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

Option 1: 0

Option 2: 1

Option 3: –1

Option 4: 2

Question : If $a+b+c$ = 6 and $ab+bc+ca$ = 11, then the value of $bc(b+c)+ca(c+a)+ab(a+b)+3abc$ is:

Option 1: 33

Option 2: 66

Option 3: 55

Option 4: 23

Question : What is the value of ${a}^3+{b}^3+{c}^3$ if $(a+b+c)=0$?

Option 1: $a^2+b^2+c^2-3abc$

Option 2: $0$

Option 3: $3abc$

Option 4: $a^2+b^2+c^2-ab-bc-ca$

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 $\frac{x-a^{2}}{b+c}+\frac{x-b^{2}}{c+a}+\frac{x-c^{2}}{a+b} = 4(a+b+c)$, then $x$ is equal to:

Option 1: $(a+b+c)^{2}$

Option 2: $a^{2}+b^{2}+c^{2}$

Option 3: $ab+bc+ca$

Option 4: $a^{2}+b^{2}+c^{2}-ab-bc-ca$