Question : Simplify the given expression. $\frac{x^3+y^3+z^3-3 x y z}{(x-y)^2+(y-z)^2+(z-x)^2}$

Option 1: $\frac{1}{3}(x+y+z)$

Option 2: $(x+y+z)$

Option 3: $\frac{1}{4}(x+y+z)$

Option 4: $\frac{1}{2}(x+y+z)$

Question : If $\small x=a\left (b-c \right),\; y=b\left (c-a \right) ,\; z=c\left (a-b \right)$, then the value of $\left (\frac{x}{a} \right)^{3}+\left (\frac{y}{b} \right)^{3}+\left (\frac{z}{c} \right)^{3}$ is:

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

Option 2: $\frac{xyz}{abc}$

Option 3: $0$

Option 4: $\frac{3xyz}{abc}$

Question : If $6^{x}=3^{y}=2^{z}$, then what is the value of $\frac{1}{y}+\frac{1}{z}-\frac{1}{x}$?

Option 1: 1

Option 2: 0

Option 3: 3

Option 4: 6

Question : If $x: y: z=3: 4: 5$, then what will be the ratio of $\left(\frac{x}{y}\right):\left(\frac{y}{z}\right):\left(\frac{z}{x}\right)$?

Option 1: 49 : 37 : 100

Option 2: 45 : 48 : 100

Option 3: 41 : 37 : 100

Option 4: 37 : 47 : 100

Question : If $x$ = $y$ = $z$, then $\frac{\left (x+y+z \right )^{2}}{x^{2}+y^{2}+z^{2}}$ is equal to:

Option 1: 4

Option 2: 2

Option 3: 3

Option 4: 1