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

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

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

Let \(\alpha,\beta\) be the roots of \(x^2-x+p=0\) and \(\gamma,\delta\) be the roots of \(x^2-4x+q=0\) where p and q are integers. If \(\alpha,\beta,\gamma,\delta\) are in geometric progression then p + q is

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

For a > b > c > 0, the minimum value of the function \(f(x)=|x-a|+|x-b|+|x-c|\) is

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…

The function \(f(x)=\frac{x^3+5x^2-8x}{3}\) is

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