Question : Expand and simplify $(x+4)^2+(x-2)^2$.

Option 1: $2(x^2+2x+10)$

Option 2: $2(x^2+2x-10)$

Option 3: $2(x^2-2x+10)$

Option 4: $2(x^2-2x-10)$

Question : If $3x–3<3+\frac{x}{2}$ and $x–2\leq 6+2x$, then $x$ can take which of the following values?

Option 1: 6

Option 2: 2

Option 3: 10

Option 4: –10

Question : If $\alpha$ and $\beta$ are the roots of equation $x^{2}-x+1=0$, then which equation will have roots $\alpha ^{3}$ and $\beta ^{3}?$

Option 1: $x^{2}+2x+1=0$

Option 2: $x^{2}-2x-1=0$

Option 3: $x^{2}+3x-1=0$

Option 4: $x^{2}-3x+1=0$

Question : If $27 x^3-64 y^3=(A x+B y)\left(C x^2-D y^2+12 x y\right)$, then the value of $4 A+B+3 C+2 D$ is:

Option 1: 5

Option 2: 3

Option 3: –3

Option 4: –4