The number $(49^{2}-4)(49^{3}-49)$ is divisible by (in $!$)

Let the digits $a, b, c$ be in $A.P.$ Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in $A.P.$ at least once. How many such numbers can be formed?

The number of all four-digit numbers which do not have four distinct digits is

In how many ways can $5$ distinct balls be distributed among $3$ persons such that each person receives at least one ball?

$A$ pack contains $n$ cards numbered from $1$ to $n$. Two consecutive numbered cards are removed from the pack and the sum of the numbers on the remaining cards is $1224$. If the smaller of the numbers on the removed cards is $k$,then $k - 20 =$

The sum of the four-digit even numbers that can be formed with the digits $0, 3, 5, 4$ without repetition is: