Question : If $xy+yz+zx=0$, then $(\frac{1}{x^2–yz}+\frac{1}{y^2–zx}+\frac{1}{z^2–xy})$$(x,y,z \neq 0)$ is equal to:

Option 1: $3$

Option 2: $1$

Option 3: $x+y+z$

Option 4: $0$

Question : If $\frac{xy}{x+y}=a$, $\frac{xz}{x+z}=b$ and $\frac{yz}{y+z}=c$, where $a,b,c$ are all non-zero numbers, $x$ equals to:

Option 1: $\frac{2abc}{ab+bc–ac}$

Option 2: $\frac{2abc}{ab+ac–bc}$

Option 3: $\frac{2abc}{ac+bc–ab}$

Option 4: $\frac{2abc}{ab+bc+ac}$

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 $\small x+y+z=6$ and $xy+yz+zx=10$, then the value of $x^{3}+y^{3}+z^{3}-3xyz$ is:

Option 1: 36

Option 2: 48

Option 3: 42

Option 4: 40

Question : If $x, y,$ and $z$ are three sums of money such that y is the simple interest on $x$ and $z$ is the simple interest on $y$ for the same time and at the same rate of interest, then we have:

Option 1: $z^{2}=xy$

Option 2: $xyz=1$

Option 3: $x^{2}=yz$

Option 4: $y^{2}=zx$