$47 \frac{1}{17} \div 1 \frac{49}{51} + 23 \frac{5}{7} + ? = 67 \frac{4}{9}$

The value of $\sqrt{2 \sqrt[3]{4 \sqrt{2 \sqrt[3]{4 \sqrt{2 \sqrt[3]{4 \ldots}}}}}}$ is

Eight persons are planning to share equally the rent of a car. If one person withdraws from the arrangement and the others share equally the entire cost of the car,then the share of each of the remaining persons increases by what fraction?

Which of the following is true?
$I.$ $\frac{1}{\sqrt[3]{12}} > \frac{1}{\sqrt[4]{29}} > \frac{1}{\sqrt{5}}$
$II.$ $\frac{1}{\sqrt[4]{29}} > \frac{1}{\sqrt[3]{12}} > \frac{1}{\sqrt{5}}$
$III.$ $\frac{1}{\sqrt{5}} > \frac{1}{\sqrt[3]{12}} > \frac{1}{\sqrt[4]{29}}$
$IV.$ $\frac{1}{\sqrt{5}} > \frac{1}{\sqrt[4]{29}} > \frac{1}{\sqrt[3]{12}}$

The value of: $\sqrt{\frac{0.324 \times 0.081 \times 4.624}{1.5625 \times 0.0289 \times 72.9 \times 64}}$

Which of the following statement$(s)$ is/are $TRUE$?
$I.$ $\frac{2}{3 \sqrt{5}} < \frac{3}{2 \sqrt{5}} < \frac{5}{4 \sqrt{3}}$
$II.$ $\frac{3}{2 \sqrt{5}} < \frac{2}{3 \sqrt{3}} < \frac{7}{4 \sqrt{5}}$