Find the value of \(p^3-27q^3\) if \(p-3q=-7\) and \(pq=-10\).

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

The value of \(\left(2.3\overline{6}-0.1\overline{4}\right)\) expressed as fraction in lowest terms is:

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 \(x\).

If \(P=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}\), then find the value of \(\sqrt{6(9-P)}\).

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).

Which of the following is correct for a number to be divisible by 8?

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?

If the mean of the observations \(k,\ (k+8),\ (2k-1),\ (k+12),\ 12\) and \(17\) is 13, then find the median of these observations.