Letters in the word $HULULULU$ are rearranged. The probability of all three $L$ being together is

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

The sum of all three-digit numbers,formed using non-zero digits,where all the digits are perfect squares of a natural number,is

Consider the following statements:
$I$. The number of positive integral solutions of $x_1+x_2+x_3+x_4=10$ is $286$.
$II$. If $25! = 10^n \times k, (k \in N)$,then $n=6$.
Which one of the following options is true?

Let $m$ and $n$ $(m < n)$ be two $2$-digit numbers. Then the total number of pairs $(m, n)$ such that $\operatorname{gcd}(m, n) = 6$ is . . . . . . .

The number of ways of getting a sum of $16$ when throwing a die four times is: