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 : $a, b, c$ are the lengths of three sides of a triangle ABC. If $a, b, c$ are related by the relation $a^{2}+b^{2}+c^{2}=ab+bc+ca$, then the value of $\sin^{2}A+\sin^{2}B+\sin^{2}C$ is:

Option 1: $\frac{3}{2}$

Option 2: $\frac{3\sqrt3}{2}$

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

Option 4: $\frac{9}{4}$

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

Option 1: $0$

Option 2: $–1$

Option 3: $1$

Option 4: $ab$

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 $a+\frac{1}{b}=b+\frac{1}{c}=c+\frac{1}{a}$ 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