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
SURDS A surd is a square root which cannot be reduced to a rational number. For example, is not a surd. However is a surd. If you use a calculator, you will see that and we will need to round the answer correct to a few decimal places. This makes it less accurate. If … Read more
HCF & LCM HCF & LCM are acronym for words, Highest common factor and Lowest common multiple respectively. 1. H. C. F While we all know what a multiplication is like 2 * 3 = 6. HCF is just the reverse of multiplication which is known as Factorization. Now factorization is breaking … Read more
Computer Binary digit system The binary Number System, also called the base-2 number system, is a method of representing numbers that counts by using combinations of only two numerals: zero (0) and one (1). Computers use the binary number system to manipulate and store all of their data including numbers, words, Videos, graphics, … 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
Shrinivas Ramanujan: Contribution to mathematics Srinivasa Ramanujan, an Indian mathematician was born in 22nd December, 1887 in Madras, India. Like Sophie Germain, he received no formal Education in mathematics but made important contributions to advancement of mathematics. His chief contribution in mathematics lies mainly in analysis, game theory and infinite series. He made … Read more
Percentage Percent means for every 100 So, when percent is calculated for any value, it means that we calculate the value for every 100 of the reference value. percent is denoted by the symbol %. For example, x percent is denoted by x% x%=x/100 Example : 25%=25/100=1/4 To express x/y as a percent,we have x/y=(x/y×100)% Example : … Read more
Reasoning & Mental AbilityFor Notes Click Here Logical Reasoning (Deductive, Inductive, Abductive): · Statement and Assumptions, Statement and Argument, Statements and Conclusion, Courses of Action. · Analytical Reasoning. Mental Ability : Number series, Letter series, Odd man out, Coding-Decoding, Problems relating to Relations, Shapes and their sub sections. Basic Numeracy : – Elementary knowledge of … Read more
The Two Houses of Indian Parliament: A Comparative Analysis of Lok Sabha and Rajya Sabha The Indian Parliament, the supreme legislative body of the country, is a bicameral legislature, meaning it comprises two houses: the Lok Sabha (House of the People) and the Rajya Sabha (Council of States). While both houses play crucial roles in … Read more