Question : The numerical value of $\frac{(a–b)^{2}}{(b–c)(c–a)}+\frac{(b–c)^{2}}{(c–a)(a–b)}+\frac{(c–a)^{2}}{(a–b)(b–c)}$ is: $(a\neq b\neq c)$

Option 1: $0$

Option 2: $1$

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

Option 4: $3$

Question : If $x=\frac{8ab}{a+b}(a\neq b),$ then the value of $\frac{x+4a}{x–4a}+\frac{x+4b}{x–4b}$ is:

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: 4

Question : If $a+b=2c$, then find $\frac{a}{a–c}+\frac{c}{b–c}$:

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: –1

Question : If $\frac{x}{(b–c)(b+c–2a)}=\frac{y}{(c–a)(c+a–2b)}=\frac{z}{(a–b)(a+b–2c)}$, then $(x+y+z)$ is:

Option 1: $a+b+c$

Option 2: $0$

Option 3: $a^2+b^2+c^2$

Option 4: $2$

Question : If $\left (2a-3 \right )^{2}+\left (3b+4 \right )^{2}+\left ( 6c+1\right)^{2}=0$, then the value of $\frac{a^{3}+b^{3}+c^{3}-3abc}{a^{2}+b^{2}+c^{2}}+3$ is:

Option 1: $abc+3$

Option 2: $6$

Option 3: $0$

Option 4: $3$