Question : The maximum value of $5+20x-4x^{2}$, when $x$ is a real number, is:

Option 1: 1

Option 2: 5

Option 3: 25

Option 4: 30

Question : If $x^2-5 x+1=0$, then the value of $\frac{x^6+x^4+x^2+1}{5 x^3}=?$

Option 1: 30

Option 2: 25

Option 3: 23

Option 4: 28

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 $\frac{\sqrt{5+x}+\sqrt{5-x}}{\sqrt{5+x}-\sqrt{5-x}}=3$, what is the value of $x$?

Option 1: $\frac{5}{2}$

Option 2: $\frac{25}{3}$

Option 3: $4$

Option 4: $3$

Question : Simplify the following expression.
$(4 x + 1)^2 - (4 x + 3)(4 x - 1)$

Option 1: $(4 x + 1)$

Option 2: $4$

Option 3: $(4x- 3)$

Option 4: $4x$

Question : If $x=2+\sqrt3$, then the value of $\frac{x^{2}-x+1}{x^{2}+x+1}$ is:

Option 1: $\frac{2}{3}$

Option 2: $\frac{3}{4}$

Option 3: $\frac{4}{5}$

Option 4: $\frac{3}{5}$