All the five-digit numbers in which each successive digit exceeds its predecessor are arranged in increasing order of their magnitude. The $97^{th}$ number in the list does not contain the digit:

$A$ boy needs to select five courses from $12$ available courses,out of which $5$ courses are language courses. If he can choose at most two language courses,then the number of ways he can choose five courses is

If $^{2n}C_3 : ^nC_2 = 44:3$,then for which of the following values of $r$,the value of $^nC_r$ will be $15$?

The least value of the natural number $n$ satisfying $C(n, 5)+C(n, 6)>C(n+1, 5)$ is

There are $10$ persons named $A, B, \dots, J$. We have the capacity to accommodate only $5$. In how many ways can we arrange them in a line if $A$ must be included,and $G$ and $H$ must not be included in the team of $5$?

If ${}^nC_4, {}^nC_5$ and ${}^nC_6$ are in $A.P.$,then $n$ is