Question : If $x=y+z$, then $x^{3}-y^{3}-z^{3}$ is:

Option 1: $0$

Option 2: $3xyz$

Option 3: $-3xyz$

Option 4: $1$

Question : If $x+y+z=0$, then what is the value of $\frac{x^2}{(y z)}+\frac{y^2}{(x z)}+\frac{z^2}{(x y)}$?

Option 1: 1

Option 2: 0

Option 3: 2

Option 4: 3

Question : If $x=y=333$ and $z=334$, the value of $x^3+y^3+z^3-3xyz$ is:

Option 1: $0$

Option 2: $667$

Option 3: $1000$

Option 4: $2334$

Question : $\text { If } x^2+y^2+z^2=x y+y z+z x \text { and } x=1 \text {, then find the value of } \frac{10 x^4+5 y^4+7 z^4}{13 x^2 y^2+6 y^2 z^2+3 z^2 x^2}$.

Option 1: 2

Option 2: 0

Option 3: –1

Option 4: 1

Question : If $x$,$y$ and $z$ are real numbers such that $(x-3)^2+(y-4)^2+(z-5)^2=0$, then $(x+y+z)$ is equal to:

Option 1: –12

Option 2: 0

Option 3: 8

Option 4: 12

Question : If $\frac{(x+y)}{z}=2$, then what is the value of $[\frac{y}{(y-z)}+\frac{x}{(x-z)}]?$

Option 1: $0$

Option 2: $1$

Option 3: $2$

Option 4: $–1$