What is the area of an isosceles triangle whose perimeter is 11 cm and base is 5 cm?

A wooden cuboidal box with lid has external dimensions \(80\,\text{cm}\times 49\,\text{cm}\times 30\,\text{cm}\). If thickness of the wood is 2 cm, then find the volume of the wood (in \(\text{cm}^3\)) used.

22 solid metallic cubes of side 4 cm are melted and 16 equal solid cylinders of height 7 cm are formed. Find the radius (in cm) of the cylinders so formed. \(\left(\pi=\dfrac{22}{7}\right)\)

Find the value of: \(\dfrac{\sqrt[3]{3375}+\sqrt{144}}{\sqrt[3]{729}+\sqrt[3]{1728}}\)

If \(A:B=2:3\), \(A:C=6:7\), \(C:D=14:15\), then find \(A:B:C:D\).

A vessel contains 100 liters of solution having 80 liters of spirit and the remaining is water. If 20 liters of the mixture is taken out from the vessel and replaced by water, then what will be the ratio of spirit to water in the new solution?

A shopkeeper sold two electric irons at ₹ 1344 each. He earned \(12\%\) profit on one iron and lost \(4\%\) on the other. Find his overall profit percentage (correct to 2 decimal places).

A shopkeeper allowed successive discounts of \(12\%\) and \(x\%\) on every item. A customer paid ₹ 15048 for an item marked for ₹ 18000. Find the value of \(x\).

Simplify: \((27)^{-\frac{1}{3}}\times(27)^{-\frac{1}{3}}\times\left(27^{\frac{1}{3}}-27^{\frac{2}{3}}\right)\)