Question : If $\frac{a}{b}+\frac{b}{a}=1$ and $a+b=2$, then the value of $a^3+b^3$ is:

Option 1: 0

Option 2: 3

Option 3: 1

Option 4: 2

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

Option 1: $0$

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

Option 3: $1$

Option 4: $–1$

Question : If $\frac{2+a}{a}+\frac{2+b}{b}+\frac{2+c}{c}=4$, then the value of $\frac{ab+bc+ca}{abc}$ is:

Option 1: $2$

Option 2: $1$

Option 3: $0$

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

Question : If $a+\frac{1}{a}=1$, then the value of $\frac{a^2-a+1}{a^2+a+1}$ is $(a\neq 0)$:

Option 1: 1

Option 2: –1

Option 3: 0

Option 4: 2

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

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: 3

Question : If $x+y+z=0$, then what is the value of $\frac{x^2}{yz}+\frac{y^2}{xz}+\frac{z^2}{xy}$?

Option 1: $0$

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

Option 3: $1$

Option 4: $3$