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It is given that, if two pipes of radii r1 and r2 can fill an empty tank in t1 minutes and t2 minutes respectively and the speed of the flow is same in both the pipes then t1r12 = t2r22. There are three taps of diameters 1 cm, \(1 \frac{1}{2}\) cm, and 2 cm respectively. The speed of the water flow through them is same. The widest tap can fill an empty tank in 45 minutes. If all the taps are opened simultaneously, then in how many hours the empty tank will be filled?

If the HCF of 546, 1155, 462 and 1365 is H and LCM of 252, 504, 108 is L then \(\frac{L}{H} \) =

A train can cross a platform in 18 sec with its usual speed. It can cross the same platform in 15 sec if its usual speed is increased by 15 kmph. If the length of the platform is \(1 \frac{1}{2}\) times that of the train, then the usual speed (in kmph) of the train is :

If x = \(\sqrt{3080+\sqrt{3080+\sqrt{3080+\ldots to\ \infty}}}\), y = \(\sqrt{200 \sqrt{200 \sqrt{200 \ldots to \ \infty}}} \) and .x + y = z, then \(\sqrt{z \sqrt{z \sqrt{z}}}\) =

A watch loses 5 min in every 24 hours duration and another watch gains 3 min in the same duration. If both the watches show identical time 't' at a particular point of time, then by what time duration (in days) they both show the same identical time 't' again in near future ?

The divisor of 7280 among the following is:

A sum of money invested at interest, compounded annually. amounts to Rs. 7680 in 2 years and Rs. 8192 in 3 years. Then the sum of money (in Rs.) invested is:

8 men can do a piece of work in 12 days, 9 women can do the same work in 16 days and 12 children can do it in 24 days. 6 men, 12 women and 18 children started that work and worked together for 3 days. If only women have to complete the remaining work on 4^th day, the number of women required is :

If x, y, z are any three non-zero real numbers such that x4 - y2 = z2, y4 - z2 = x2 and z4 - x2 = y2 then (x2 + 1)-1 + (y2 + 1)-1 + (z2 + 1)-1 =

\(0 . \overline{7}\) is multiplied by itself and that result is divided by \(\left(\frac{2}{9}\right)^{t h}\) part of the reciprocal of \(0 . \overline{8}\). If the value thus obtained is x, then 9√x =