The number of ordered pairs $(m, n)$,where $m, n \in \{1, 2, 3, \ldots, 50\}$,such that $6^m + 9^n$ is a multiple of $5$ is

For all $n \in N$,the product $(n+24)(n+25)(n+26)(n+27)$ is always divisible by:

For a set of $5$ true or false questions,no student has written all the correct answers and no two students have given the same sequence of answers. The maximum number of students in the class for this to be possible is

In the product $(1 + x) (1 + x + x^2) (1 + x + x^2 + x^3) \dots (1 + x + x^2 + \dots + x^{100})$,when written in ascending powers of $x$,the highest exponent of $x$ is . . . . . . .

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

The number of ways in which $4$ different things can be distributed to $6$ persons so that no person gets all the things is