Question : If A : B = 2 : 3 and B : C = 3 : 7, then (A + B) : (B + C) : (C + A) is:

Option 1: 4 : 8 : 9

Option 2: 5 : 8 : 9

Option 3: 5 : 10 : 9

Option 4: 4 : 10 : 9

Question : If $a+b+c=5, a^3+b^3+c^3=85$, and $abc=25$, then find the value of $a^2+b^2+c^2-a b- bc - ca$.

Option 1: 2

Option 2: 4

Option 3: 6

Option 4: 8

Question : If A : B = $\frac{1}{2}:\frac{1}{3}$, B : C = $\frac{1}{5}:\frac{1}{3}$ ,then (A + B) : (B + C) is equal to:

Option 1: 5 : 8

Option 2: 9 : 10

Option 3: 15 : 16

Option 4: 6 : 15

Question : If $a+b+c=6$ and $a^2+b^2+c^2=14$, then what is the value of $(a-b)^2+(b-c)^2+(c-$ a) ${ }^2$?

Option 1: –8

Option 2: 8

Option 3: 10

Option 4: 6

Question : If $\frac{A}{3}=\frac{B}{2}=\frac{C}{5}$, what is the value of ratio $(C+A)^{2}:(A+B)^{2}:(B+C)^{2}$?

Option 1: $9:4:25$

Option 2: $25:4:9$

Option 3: $64:25:49$

Option 4: $49:25:64$