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 and asked about his/her family size. The average family size computed by sampling 1000 such persons from the village would be closest to

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

The inequality…

The number of terms common to both the arithmetic progressions 2, 5, 8, 11, ...., 179 and 3, 5, 7, 9, ....., 101 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________

If \((1+x-2x^2)^6=A_0+\sum_{r=1}^{12}A_rx^r\), then value of \(A_2+A_4+A_6+\cdots+A_{12}\) is

Determine the greatest number among the following four numbers