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 $a+b+c = 0$, then the value of $\small \frac{1}{(a+b)(b+c)}+\frac{1}{(b+c)(c+a)}+\frac{1}{(c+a)(a+b)}$ is:

Option 1: 0

Option 2: 1

Option 3: 3

Option 4: 2

Question : If $a+b=2c$, then the value of $\frac{a}{a–c}+\frac{c}{b–c}$ is equal to (where $a\neq b\neq c$):

Option 1: $–1$

Option 2: $1$

Option 3: $0$

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

Question : If $a$ and $b$ are rational numbers and $(a-1)\sqrt2+3=b\sqrt2+a$; then the value of $(a+b)$ is:

Option 1: $–5$

Option 2: $3$

Option 3: $–3$

Option 4: $5$

Question : If $(a+\frac{1}{a})=–2$, then the value of $a^{1000}+a^{–1000}$ is:

Option 1: $2$

Option 2: $0$

Option 3: $1$

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