The number of positive integral values of $\mathrm{x}$ that satisfy ${\mathrm{x}}^3-32\mathrm{x}-5{\mathrm{x}}^2+64\le 0$ is/are:

The variance $p$, $q$, $r$, and $s$ are correlated with each other with the following relationship: $\frac{s^{0.5}}{p}=\frac{q}{r^2}$

The ranges of values for $p$, $q$ and $r$ are respectively:

$-0.04\le p\le -0.03$, $-0.25\le q\le -0.09$, $1\le r\le 7$

Determine the difference between the maximum and minimum value of $s$?

If the graph $y=f\left(x\right)$ is shown in the diagram below, then answer the following question:

If $f\left(x\right)=0$ has '$n$' real roots then n$=$?

If the graph $y=f\left(x\right)$ is shown in the diagram below, then answer the following question:

Sum of all roots of $f\left(x\right)=0$ is:

If the graph $y=f\left(x\right)$ is shown in the diagram below, then answer the following question:

Total number of roots of $f\left(x\right)=2$ is:

If the graph $y=f\left(x\right)$ is shown in the diagram below, then answer the following question:

The total number of roots of $f\left(\left|x\right|\right)=0$ is:

If $m$, $n$ are the roots of $p{x}^2+qx+r=0$ and $m+k$, $n+k$ are the roots of the equation $a{x}^2+bx+c=0$ then $k=$?