Given: $\text{R}: \mathbb{N}\times \mathbb{N}\rightarrow \mathbb{N}\times \mathbb{N}$, defined by $(a, b)\; \text{R}…

Math Quiz Welcome to Math Quiz Start Quiz …

(i) $f(x)=3x-2$ where $f: \mathbb{R}\rightarrow \mathbb{R}$ # Method 1: Let $x_1, \; x_2$ be any element of $\mathbb{…

Given:   $\hspace{0.3cm}A=\mathbb{R}-\{3\}$ $\hspace{0.3cm}B=\mathbb{R}-\{1\}$ $\hspace{0.3cm}f:A\rightarrow B$ s…

Numbers which have atleast one factor other than $𝟏$ and the number itself are called composite numbers. Example: $4…

Fundamental Theorem of Arithmetic (FTA) states that every composite number can be uniquely expressed as a product of pr…

Given: $\sqrt{3}$ is irrational. To Prove: $5+2\sqrt{3}$ is irrational. Proof: Suppose that $5+2\sqrt{3}$ is a ration…

Statement: Angle subtended by an arc at the centre is double the angle subtended by it on the remaining part of the cir…

Statement: The line segment joining mid-points of two sides of a triangle is parallel to the third side of the triangle…

Suppose that $\sqrt{3}$ is a rational number. Then, it can be written in $\frac{p}{q}$ form where integers $p$ and $q$ …

Statement:  If a line is drawn parallel to the one side of the triangle to intersect other two sides of the triangle i…