Question : If $a(x+y)=b(x-y)=2ab$, then the value of $2(x^2+y^2)$ is:

Option 1: $2(a^2-b^2)$

Option 2: $2(a^2+b^2)$

Option 3: $4(a^2-b^2)$

Option 4: $4(a^2+b^2)$

Question : If $(x+y)^3+8(x-y)^3=(3 x+A y)\left(3 x^2+B x y+C y^2\right)$, then the value of (A + B + C) is:

Option 1: 0

Option 2: 4

Option 3: 2

Option 4: 3

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

Option 1: 4

Option 2: 8

Option 3: 16

Option 4: 64

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 $x=\sqrt[3]{28}, y=\sqrt[3]{27}$, then the value of $x+y-\frac{1}{x^{2}+xy+y^{2}}$ is:

Option 1: 8

Option 2: 7

Option 3: 6

Option 4: 5

Question : If $x^2- 2xy = 84$ and $x-y=-10$, then the value of $y$ is:

Option 1: 2

Option 2: 1

Option 3: 4

Option 4: 3