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

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

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

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

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.

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

Aniket can row a boat, 21 km downstream in 1 hr 30 min and 20 km upstream in 2 hours. He can row the boat in still water at the speed of (in km/h).

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 \(x\).

To reduce the usual time taken to cover a distance of 300 km by 1 hour, the speed of a bus is increased by 10 km/h. The usual speed of the bus (in km/h) is: