Question : If a + b + c = 1, ab + bc + ca = –1, and abc = –1, then what is the value of a³ + b³ + c³?

Option 1: 1

Option 2: 5

Option 3: 3

Option 4: 2

Question : If a + b + c = 0, then the value of (a + b – c)² + ( b + c – a)² + ( c + a – b)² is:

Option 1: 0

Option 2: 8abc

Option 3: 4(a² + b² + c²)

Option 4: 4(ab + bc + ca)

Question : If $a+b+c=5$ and $a^2+b^2+c^2=15$, then find the value of $a^3+b^3+c^3-3 a b c-27$.

Option 1: 23

Option 2: 27

Option 3: 25

Option 4: 21

Question : If p + q = 7 and p² + q² = 25, then find the value of pq.

Option 1: 24

Option 2: 12

Option 3: 18

Option 4: 36

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

Option 1: 1

Option 2: 2

Option 3: 3

Option 4: 0