Question : If $3x-2y=3$ and $xy=9$, then find the value of $3x+2y$.

Option 1: 16

Option 2: 13

Option 3: 14

Option 4: 15

Question : If $a =\cot A+\cos A$ and $b =\cot A-\cos A$, then find the value of $a^2-b^2-4 \sqrt{ab}$.

Option 1: 0

Option 2: –1

Option 3: 1

Option 4: –4

Question : If $(a-b)=9$, and $(a^3-b^3)$ = 4401, find the value of $ab$.

Option 1: 190

Option 2: 112

Option 3: 162

Option 4: 136

Question : If a : b : c = 2 : 3 : 5 and 5b – a + 2c = 115, then what is the value of b?

Option 1: 15

Option 2: 12

Option 3: 6

Option 4: 24

Question : If $a^3+b^3=9$ and $a+b=3$, then the value of $\frac{1}a+\frac{1}b$ is:

Option 1: $\frac{1}2$

Option 2: $\frac{3}2$

Option 3: $\frac{5}2$

Option 4:  $–1$