In the diagram, POS and ROT are straight lines. OPQR is a parallelogram, $\left| OS \right|=\left| OT \right|$ and $\angle OST=50{}^\circ $ . Calculate the value of $\angle OPQ$

A rectangular board has length 15cm and width xcm. If its sides are doubled, find its new area.

. Find the angle which an arc of length 22cm subtends at the centre of a circle of radius 15cm [Take $\pi =\tfrac{22}{7}$]

Eric sold his house through an agent who charged 8% commission on the selling price.
If Eric received $117,760.00 after the sale, what was the selling price of the house?

Make b the subject of the relation$lb=\tfrac{1}{2}(a+b)h$

An arc subtends an angle of 72^o at the centre of a circle. Find the length of the arc if the radius of the circle is 3.5cm [Take $\pi=\frac{22}{7}$

If ${{\log }_{x}}2=0.3$ evaluate ${{\log }_{x}}8$

In $\Delta XYZ$, $\left| YZ \right|=32cm$, $\angle YXZ=52{}^\circ $ and $\angle XZY=90{}^\circ $ Find, correct to the nearest centimetre, $\left| XZ \right|$

If ${{2}^{a}}=\sqrt{64}$ and $\frac{b}{a}=3$, evaluate ${{a}^{2}}+{{b}^{2}}$

The total surface area of a solid cylinder is 165cm². If the base diameter is 7cm, calculate its height [Take $\pi =\tfrac{22}{7}$]