Let us express date in the DDMMYYYY format, where DD represents the day of the month, MM represents the month, and YYYY represents the year. If the last possible date in the ${20}^{\mathrm{th}}$ century with all the eight digits (in the date as expressed in the above format) being odd is a Sunday, then what day of the week will the first date of the ${21}^{\mathrm{st}}$century with all the eight digits even will be?

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

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