The missing term in the following table is
$\begin{array}{|c|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 & 4 \\ \hline y=f(x) & 1 & 3 & 9 & ? & 81 \\ \hline \end{array}$

If $U$ is the universal set and $A \cup B \cup C = U$,then ${(A - B) \cup (B - C) \cup (C - A)}'$ is equal to:

For a real number $x$,$[x]$ denotes the greatest integer less than or equal to $x$. Then the value of $\left[\frac{1}{2}\right] + \left[\frac{1}{2} + \frac{1}{100}\right] + \left[\frac{1}{2} + \frac{2}{100}\right] + \left[\frac{1}{2} + \frac{3}{100}\right] + \ldots + \left[\frac{1}{2} + \frac{99}{100}\right] = $

Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers,with $\text{HCF}(x, y) = 16$ and $\text{LCM}(x, y) = 48000$. The number of elements in $S$ is

Let $A$ be the set of first $101$ terms of an $A$.$P$.,whose first term is $1$ and the common difference is $5$,and let $B$ be the set of first $71$ terms of an $A$.$P$.,whose first term is $9$ and the common difference is $7$. Then,the number of elements in $A \cap B$ which are divisible by $3$ is:

If a set $A$ has $5$ elements,then the number of ways of selecting two subsets $P$ and $Q$ from $A$ such that $P$ and $Q$ are mutually disjoint,is