Question : If $5 x-\frac{5}{x}+6=0$, then $x^2+\frac{1}{x^2}$ is:

Option 1: $\frac{86}{25}$

Option 2: $\frac{43}{12}$

Option 3: $\frac{81}{10}$

Option 4: $\frac{86}{11}$

Question : If $x-\frac{1}{x}=5, x \neq 0$, then what is the value of $\frac{x^6+3 x^3-1}{x^6-8 x^3-1} ?$

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

Option 2: $\frac{13}{12}$

Option 3: $\frac{4}{9}$

Option 4: $\frac{11}{13}$

Question : If $2 x^2-7 x+5=0$, then what is the value of $x^2+\frac{25}{4 x^2} ?$

Option 1: $5 \frac{1}{2}$

Option 2: $7 \frac{1}{4}$

Option 3: $9 \frac{1}{2}$

Option 4: $9 \frac{3}{4}$

Question : If $x^2-5 x+1=0$, then the value of $\frac{x^6+x^4+x^2+1}{5 x^3}=?$

Option 1: 30

Option 2: 25

Option 3: 23

Option 4: 28

Question : If $x+\frac{1}{x}=6$, then find the value of $\frac{3 x}{2 x^2-5 x+2}$.

Option 1: $1$

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

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

Option 4: $0$

Question : If $\cos x+\sec x=\frac{7}{2 \sqrt{3}}$, then the value of $\cos ^2 x+\sec ^2 x$ will be_____.

Option 1: $\frac{15}{12}$

Option 2: $\frac{10}{12}$

Option 3: $\frac{25}{10}$

Option 4: $\frac{25}{12}$