Notes and Study material for Exams
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
Change of binary number to decimal number and decimal number to binary number Binary Number System Digital computer represents all kinds of data and information in the binary system. Binary Number System consists of two digits 0 and 1. Its base is 2. Each digit or bit in binary number system can be … Read more
Contribution of aryabhatta in mathematics Number notation Numerical values He made a notation system in which digits are denoted with the help of alphabet numerals e.g., 1 = ka, 2 = Kha, etc. Aryabhatta assigned numerical values to the 33 consonants of the Indian alphabet to represent 1,2,3…25,30,40,50,60,70,80,90,100. Notation system He invented a … Read more
Fractions Any unit can be divided into any numbers of equal parts, one or more of this parts is called fraction of that unit. e.g. one-forth (1/4), one-third (1/3), three-seventh (3/7) etc. The lower part indicates the number of equal parts into which the unit is divided, is called denominator. The upper part, which indicates the number of … Read more
Ratio Introduction: Ratio is the relation which one quantity bears to another of the same kind. The ratio of two quantities a and b is the fraction a/b and we write it as a: b. In the ratio a: b, we call a as the first term or antecedent and b, the second term or consequent. … Read more
Aryabhata, an ancient Indian mathematician and astronomer, made significant contributions to the fields of Mathematics and Astronomy during the 5th century CE. His groundbreaking work laid the foundation for many advancements in these disciplines, influencing scientific thought for centuries to come. In this article, we will explore the remarkable contributions of Aryabhata, higting his … Read more