Question : If the six-digit number 5x2y6z is divisible by 7, 11 and 13, then the value of $(x-y+3 z)$ is:

Option 1: 7

Option 2: 4

Option 3: 0

Option 4: 9

Question : If a nine-digit number 785$x$3678$y$ is divisible by 72, then the value of ($x$ + $y$) is:

Option 1: 20

Option 2: 12

Option 3: 10

Option 4: 5

Question : If the six-digit number 479xyz is exactly divisible by 7, 11, and 13, then {(y + z) ÷ x} is equal to:

Option 1: $4$

Option 2: $\frac{11}{9}$

Option 3: $\frac{7}{13}$

Option 4: $\frac{13}{7}$

Question : If $x^4+x^2 y^2+y^4=133$ and $x^2-x y+y^2=7$, then what is the value of $xy$?

Option 1: 8

Option 2: 12

Option 3: 4

Option 4: 6

Question : If the 9-digit number $72 x 8431y 4$ is divisible by 36, what is the value of $(\frac{x}{y}-\frac{y}{x})$ for the smallest possible value of $y$, given that $x$ and $y$ are natural numbers?

Option 1: $1 \frac{5}{7}$

Option 2: $2 \frac{1}{10}$

Option 3: $1 \frac{2}{5}$

Option 4: $2 \frac{9}{10}$