Question : If $p=3+\frac{1}{p}$, then the value of $(p^4+\frac{1}{p^4})$ is:

Option 1: 81

Option 2: 27

Option 3: 120

Option 4: 119

Question : If $x\left(3-\frac{2}{x}\right)=\frac{3}{x}$, then the value of $x^3-\frac{1}{x^3}$ is equal to:

Option 1: $\frac{8}{27}$

Option 2: $\frac{61}{27}$

Option 3: $\frac{62}{27}$

Option 4: $\frac{52}{27}$

Question : If $2x-\frac{1}{2x}=5,x\neq0$, then the value of $(x^2+\frac{1}{16x^2}-2)$is:

Option 1: $\frac{19}{4}$

Option 2: $\frac{23}{4}$

Option 3: $\frac{27}{4}$

Option 4: $\frac{31}{4}$

Question : If $\cot B=9 $, then what will be the value of $\sec ^2 B$?

Option 1: $\frac{98}{81}$

Option 2: $\frac{92}{81}$

Option 3: $\frac{42}{81}$

Option 4: $\frac{82}{81}$

Question : If $x^{4}+\frac{1}{x^{4}}=119$, then the value of $x-\frac{1}{x}$ is:

Option 1: 6

Option 2: 12

Option 3: 11

Option 4: 3

Question : If $x=2+\sqrt3$, then the value of $\frac{x^{2}-x+1}{x^{2}+x+1}$ is:

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

Option 2: $\frac{3}{4}$

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

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