Question : If cos A = $\frac{5}{13}$, then what is the value of (tan A + cot A)?

Option 1: $\frac{60}{169}$

Option 2: $\frac{109}{169}$

Option 3: $\frac{169}{60}$

Option 4: $\frac{169}{109}$

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 $3x+\frac{1}{5x}=7$, then what is the value of $\frac{5x}{(15x^{2}+15x+1)}?$

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

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

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

Option 4: $10$

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 $3 \operatorname{cosec} A=7$, then what is the value of $\cos A \tan A$?

Option 1: $\frac{2 \sqrt{10}}{7}$

Option 2: $\frac{3}{7}$

Option 3: $\frac{4}{7}$

Option 4: $\frac{\sqrt{10}}{7}$