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

Option 1: 1

Option 2: 3

Option 3: 4

Option 4: 2

Question : If $x+\frac{1}{x}=0$, then the value of $x^{5}+\frac{1}{x^{5}}$ is:

Option 1: 2

Option 2:  –1

Option 3: 1

Option 4: 0

Question : If $x^4+\frac{1}{x^4}=194, x>0$, then find the value of $x^3+\frac{1}{x^3}+x+\frac{1}{x}$

Option 1: 76

Option 2: 66

Option 3: 56

Option 4: 46

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

Option 1: $\frac{4}{3}$

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

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

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

Question : If $x+\frac{1}{x}=2$, then find the value of $x^{1823}+\frac{1}{x^{1929}}$.

Option 1: 2

Option 2: 1

Option 3: 0

Option 4: –1