Question : A complete factorisation of $(x^4+64)$ is:

Option 1: $(x^2+8)^2$

Option 2: $(x^2+8)$$(x^2-8)$

Option 3: $(x^2-4x+8)(x^2-4x-8)$

Option 4: $(x^2+4x+8)$$(x^2-4x+8)$

Question : If $x$,$y$ and $z$ are real numbers such that $(x-3)^2+(y-4)^2+(z-5)^2=0$, then $(x+y+z)$ is equal to:

Option 1: –12

Option 2: 0

Option 3: 8

Option 4: 12

Question : If $x=\sqrt{–\sqrt{3}+\sqrt{3+8 \sqrt{7+4 \sqrt{3}}}}$ where $x > 0$, then the value of $x$ is equal to:

Option 1: 3

Option 2: 4

Option 3: 1

Option 4: 2

Question : If $x+y=1+xy$, then $x^3+y^3-x^3y^3$ is equal to:

Option 1: 0

Option 2: 1

Option 3: –1

Option 4: 2

Question : If $\alpha$ and $\beta$ are the roots of equation $x^{2}-2x+4=0$, then what is the equation whose roots are $\frac{\alpha ^{3}}{\beta ^{2}}$ and $\frac{\beta ^{3}}{\alpha ^{2}}?$

Option 1: $x^{2}-4x+8=0$

Option 2: $x^{2}-32x+4=0$

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

Option 4: $x^{2}-16x+4=0$