Question : If $x$% of $y$% of 80 is the same as 25% of 900, then the value of $xy$ is:

Option 1: 30100

Option 2: 32500

Option 3: 28125

Option 4: 34200

Question : If $2 x+5 y=15$ and $x y=6$, then the value of $4 x^2+25 y^2$ is:

Option 1: 105

Option 2: 95

Option 3: 100

Option 4: 90

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 : If $x^3=270+y^3$ and $x=(6+y)$, then what is the value of $(x+y)? $(given that $x>0$ and $y>0$)

Option 1: $2 \sqrt{3}$

Option 2: $\sqrt{3}$

Option 3: $4 \sqrt{3}$

Option 4: $4 \sqrt{2}$

Question : If $\tan (x + y)=1$ and $\cos (x-y)={\frac{\sqrt3}{2}}$, then what is the value of $x$ and $y$?

Option 1: $x = 3^\circ, y = 4.5^\circ$

Option 2: $x = 37.5^\circ, y = 7.5^\circ$

Option 3: $x = 7.5^\circ, y = 37.5^\circ$

Option 4: $x = 4.5^\circ, y = 3^\circ$

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

Option 1: 24

Option 2: 4

Option 3: 16

Option 4: 8