Question : Solve the following:
$(a + b + c) (ab + bc + ca) - abc = ?$

Option 1: $(a + b) (b + c) ( c - a)$

Option 2: $(a + b) (b - c) (c + a)$

Option 3: $(a + b) (b + c) (c + a)$

Option 4: $(a - b) (b - c) (c - a)$

Question : If $a+b+c=1, ab+bc+ca=-1$ and $abc=-1$, then the value of $a^{3}+b^{3}+c^{3}$ is:

Option 1: 1

Option 2: – 1

Option 3: 2

Option 4: – 2

Question : In $\triangle ABC, \angle A+\angle B=145^{\circ}$ and $\angle C+2\angle B=180^{\circ}$. State which one of the following relations is true.

Option 1: CA = AB

Option 2: CA < AB

Option 3: BC > AB

Option 4: CA > AB

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 $a+b+c=0$, 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 $a, b, c$ are all non-zero and $a+b+c=0$, then find the value of $\frac{a^2}{b c}+\frac{b^2}{c a}+\frac{c^2}{ab}$.

Option 1: $3$

Option 2: $4$

Option 3: $1$

Option 4: $\frac{1}{2}$