Question : If $a + 5b = 13$ and $ab = 9$, then find the value of $a^2 + 25b^2$.

Option 1: 69

Option 2: 79

Option 3: 49

Option 4: 59

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 $a-b = 5$ and $ab = 24$, find the value of $a^3-b^3$.

Option 1: 455

Option 2: 485

Option 3: 385

Option 4: 360

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 $a+b=10$ and $a^2+b^2=58$, find the value of $ab$

Option 1: 24

Option 2: 27

Option 3: 30

Option 4: 21