Question : If $405:y::y:125$ and $y>0$, then find the value of $y$.

Option 1: 225

Option 2: 205

Option 3: 215

Option 4: 235

Question : If $x^2+y^2=29$ and $xy=10$, where $x>0,y>0$ and $x>y$. Then the value of $\frac{x+y}{x-y}$ is:

Option 1: $- \frac{7}{3}$

Option 2: $\frac{7}{3}$

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

Option 4: $-\frac{3}{7}$

Question : If $x^2+4y^2=17$ and $xy = 2$, where $x > 0, y > 0$, then what is the value of $x^3+8y^3$?

Option 1: 95

Option 2: 85

Option 3: 65

Option 4: 76

Question : If $x=(0.25)^\frac{1}{2}$, $y=(0.4)^{2}$, and $z=(0.216)^{\frac{1}{3}}$, then:

Option 1: $y>x>z$

Option 2: $x>y>z$

Option 3: $z>x>y$

Option 4: $x>z>y$

Question : If $x^{2}+y^{2}+2x+1=0$, then the value of $x^{31}+y^{35}$ is:

Option 1: –1

Option 2: 0

Option 3: 1

Option 4: 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