Question : If $x+\left [\frac{1}{(4x)} \right]=\frac{5}{2}$; then, what is the value of $\frac{64x^{6}+1}{8x^{3}} \;?$

Option 1: 110

Option 2: 115

Option 3: 125

Option 4: 140

Question : If $a+\frac{1}{a}=5$, then determine the value of $a^3+\frac{1}{a^3}$.

Option 1: 90

Option 2: 125

Option 3: 105

Option 4: 110

Question : If $x+\frac{1}{x}=3$, then the value of $\frac{3x^{2}-4x+3}{x^{2}-x+1}$ is:

Option 1: $\frac{4}{3}$

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

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

Option 4: $\frac{5}{3}$

Question : If $\sec \beta+\tan \beta=2$, then what is the value of $\cot \beta$?

Option 1: $\frac{5}{3}$

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

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

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

Question : If $\tan \theta=\frac{8}{15}$, then the value of $\sqrt{\frac{1-\sin \theta}{1+\sin \theta}}$ is:

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

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

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

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