Question : If $a-b=9$ and $a b=20$, then $a^2+b^2$:

Option 1: 111

Option 2: 115

Option 3: 121

Option 4: 118

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 : If $a+b=3$ and $a b=2$, then what is the value of $2 a^3+2 b^3$?

Option 1: 25

Option 2: 27

Option 3: 18

Option 4: 20

Question : If $A+\frac{1}{A}=-1$, then find the value of $\frac{{A}^6+{A}^3-1}{{~A}^9+{A}^3-1}$.

Option 1: 0

Option 2: –1

Option 3: 2

Option 4: 1

Question : If $A:B=3:4$ and $B:C=6:5$, then $C:A$ is

Option 1: $10:9$

Option 2: $9:10$

Option 3: $8:9$

Option 4: $9:8$

Question : If $\left(3 y+\frac{3}{y}\right)=8$, then find the value of $\left(y^2+\frac{1}{y^2}\right)$.

Option 1: $5\frac{1}{9}$

Option 2: $4\frac{5}{6}$

Option 3: $7\frac{1}{9}$

Option 4: $9\frac{1}{9}$