The total number of words that can be formed using the letters $a, b, c, d, e, f$ taken $3$ at a time such that each word contains at least one vowel is:

If all the letters of the word $CRICKET$ are permuted in all possible ways and the words (with or without meaning) thus formed are arranged in the dictionary order,then the rank of the word $CRICKET$ is

If $^{12}P_r = 1320$,then $r$ is equal to

For $n = 1, 2, 3, . . . , 50$,let $A = \{ a_n \mid a_n = \begin{cases} (-1)^{\frac{n}{2}} (\frac{n}{2}), & \text{if } n \text{ is even} \\ (-1)^{\frac{n-1}{2}} (\frac{n-1}{2}), & \text{if } n \text{ is odd} \end{cases} \}$ and $B$ be the set of all distinct elements of $A$. The number of permutations of all the elements of set $B$ such that even integers are in increasing order is:

$A$ three-digit number $n$ is such that the last two digits are equal and differ from the first digit. The number of such $n$'s is:

The number of five-digit numbers greater than $50000$ that can be formed by using all the digits $0, 1, 3, 5, 9$ only once is