All the possible two-character codes are formed using the digits $0$ to $9$and the capital letters of the English alphabet A to Z. How many such codes are there, which upon writing the code on a piece of paper and then turning the paper around to read the code upside down will be mistaken for another code? There is no confusion between zero and the letter O or the number $1$and the letter I.

A Computer Science student was using the following algorithm on his computer:

Step $1$: Read $\mathrm{A}$

Step $2: \mathrm{B} = 1$

Step $3:$ If $\mathrm{A}>1$, then $\mathrm{B}=\mathrm{B}\times \mathrm{A}$

Step $4$ : If $\mathrm{A}\le 1$, then print $\mathrm{B}$ and stop

Step $5$ $:\mathrm{A}=\mathrm{A}-1$

Step $6$ : go to step $3$

If A is a non-negative integer, then what is the student trying to find using the algorithm?

A club with x members is organized into$4$committees according to the following rules:

1. Each member belongs to exactly two committees.

2. Each pair of committees has exactly one member in common.

Then, which of the following is true regarding the value of x ?

How many integers satisfy the inequality

$\frac{(\mathrm{x}-1)(\mathrm{x}+4)(\mathrm{x}+2)}{(\mathrm{x}-3)(\mathrm{x}+8)(\mathrm{x}+3)}<0?$