Question : If $a+\frac{1}{a}=2$ and $b+\frac{1}{b}=-2$, then what is the value of $a^2+\frac{1}{a^2}+b^2+\frac{1}{b^2} ?$

Option 1: 0

Option 2: 2

Option 3: 8

Option 4: 4

Question : If $a^2+\frac{1}{a^2}=\frac{7}{3}$, then what is the value of $\left(a^3-\frac{1}{a^3}\right)?$

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

Option 2: $\frac{10}{3 \sqrt{3}}$

Option 3: $\frac{7}{3 \sqrt{3}}$

Option 4: $\frac{8}{3 \sqrt{3}}$

Question : If $\sec A=\frac{17}{15}$, then what is the value of $\cot A$?

Option 1: $\frac{15}{21}$

Option 2: $\frac{15}{7}$

Option 3: $\frac{8}{15}$

Option 4: $\frac{15}{8}$

Question : Find the value of the given expression:
$\frac{(4\frac{1}{3}+3\frac{1}{3}\times 1\frac{4}{5}\div 3\frac{3}{4}\times (1\frac{1}{2}+1\frac{1}{3}))}{(\frac{2}{3}\div \frac{5}{6}\times \frac{2}{3})}$

Option 1: $11 \frac{3}{8}$

Option 2: $10\frac{1}{8}$

Option 3: $14\frac{3}{8}$

Option 4: $16\frac{5}{8}$

Question : If $2 x+\frac{2}{x}=5$, then the value of $\left(x^3+\frac{1}{x^3}+2\right)$ will be:

Option 1: $\frac{81}{11}$

Option 2: $\frac{81}{7}$

Option 3: $\frac{71}{8}$

Option 4: $\frac{81}{8}$