Question : If $\frac{x}{y}+\frac{y}{x}=1$ and $x+y=2$, then the value of $x^3+y^3$ is:

Option 1: 1

Option 2: 3

Option 3: 0

Option 4: 2

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

Option 1: 2

Option 2: 0

Option 3: 1

Option 4: 3

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

Option 1: 2

Option 2: 4

Option 3: 8

Option 4: 16

Question : $\left(4 x^3 y-6 x^2 y^2+4 x y^3-y^4\right)$ can be expressed as:

Option 1: $(x+y)^4-x^4$

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

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

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