Question : If $(a+b+c)=17$ and $\left(a^2+b^2+c^2\right)=101$, then find the value of $(a-b)^2+(b-c)^2+(c-a)^2$.

Option 1: 12

Option 2: 14

Option 3: 10

Option 4: 16

Question : If $9 a+9 b+9 c=81$ and $4 a b+4 b c+4 c a=160$, then what is the value of $6 a^2+6 b^2+6 c^2$?

Option 1: 1

Option 2: 3

Option 3: 4

Option 4: 6

Question : In a triangle ABC; 8$\angle$A = 6$\angle$B = 3$\angle$C. What are the degree measures of $\angle$ A, $\angle$ B, and $\angle$C?

Option 1: $48^{\circ}, 96^{\circ}, \text{and } 36^{\circ}$

Option 2: $36^{\circ}, 96^{\circ}, \text{and } 48^{\circ}$

Option 3: $36^{\circ}, 48^{\circ}, \text{and } 96^{\circ}$

Option 4: $96^{\circ}, 48^{\circ}, \text{and } 36^{\circ}$

Question : Simplify:
$(2 a-3 b-c)^2-(a+2 b+c)^2$

Option 1: $3 a^2+5 b^2-16 a b+2 b c-8 a c$

Option 2: $3 a^2+5 b^2-8 a b+2 b c-6 a c$

Option 3: $3 a^2+5 b^2-16 a b-6 a c$

Option 4: $3 a^2+5 b^2-16 a b+2 b c-6 a c$

Question : If $a+b+c=5$ and $a^2+b^2+c^2=15$, then find the value of $a^3+b^3+c^3-3 a b c-27$.

Option 1: 23

Option 2: 27

Option 3: 25

Option 4: 21