The number of elements in the set $\{n \in \mathbb{Z} : |n^2 - 10n + 19| < 6\}$ is $...........$

$A$ solution of $9 \%$ acid is to be diluted by adding $3 \%$ acid solution to it. The resulting mixture is to be more than $5 \%$ but less than $7 \%$ acid. If there is $460 \text{ L}$ of the $9 \%$ solution,how many litres of $3 \%$ solution will have to be added?

The $I.Q.$ of a person is given by the formula $I.Q. = \frac{MA}{CA} \times 100$,where $MA$ is mental age and $CA$ is chronological age. If $75 < I.Q. < 125$ for a group of $16$ year old children,find the range of their mental age.

In an experiment,a solution of hydrochloric acid is to be kept between $30^{\circ} \text{C}$ and $35^{\circ} \text{C}$. What is the range of temperature in degree Fahrenheit if the conversion formula is given by $C = \frac{5}{9}(F - 32)$,where $C$ and $F$ represent temperature in degree Celsius and degree Fahrenheit,respectively?

Solve for $x$ the following inequality: $\frac{1}{|x|-3} \leq \frac{1}{2}$

$A$ solution is to be kept between $68\,^{\circ} F$ and $77\,^{\circ} F$. What is the range in temperature in degree Celsius $(C)$ if the Celsius/Fahrenheit $(F)$ conversion formula is given by $F = \frac{9}{5} C + 32$?