Question : If $(a+b+c)=20$ and $a^2+b^2+c^2=152$, find the value of $a^3+b^3+c^3-3 abc$.

Option 1: 560

Option 2: 640

Option 3: 480

Option 4: 720

Question : If $(a + b + c) = 13$ and $(ab + bc + ca) = 54$, find the value of $\left(a^2+b^2+c^2\right)$.

Option 1: 63

Option 2: 65

Option 3: 61

Option 4: 59

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

Option 1: 9

Option 2: 18

Option 3: 27

Option 4: 1

Question : Directions: If A denotes +, B denotes –, C denotes × and D denotes ÷, then which of the following equations is true?

Option 1: 8 B 6 D 2 A 4 C 3 = 15

Option 2: 8 A 8 B 8 C 8 = – 48

Option 3: 9 C 9 B 9 D 9 A 9 = 17

Option 4: 3 A 3 B 3 C 3 A 3 D 3 = 4

Question : If $a+b-c=20$ and $a^2+b^2+c^2=152$, find the value of $a^3+b^3-c^3+3abc$.

Option 1: 480

Option 2: 720

Option 3: 640

Option 4: 560