Question : If $\frac{x}{2}-\frac{\left [4\left (\frac{15}{2}-\frac{x}{3} \right ) \right ]}{3} = –\frac{x}{18}$ then what is the value of $x$?

Option 1: –$10$

Option 2: $\frac{9}{8}$

Option 3: $10$

Option 4: $–\frac{9}{8}$

Question : The value of $5–\frac{8+2\sqrt{15}}{4}–\frac{1}{8+2\sqrt{15}}$ is equal to:

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

Option 2: $1$

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

Option 4: $\frac{1}{2}$

Question : Which of the following is TRUE?
I. $\frac{1}{\sqrt[3]{12}}>\frac{1}{\sqrt[4]{29}}>\frac{1}{\sqrt5}$
II. $\frac{1}{\sqrt[4]{29}}>\frac{1}{\sqrt[3]{12}}>\frac{1}{\sqrt5}$
III. $\frac{1}{\sqrt5}>\frac{1}{\sqrt[3]{12}}>\frac{1}{\sqrt[4]{29}}$
IV. $\frac{1}{\sqrt5}>\frac{1}{\sqrt[4]{29}}>\frac{1}{\sqrt[3]{12}}$

Option 1: Only I

Option 2: Only II

Option 3: Only III

Option 4: Only IV

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 : If $x+\left [\frac{1}{(x+7)}\right]=0$, what is the value of $x-\left [\frac{1}{(x+7)}\right]$?

Option 1: $3\sqrt{5}$

Option 2: $3\sqrt{5}-7$

Option 3: $3\sqrt{5}+7$

Option 4: $8$