If $a$ and $b$ are rational numbers and $(a-1) \sqrt{2} + 3 = b \sqrt{2} + a$,then the value of $(a+b)$ is

If $\frac{x}{y} = \frac{4}{5}$,then the value of $\left(\frac{4}{7} + \frac{2y - x}{2y + x}\right)$ is

If $x^{2} + \frac{1}{x^{2}} = 1$,then what is the value of $x^{48} + x^{42} + x^{38} + x^{30} + x^{24} + x^{18} + x^{12} + x^{6} + 1$?

If $a^{2}+b^{2}+c^{2}=2(a-b-c)-3,$ then the value of $(a-b+c)$ is

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

What approximate value will come in place of the question mark $(?)$ in the given equation? (You are not expected to calculate the exact value)
$2775 \times \frac{160}{\sqrt{?}} = 5550$