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 : 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 $x : y$ is the ratio of two whole numbers and $z$ is their HCF, then the LCM of those two numbers is:

Option 1: $yz$

Option 2: $\frac{xz}{y}$

Option 3: $\frac{xy}{z}$

Option 4: $xyz$

Question : x, y, and z are 3 values, such that x + y = 12, y + z = 17 and z + x = 19. What is the average of x, y, and z?

Option 1: 10

Option 2: 8

Option 3: 6

Option 4: 4

Question : If $x+y+z=13$ and $x^2+y^2+z^2=69$, then $xy+z(x+y)$ is equal to:

Option 1: 70

Option 2: 40

Option 3: 50

Option 4: 60