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Discrete mathematics plays an important role in mathematics in solving nad mathematical reasoning.The topics involved in grade 10 are: Modular Arithmetic Mathematical Reasoning Graph Theo..

Discrete Mathematics

Discrete mathematics includes Modular arithmetic, Mathematical reasoning and Graph theory. Modular arithmetic covers Modular addition and multiplication and Examples on modular arithmetic. 10th grade Mathematical reasoning contains Different types of compound statements, Algebra of statements and Solved ..

Discrete Maths

A set is a collection of individual elements in the domain D. The universal set U contains every element in D. The null set contains no element. If A is a set in the domain D, A must be a subset of the universal set U, denoted as A subeU If A consists of some but not all elements, A is then called a proper subset of U, denoted as A `sub` ..

discrete series

In finding the median in case of discrete series, we use the following procedure i) Arrange the data according to their ascending order of their magnitudes. ii) Form the cumulative frequency table. iii) Use the formula, Median = value of $\left[\frac{N+1}{2}\right]^{th}$ item...........(xiii) where N= total frequency. iv) No..

mean of a discrete random variable illustration

ILLUSTRATION 3 A dealer in refrigerators estimates from his past experience the probabilities of his selling refrigerators in a day. These are as follows: No. of refrigerators sold in a day : 0 1 2 3 4 5 6 Probability: 0.03 0.20 0.23 0.25 0.12 0.10 0.07 ..

mean of a discrete random variable

DEFINITION If $X$ is a discrete random variable which assumes values $x_{1},x_{2},x_{3},\ldots.,x_{n}$ with respective probabilities $p_{1},p_{2/}p_{3},\ \ldots,p_{n}$, then the mean $\overline{\mathrm{X}}$ of $X$ is defined as $\overline{X}=p_{1}x_{1}+p_{2}x_{2}+\ldots.+p_{n}x_{n}$ or, ${\displaystyle \overline{X}..

variance of a discrete random variable

DEFINITION If X is a discrete random variable which assumes values $x_{1/}x_{2},x_{3},\ \ldots.,x_{n}$ with the respective probabilities $p_{1^{j}}p_{2},\ldots.,p_{n}$, then variance of X is defined as Var$(X)=p_{1}(x_{1}-\overline{\mathrm{X}})^{2}+p_{2}(x_{2}-\overline{\mathrm{X}})^{2}+\ldots+p_{n}(x_{n}-\overl..

solution

Trigonometric Functions and Identities LEVEL-I 1. Here L.H.S. $\sin^{2}12^{\circ}+\sin^{2}21^{\circ}+(\sin^{2}39^{\circ}-\sin^{2}9^{\circ})+(\sin^{2}48^{\circ}-\sin^{2}18^{\circ})$ $\Rightarrow\sin^{2}12^{\circ}+\sin^{2}21^{\circ}+\sin(48^{\circ}).\sin(30^{\circ})+\sin(30^{\circ}).\sin(66^{\circ})$ ..

solutions

LEVEL II 1. We know from Napier's analogy that : $\qquad\qquad{\displaystyle \tan\left(\frac{B-C}{2}\right)=\frac{b-c}{b+c}\cot\frac{A}{2}}$ $\qquad\qquad{\displaystyle \tan\left(\frac{A-B}{2}\right)=\frac{a-b}{a+b}\cot\frac{C}{2}}$ $\qquad\qquad{\displaystyle \tan\left(\frac{C-A}{2}\right)=\frac{c-a}{c+a..

Discrete Frequency Distrubition: Example

Consider the data set of blood groups of 20 blood donors in a blood donation camp. O A A A AB B O AB B O AB A B B O B A A AB A Construct a frequency distribution for the above data set. Solution:..

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