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

Option 1: 1

Option 2: 3

Option 3: - 1

Option 4: 0

Question : If $a+b+c=0$, then the value of $\frac{a^{2}+b^{2}+c^{2}}{ab+bc+ca}$ is:

Option 1: 2

Option 2: –2

Option 3: 0

Option 4: 4

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

Option 1: 3

Option 2: 2

Option 3: 0

Option 4: 1

Question : If for a non-zero $x$, $3x^{2}+5x+3=0,$ then the value of $x^{3}+\frac{1}{x^{3}}$ is:

Option 1: $\frac{10}{27}$

Option 2: $-\frac{10}{27}$

Option 3: $\frac{2}{3}$

Option 4: $-\frac{2}{3}$

Question : If $(a^2 = b + c)$, $(b^2 = a + c)$, $(c^2 = b + a)$. Then, what will be the value of $(\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1})$?

Option 1: –1

Option 2: 2

Option 3: 1

Option 4: 0