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 : 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 $x(x+y+z)=20$, $y(x+y+z)=30$, and $z(x+y+z)=50$, then the value of $2(x+y+z)$ is:

Option 1: 20

Option 2: –10

Option 3: 15

Option 4: 18

Question : Rs. 13000 is divided among X, Y, and Z such that 2 times X's share is equal to 3 times Y's share which is equal to 4 times Z's share. What is the share of Y?

Option 1: Rs. 3200

Option 2: Rs. 4800

Option 3: Rs. 5600

Option 4: Rs. 4000

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