Question : If $x = 32.5$, $y = 34.6$ and $z = 30.9$, then the value of $x^3+y^3+z^3-3xyz$ is $0.98k$, where $k$ is equal to:
 

Option 1: 1033

Option 2: 933

Option 3: 1026

Option 4: 921

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 : The value of $\frac{(x-y)^3+(y-z)^3+(z-x)^3}{6(x-y)(y-z)(z-x)}$, where $x \neq y \neq z$, is equal to:

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

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

Option 3: $\frac{1}{3}$

Option 4: $\frac{1}{9}$

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 : What is the simplified value of $\frac{(x+y+z)(x y+y z+z x)–x y z}{(x+y)(y+z)(z+x)}$?

Option 1: $y$

Option 2: $z$

Option 3: $1$

Option 4: $x$

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