Question : If $a+\frac{1}{b}=b+\frac{1}{c}=c+\frac{1}{a}$ where $a \neq b\neq c\neq 0$, then the value of $a^{2}b^{2}c^{2}$ is:

Option 1: –1

Option 2: abc

Option 3: 0

Option 4: 1

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 $x+\frac{1}{x}=c+\frac{1}{c}$, then the value of $x$ is:

Option 1: $c,\frac{1}{c}$

Option 2: $c,c^{2}$

Option 3: $c,2c$

Option 4: $0, 1$

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

Option 1: 1

Option 2: 2

Option 3: 3

Option 4: 4

Question : If $\frac{a^2+b^2}{c^2}=\frac{b^2+c^2}{a^2}=\frac{c^2+a^2}{b^2}=\frac{1}{k}$, $(k\neq 0)$, then $k$=?

Option 1: $2$

Option 2: $1$

Option 3: $0$

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