Question : If $x=12$ and $y=4$, then the value of $(x+y)^{\frac{x}{y}}$ is:

Option 1: 48

Option 2: 1792

Option 3: 4096

Option 4: 570

Question : If $x=a^{\frac{1}{2}}+a^{-\frac{1}{2}}$, $y=a^{\frac{1}{2}}- a^{-\frac{1}{2}}$, then the value of $(x^{4}-x^{2}y^{2}-1)+(y^{4}-x^{2}y^{2}+1)$ is:

Option 1: 16

Option 2: 13

Option 3: 12

Option 4: 14

Question : If $x^4+y^4+x^2 y^2=17 \frac{1}{16}$ and $x^2-x y+y^2=5 \frac{1}{4}$, then one of the values of $(x-y)$ is:

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

Option 2: $\frac{3}{4}$

Option 3: $\frac{5}{4}$

Option 4: $\frac{3}{2}$

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 $\frac{1}{x+\frac{1}{y+\frac{2}{z+\frac{1}{4}}}}=\frac{29}{79}$, 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 : If $2 x-y=2$ and $x y=\frac{3}{2}$, then what is the value of $x^3-\frac{y^3}{8}?$

Option 1: $\frac{9}{2}$

Option 2: $-\frac{5}{4}$

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

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