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

Question : If $2a+3b=14$ and $2a-3b=10$, then find the value of ' $ab$ '.

Option 1: 5

Option 2: 3

Option 3: 4

Option 4: 2

Question : If $\cot A=\frac{5}{12}$, find the value of the following expression:
$\frac{5\left(1-\cos^2 A\right)}{6\left(1-\sin^2 A\right)}$

Option 1: $\frac{144}{5}$

Option 2: $\frac{24}{25}$

Option 3: $\frac{144}{25}$

Option 4: $\frac{24}{5}$

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 3 cot A = 4 and A is an acute angle, then find the value of sec A.

Option 1: $\frac{3}{4}$

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

Option 3: $\frac{4}{5}$

Option 4: $\frac{5}{3}$