If $m:n=13:11$find $({{m}^{2}}-{{n}^{2}}):{{(m+n)}^{2}}$

The binary operation defined on the set of real number is such that $x\oplus y=\frac{xy}{6}$for all $x,y\in \mathbb{R}$. Find the inverse of 20 under the operation when the identity element is 6

If p varies inversely as cube of q and q varies directly as square of r. What is the relationship between p and r

Find p, q for which$\left( \begin{matrix}   2p & 8  \\   3 & -5q  \\\end{matrix} \right)\left( \begin{align}  & 1 \\ & 2 \\\end{align} \right)=\left( \begin{align}  & 24 \\ & -17 \\\end{align} \right)$

The sum of first n positive is

If $T=2\pi \sqrt{\frac{l}{g}}$make g the subject of formula

A binary operation * on the set of rational number is defined as $x*y=\frac{{{x}^{2}}-{{y}^{2}}}{2xy}$ find –5*3

If $y={{x}^{2}}-x-12,$find the range of x for which y ≥ 0

Find the roots of ${{x}^{3}}-2{{x}^{2}}-5x+6=0$

If $x=\left[ \begin{matrix}   1 & 0 & 1  \\   2 & -1 & 0  \\   -1 & 0 & 1  \\\end{matrix} \right]$ and $y=\left[ \begin{matrix}   -1 & 1 & 2  \\   0 & -1 & -1  \\   2 & -1 & -1  \\\end{matrix} \right]$find 2x – y