If $x = 1 + \sqrt{2} + \sqrt{3},$ then find the value of $x^{2} - 2x + 4$.

$\frac{3 \sqrt{2}}{\sqrt{6}-\sqrt{3}}-\frac{4 \sqrt{3}}{\sqrt{6}-\sqrt{2}}-\frac{6}{\sqrt{8}+\sqrt{12}}=?$

If the numbers $\sqrt[3]{9}, \sqrt[4]{20}, \sqrt[6]{25}$ are arranged in ascending order,then the correct arrangement is:

What should come in place of the question mark $(?)$ in the following expression?
$820.15 + 2379.85 + 140.01 \times 4.99 = ?$

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 $\frac{M}{N}$?

If $\frac{a}{b} = \frac{1}{2},$ then $\frac{3a + 2b}{3a - 2b}$ is equal to