Question : If $x+y+z=0$ and $x^2+y^2+z^2=40$, then what is the value of $x y+y z+z x?$

Option 1: –20

Option 2: 5

Option 3: –5

Option 4: –10

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 $\frac{(x+y)}{z}=2$, 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: $–1$

Question : If $\frac{1}{x+\frac{1}{y+\frac{2}{z+\frac{1}{4}}}}=\frac{29}{79}$, where x, y, and z are natural numbers, then the value of $(2 x+3 y-z)$ is:

Option 1: 0

Option 2: 4

Option 3: 1

Option 4: 2

Question : Let $x, y, z$ be fractions such that $x<y<z$. If $z$ is divided by $x$, the result is $\frac{5}{2}$, which exceeds $y$ by $\frac{7}{4}$. If $x+y+z=1 \frac{11}{12}$, then the ratio of $(z-x):(y-x)$ is:

Option 1: 6 : 5

Option 2: 9 : 5

Option 3: 5 : 6

Option 4: 5 : 9