Question : If $A=\frac{\sqrt{0.0004} \times \sqrt[3]{0.000008}}{\sqrt[4]{16000} \times \sqrt[3]{125000} \times \sqrt[4]{810}}$ and $B=\frac{\sqrt[3]{0.729} \times \sqrt[4]{0.0016}}{\sqrt{0.16}}$, then what is $A \times B$?

Option 1: $6 \times 10^{–7}$

Option 2: $\frac{7}{4} \times 10^{–8}$

Option 3: $5 \times 10^{–8}$

Option 4: $\frac{7}{3} \times 10^{–7}$

Question : The value of $\frac{1}{4-\sqrt{15}}-\frac{1}{\sqrt{15}-\sqrt{14}}+\frac{1}{\sqrt{14}-\sqrt{13}}-\frac{1}{\sqrt{13}-\sqrt{12}}+\frac{1}{\sqrt{12}-\sqrt{11}}-\frac{1}{\sqrt{11}-\sqrt{10}}+\frac{1}{\sqrt{10}-3}-\frac{1}{3-\sqrt{8}}$ is:

Option 1: $2-2 \sqrt{2}$

Option 2: $4+2 \sqrt{2}$

Option 3: $4-2 \sqrt{2}$

Option 4: $2+2 \sqrt{2}$

Question : Simplify the following expression.
$\frac{7}{10} \div \frac{3}{7}$ of $\left(2 \frac{3}{10}+2 \frac{3}{5}\right)+\frac{1}{5} \div 1 \frac{2}{5}-\frac{2}{7}$

Option 1: $-\frac{4}{21}$

Option 2: $\frac{5}{21}$

Option 3: $\frac{4}{21}$

Option 4: $-\frac{5}{21}$

Question : If $3\sqrt{\frac{1-a}{a}}+9=19-3\sqrt{\frac{a}{1-a}};$ then, what is the value of $a?$

Option 1: $\frac{3}{10}$ and $\frac{7}{10}$

Option 2: $\frac{1}{10}$ and $\frac{9}{10}$

Option 3: $\frac{2}{5}$ and $\frac{3}{5}$

Option 4: $\frac{1}{5}$ and $\frac{4}{5}$

Question : What is the value of $6-(6\div 2-3+7-2) \times[\{3-2 \div 2\} \times 5-6]?$

Option 1: – 4

Option 2: – 14

Option 3: – 12

Option 4: – 16