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 $a^2+b^2+c^2=14$ and $a+b+c=6$, then the value of $(ab+bc+ca)$ is:

Option 1: 11

Option 2: 12

Option 3: 13

Option 4: 14

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 $a+b+c=7$ and $a^3+b^3+c^3-3abc=175$, then what is the value of $(a b+b c+c a)$?

Option 1: 8

Option 2: 9

Option 3: 7

Option 4: 6

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: $\frac{1}{2}$