Find the value of the following expression up to four places of decimals:
$\left[1+\frac{1}{1 \times 2}+\frac{1}{1 \times 2 \times 4}+\frac{1}{1 \times 2 \times 4 \times 8}+\frac{1}{1 \times 2 \times 4 \times 8 \times 16}\right]$

If $a+b+c=6, a^{2}+b^{2}+c^{2}=14$ and $a^{3}+b^{3}+c^{3}=36,$ then the value of $abc$ 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 $\frac{M}{N}$?

What value will come in place of the question mark (?) in the following question? (You are not expected to calculate the exact value)
$10^{3} \times 100^{3} + 999999999 = 10^{?} + 10^{?}$

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

If $x = \frac{a}{a-1}$ and $y = \frac{1}{a-1}$,then