Question : If $(a+1)^2+(a+2)^2=16$, then what is the value of $40+12 a+4 a^2 ?$

Option 1: 56

Option 2: 62

Option 3: 74

Option 4: 52

Question : If $8 a^3+27 b^3=16$ and $2 a+3 b=4$, then find the value of $16 a^4+81 b^4$.

Option 1: 26

Option 2: 30

Option 3: 28

Option 4: 32

Question : If $a^3-b^3=56$ and $a-b=2$, what is the value of $(a^2+b^2)$?

Option 1: 12

Option 2: 20

Option 3: 28

Option 4: 32

Question : If $\small a^{4}+1=\left [\frac{a^{2}}{b^{2}}\right ]\left (4b^{2}-b^{4}-1\right),$ then what is the value of $a^{4}+b^{4}?$

Option 1: 2

Option 2: 16

Option 3: 32

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 $(a+\frac{1}{a})^{2}=3$, then the value of $a^{18}+a^{12}+a^{6}+1$ is:

Option 1: 3

Option 2: 1

Option 3: 0

Option 4: 2