Question : If $4 x^2+y^2=40$ and $x y=6$, find the positive value of $2 x+y$.

Option 1: 8

Option 2: 6

Option 3: 5

Option 4: 4

Question : If $x+ \sqrt{5} = 5+\sqrt{y}$ are positive integers, then the value of $\frac{\sqrt{x}+y}{x+ \sqrt{y}}$ is:

Option 1: 1

Option 2: 2

Option 3: $\sqrt{5}$

Option 4: 5

Question : If $x=\frac{\sqrt{5}+1}{\sqrt{5}-1}$ and $y=\frac{\sqrt{5}-1}{\sqrt{5}+1}$, then the value of $\frac{x^{2}+xy+y^{2}}{x^{2}-xy+y^{2}}$ is:

Option 1: $\frac{3}{4}$

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

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

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

Question : The third proportional of the following numbers $(x-y)^2, (x^2-y^2)^2$ is:

Option 1: $(x+y)^3(x-y)^2$

Option 2: $(x+y)^4(x-y)^2$

Option 3: $(x+y)^2(x-y)^2$

Option 4: $(x+y)^2(x-y)^3$

Question : X is directly proportional to the square of Y. When X is 12, then Y is 2. Find the value of X when Y is 3.

Option 1: 30

Option 2: 9

Option 3: 27

Option 4: 18