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 : 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

Question : If $a + b + c = 12$ and $ab + bc + ca = 22$, then what is the value of $a^3 + b^3 + c^3 - 3abc ?$

Option 1: 1052

Option 2: 936

Option 3: 924

Option 4: 876

Question : If $a+b+c=0$ and $a^2+b^2+c^2=40$, then what is the value of $a b+b c+c a$?

Option 1: –30

Option 2: –20

Option 3: –25

Option 4: –40