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 $8 a^3+27 b^3=16$ 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 $(a+1)^2+(a+2)^2=16$, 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 $\small a^{4}+1=\left [\frac{a^{2}}{b^{2}}\right ]\left (4b^{2}-b^{4}-1\right),$ then what is the value of $a^{4}+b^{4}?$

Option 1: 2

Option 2: 16

Option 3: 32

Option 4: 64

Question : If $\small a^{3}+3a^{2}+9a=1$, then what is the value of $a^{3}+\frac{3}{a}$?

Option 1: 31

Option 2: 26

Option 3: 28

Option 4: 24

Question :  The value of $1 \frac{3}{4}+1 \frac{5}{7} \div 2 \frac{3}{7} \times 2 \frac{3}{7}=$?

Option 1: $1 \frac{11}{28}$

Option 2: $2 \frac{13}{28}$

Option 3: $3 \frac{13}{28}$

Option 4: $4 \frac{23}{28}$