Question : If $5A=12B=13C$, then find $A: B: C$.

Option 1: $60:65:156$

Option 2: $65:156:60$

Option 3: $156:65:60$

Option 4: $3:12:5$

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 $\frac{a^2}{b+c}=\frac{b^2}{c+a}=\frac{c^2}{a+b}=1$, then find the value of $\frac{2}{1+a}+\frac{2}{1+b}+\frac{2}{1+c}$.

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: 3

Question : If $(a+b+c)=14$ and $\left(a^3+b^3+c^3-3 a b c\right)=98$, find the value of $(ab+bc+ca)$.

Option 1: 60

Option 2: 64

Option 3: 65

Option 4: 63

Question : If a : b = 4 : 5 and b : c = 3 : 10, then a : c is:

Option 1: 4 : 10

Option 2: 5 : 3

Option 3: 25 : 6

Option 4: 6 : 25

Question : If $\frac{a^2}{b+c}=\frac{b^2}{c+a}=\frac{c^2}{a+b}=1$, then $\frac{1}{1+a}+\frac{1}{1+b}+\frac{1}{1+c}$ is:

Option 1: 1

Option 2: 2

Option 3: 3

Option 4: 4