The inequality \(\log_a f(x)<\log_a g(x)\) implies that

The value of \((\log_3 30)^{-1}+(\log_4 900)^{-1}+(\log_5 30)^{-1}\) is

Three cubes with integer edge lengths are given. It is known that the sum of their surface areas is 564 \(cm^2\). Then the possible values of the sum of their volumes are________

In a given village there are only three sizes of families: families with 2 members, families with 4 members and families with 6 members. The proportion of families with 2, 4 and 6 members are roughly equal. A poll is conducted in this village wherein a person is chosen at random…

Determine the greatest number among the following four numbers

A die is thrown three times and the sum of the three numbers is found to be 15. The probability that the first throw was a four is

The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0, 0), (0, 31), and (31, 0) is

From a pack of 52 cards, we draw one by one, without replacement. If f(n) is the probability that an Ace will appear at the nth turn, then

Two small insects, which are x metres apart, take u minutes to pass each other when they are flying towards each other, and v minutes to meet each other when they are flying in the same direction. Then, the ratio of the speed of the slower insect to that of the faster insect is