Question : If $\left (x+\frac{1}{x} \right)=5$, what is the value of $\left (x^{5}+\frac{1}{x^{5}} \right)$?

Option 1: 1875

Option 2: 2525

Option 3: 2530

Option 4: 3120

Question : If $x^{2} -3x +1=0$, then the value of $\frac{\left(x^4+\frac{1}{x^2}\right)}{\left(x^2+5 x+1\right)}$ is:

Option 1: $\frac{9}{4}$

Option 2: $\frac{27}{8}$

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

Option 4: $2$

Question : If $\frac{5}{2}-\left (\frac{6}{5}\right )\left (x-\frac{15}{2} \right)=\frac{-x}{5}$, then what is the value of $x$?

Option 1: $-\frac{23}{2}$

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

Option 3: $-\frac{13}{2}$

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

Question : If $2x+\frac{1}{2x}=2,$ what is the value of $\sqrt{2\left (\frac{1}{x}\right)^{4}+\left (\frac{1}{x}\right)^{5}}\; ?$

Option 1: 1

Option 2: 2

Option 3: 4

Option 4: 8

Question : If $x+\left [\frac{1}{(x+7)}\right]=0$, what is the value of $x-\left [\frac{1}{(x+7)}\right]$?

Option 1: $3\sqrt{5}$

Option 2: $3\sqrt{5}-7$

Option 3: $3\sqrt{5}+7$

Option 4: $8$

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

Option 1: $\left(1-a^4\right)^\frac{1}{4}$

Option 2: $a$

Option 3: $\left(a^4-1\right)^\frac{1}{4}$

Option 4: $\left(a^4+1\right)^\frac{1}{4}$