Question : If $x^{2}+\frac{1}{x^{2}}=1$, then, what is the value of $x^{48}+x^{42}+x^{36}+x^{30}+x^{24}+x^{18}+x^{12}+x^{6}+1$?

Option 1: – 9

Option 2: 0

Option 3: 1

Option 4: 9

Question : If ${x^2+y^2+z^2=2(x+z-1)}$, then the value of $x^3+y^3+z^3$ is equal to:

Option 1: 6

Option 2: 1

Option 3: 2

Option 4: 8

Question : Which of the following expressions is equal to the expression $\frac{x^2-3 x+2}{x^2-4}$?

Option 1: $\frac{x+1}{x-2}$

Option 2: $\frac{x-1}{x+2}$

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

Option 4: $\frac{x-1}{x-2}$

Question :  If $x^2+\frac{1}{x^2}=7$, then what is the value of $x^3+\frac{1}{x^3}$?

Option 1: 9

Option 2: 18

Option 3: 27

Option 4: 36

Question : If $x+\frac{1}{x}=\sqrt{3}$ then, the value of $x^{30}+x^{24}+x^{18}+x^{12}+x^{6}+1$ is:

Option 1: $\sqrt{3}$

Option 2: $-\sqrt{3}$

Option 3: $1$

Option 4: $0$