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

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:

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 $S = \{(m, n): m, n \in \{1, 2, 3, \ldots, 50\}\}$. If the number of elements $(m, n)$ in $S$ such that $6^{m} + 9^{n}$ is a multiple of $5$ is $p$ and the number of elements $(m, n)$ in $S$ such that $m + n$ is a square of a prime number is $q$, then $p + q$ is equal to :

$A$ two-digit number $\overline{ab}$ is called almost prime if one obtains a two-digit prime number by changing at most one of its digits $a$ or $b$. (For example,$18$ is an almost prime number because $13$ is a prime number). The number of almost prime two-digit numbers is:

Let $A = \{\theta \in R \mid \cos^2(\sin \theta) + \sin^2(\cos \theta) = 1\}$ and $B = \{\theta \in R \mid \cos(\sin \theta) \sin(\cos \theta) = 0\}$. Then,$A \cap B$ is: