What should come in place of the question mark $(?)$ in the following equation?
$30.01^{2} - 19.98^{2} - ? = 21.81^{2}$

If $M = 0.1 + (0.1)^{2} + (0.001)^{2}$ and $N = 0.3 + (0.03)^{2} + (0.003)^{2}$,then what is the value of $M + N$?

$(2 + \frac{3}{x}) \times (y + \frac{1}{2}) = \frac{31}{4}$,find the values of $x$ and $y$ if $x$ and $y$ are positive integers.

If $x = \sqrt{3} + \frac{1}{\sqrt{3}}$,then the value of $\left(x - \frac{\sqrt{126}}{\sqrt{42}}\right) + \left(x - \frac{1}{x - \frac{2\sqrt{3}}{3}}\right)$ is

In an examination,a student was asked to find $\frac{3}{14}$ of a certain number. By mistake,he found $\frac{3}{4}$ of it. His answer was $150$ more than the correct answer. The given number is

If $M = \left(\frac{3}{7}\right) \div \left(\frac{6}{5}\right) \times \left(\frac{2}{3}\right) + \left(\frac{1}{5}\right) \times \left(\frac{3}{2}\right)$ and $N = \left(\frac{2}{5}\right) \times \left(\frac{5}{6}\right) \div \left(\frac{1}{3}\right) + \left(\frac{3}{5}\right) \times \left(\frac{2}{3}\right) \div \left(\frac{3}{5}\right)$,then what is the value of $\frac{M}{N}$?