Simplify $\frac{3\tfrac{2}{3}\times \tfrac{5}{6}\times \tfrac{2}{3}}{\tfrac{11}{15}\times \tfrac{3}{4}\times \tfrac{2}{27}}$

If the number M,N,Q are in the ratio 5:4:3. Find the value of $\frac{2N-Q}{M}$

If ${{\log }_{3}}18+{{\log }_{3}}3-{{\log }_{3}}x=\log 3,$ find x

Simplify $\left( \sqrt{2}+\frac{1}{\sqrt{3}} \right)\left( \sqrt{2}-\frac{1}{\sqrt{3}} \right)$

Raila has 7 different posters to be hanged in her bedroom, living room and kitchen. Assuming she has plans to place at least a poster in each of the 3 rooms how many choices does she have?

Find the remainder when ${{x}^{3}}-2{{x}^{2}}+3x-3$is divided by ${{x}^{2}}+1$

Solve for x and y respectively in the simultaneous equations$\begin{align}  & -2x-5y=3 \\ & x+3y=0 \\\end{align}$

T varies inversely as the cubes of R, when R =3, T = $\tfrac{2}{81}$, find T when R = 2

Solve the inequality $-6(x+3)\le 4(x-2)$

Find the sum of the first 18 terms of the series 3, 6, 9, -, -, -, 36.

A binary operation $\oplus $on real number us defined by $x\oplus y=xy+x+y$for two real numbers x and y. Find the value of $3\oplus -\tfrac{2}{3}$

Evaluate $\left| \begin{matrix}   4 & 2 & -1  \\   2 & 3 & -1  \\   -1 & 1 & 3  \\\end{matrix} \right|$

What is the size of each interior angle of a 12–sided regular polygon? 

A chord of a circle of radius 7cm is 5cm from the centre of the circle. What is the length of the chord?

The perpendicular bisector of a line XY is the locus of a point.

The midpoint of P (x, y) and Q (8, 6) is (5, 8). Find x and y.

In a right angle triangle, if tan θ = ¾ what is cos θ – sin θ

The derivative of $(2x+1)(3x+1)$ is

Find the value of x at the minimum point of the curve $y={{x}^{3}}+{{x}^{2}}-x+1$