Question : If $a+b-c=20$ and $a^2+b^2+c^2=152$, find the value of $a^3+b^3-c^3+3abc$.

Option 1: 480

Option 2: 720

Option 3: 640

Option 4: 560

Question : If $a+b+c=5, a^3+b^3+c^3=85$, and $abc=25$, then find the value of $a^2+b^2+c^2-a b- bc - ca$.

Option 1: 2

Option 2: 4

Option 3: 6

Option 4: 8

Question : If $(a^3+b^3+c^3-3 a b c)=405$ and $(a-b)^2+(b-c)^2+(c-a)^2=54$, find the value of $(a + b + c)$.

Option 1: 15

Option 2: 45

Option 3: 9

Option 4: 27

Question : If $a, b, c$ are real numbers and $a^{2}+b^{2}+c^{2}=2(a-b-c)-3,$ then the value of $a+b+c$ is:

Option 1: –1

Option 2: 1

Option 3: 3

Option 4: 0

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