Question : If $a+b=3$, then the value of $a^{3}+b^{3}+9ab-27$ is:

Option 1: 24

Option 2: 25

Option 3: 0

Option 4: 27

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 : a³ – b³ = 91 and a – b = 1, what is the value of (ab)?

Option 1: 27

Option 2: 6

Option 3: 9

Option 4: 30

Question : What is the possible value of (a + b + c) – 3, if a² + b² + c² = 9 and ab + bc + ca = 8?

Option 1: 5

Option 2: 3

Option 3: 9

Option 4: 2

Question : For what value of k will the expression x⁶ – 18x³ + k be a perfect square?

Option 1: –9

Option 2: –81

Option 3: 9

Option 4: 81