Question : If $\left(x-\frac{1}{x}\right)=10$, what is the value of $\left(x^4+\frac{1}{x^4}\right)?$

Option 1: 10404

Option 2: 10402

Option 3: 10406

Option 4: 10400

Question : If $\frac{x}{2}-\frac{\left [4\left (\frac{15}{2}-\frac{x}{3} \right ) \right ]}{3} = –\frac{x}{18}$ then what is the value of $x$?

Option 1: –$10$

Option 2: $\frac{9}{8}$

Option 3: $10$

Option 4: $–\frac{9}{8}$

Question : If $\left(x+\frac{1}{x}\right)=10$, what is the value of $\left(x^4+\frac{1}{x^4}\right)?$

Option 1: 9604

Option 2: 9602

Option 3: 9600

Option 4: 9606

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

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 $2x+\frac{1}{2x}=2,$ 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