$15 \frac{2}{3} \times 3 \frac{1}{6} + 6 \frac{1}{3} = 11 \frac{7}{18} + ?$

The value of $1001 \div 11 \text{ of } 13$ is

Which of the following statement$(s)$ is/are $TRUE$?
$I.$ $\sqrt{11}+\sqrt{7} < \sqrt{10}+\sqrt{8}$
$II.$ $\sqrt{17}+\sqrt{11} > \sqrt{15}+\sqrt{13}$

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 $\frac{M}{N}$?

When $\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}\right)$ is divided by $\left(\frac{2}{5}-\frac{5}{9}+\frac{3}{5}-\frac{7}{18}\right),$ the result is:

The simplification of $\left[\frac{1}{2}+\frac{1}{2}\left\{\frac{3}{4}-\frac{1}{2}\left(\frac{7}{8}-\frac{3}{4}\right)\right\}\right]$ yields