Find the locus of a particle which moves in the first quadrant so that it is equidistant from the line x = 0 and y = 0 (where k is a constant)

Find the radius of a sphere whose surface area is 154 cm²

A chord is drawn 5cm away from the centre of a circle of radius is 13cm. Calculate the length of the chord.

If the hypotenuse of a right – angle isosceles triangle is 2cm. What is the area of the triangle?

In the figure above $TS\parallel XY$and XY = TY, $\angle STZ={{34}^{\circ }},\text{ }\angle TXY={{47}^{\circ }}$find the angle marked n

A regular polygon has 150^o as the size of each interior angle. How many sides does it have?

Find the angle between the straight line $y=x\,\text{and }y=\sqrt{3}x$

If $\left( \begin{matrix}   x+3 & x+2  \\   x+1 & x-1  \\\end{matrix} \right)$, evaluate x if $\left| P \right|=-10$

If $Q=\left( \begin{matrix}   9 & -2  \\   -7 & 4  \\\end{matrix} \right),\text{then }\left| Q \right|\text{is}$

A binary operation $\otimes $defined on the set of integers is such that m$\otimes $n = m + n + mn for all integers m and n. Find the inverse of  –5 under this operation, if the identity element is 0