involving numbers is one of the basic tasks in arithmetic. If an expression contains addition (+), subtraction (-), multiplication (x), division (÷), bracket (), and Of (of), then the precedence of simplification of the operation is given by “BODMAS rule”. First, we have to know that what is  BODMAS rule ? Or What is BODMAS formula? BODMAS rule  is a rule or order that is used to simplify the arithmetic expression involving more operators in mathematics. When an equation involving more operators first we have to know that in which order we have to solve the expression. This problem is solved with the help of BODMAS rule. The full form of BODMAS is: B rackets (Parts of a calculation inside the bracket always come first). Precedence of brackets are : [{(bar)}] O rders (powers and square roots) D ivision M ultiplication A ddition S ubtraction Each letter of the word stands for the first letter of an operator. If an expressio...
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History of graph

The paper written by Leonhard Euler on the Seven Bridges of Königsberg and published in 1736 is regarded as the first paper in the history of graph theory.[20] This paper, as well as the one written by Vandermonde on the knight problem, carried on with the analysis situs initiated by Leibniz. Euler's formula relating the number of edges, vertices, and faces of a convex polyhedron was studied and generalized by Cauchy[21] and L'Huilier,[22] and represents the beginning of the branch of mathematics known as topology. More than one century after Euler's paper on the bridges of Königsberg and while Listing was introducing the concept of topology, Cayley was led by an interest in particular analytical forms arising from differential calculus to study a particular class of graphs, the trees.[23] This study had many implications for theoretical chemistry. The techniques he used mainly concern the enumeration of graphs with particular properties. Enumerative graph theory then arose...
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