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

Question : The factors of $x^2+4 y^2+4 y-4 x y-2 x-8$ are:

Option 1: $(x-2 y-4)(x-2 y+2)$

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

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

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

Question : If $\sin Y=x$, then what will be the value of $\cos 2Y\left(\right.$ where $\left.0 \leq Y \leq 90^{\circ}\right)$?

Option 1: $(\sqrt{ 2} -1) x$

Option 2: $\sqrt{2} x$

Option 3: $1-2 x$

Option 4: $1-2 x^2$

Question : If $x^{2} -3x +1=0$, then the value of $\frac{\left(x^4+\frac{1}{x^2}\right)}{\left(x^2+5 x+1\right)}$ is:

Option 1: $\frac{9}{4}$

Option 2: $\frac{27}{8}$

Option 3: $\frac{5}{2}$

Option 4: $2$

Question : If $x+y+z=0$, then what is the value of $\frac{x^2}{(y z)}+\frac{y^2}{(x z)}+\frac{z^2}{(x y)}$?

Option 1: 1

Option 2: 0

Option 3: 2

Option 4: 3