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 : 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

Question : Directions: W, X, Y, and Z are four friends. W is shorter than X but taller than Y, who is shorter than Z. Who is the shortest among all?

Option 1: W

Option 2: X

Option 3: Y

Option 4: Z

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 : Directions: The information given below represents the number codes for the given letters. Select the combination of numbers so that the letters arranged accordingly will form a meaningful word.
R = 1, E = 2, A = 3, C = 4, T = 5, I = 6, V = 7, E = 8

Option 1: 4, 1, 2, 3, 5, 8, 7, 6

Option 2: 4, 1, 2, 3, 5, 6, 7, 8

Option 3: 7, 2, 1, 3, 8, 4, 5, 6

Option 4: 4, 3, 1, 5, 6, 7, 8, 2