Question : If $\frac{a}{b}=\frac{25}{6}$, then the value of $\frac{a^{2}-b^{2}}{a^{2}+b^{2}}$ is:

Option 1: $\frac{589}{661}$

Option 2: $\frac{661}{589}$

Option 3: $\frac{625}{36}$

Option 4: $\frac{589}{651}$

Question : If $\sin\phi=\frac{5}{6}$, the value of $\cot\phi \cdot \sin\phi \cdot \cos\phi$ is:

Option 1: $\frac{6}{5}$

Option 2: $\frac{25}{36}$

Option 3: $\frac{5}{6}$

Option 4: $\frac{11}{36}$

Question : If $\left(a+\frac{1}{a}\right)=6$, then what is the value of $\frac{3}{4}\left(a^2+\frac{1}{a^2}\right)$?

Option 1: 22.5

Option 2: 34

Option 3: 25.5

Option 4: 36

Question : What is the value of $\frac{\frac{5}{6} \text { of } \frac{1}{3} \times \frac{12}{25}-\frac{1}{3} \text { of } \frac{5}{6} \times \frac{18}{25}}{\frac{25}{12} \text { of } \frac{1}{6} \times \frac{2}{5}+\frac{3}{8} \text { of } \frac{12}{25} \times \frac{5}{6}}$?

Option 1: $-\frac{3}{13}$

Option 2: $-\frac{5}{13}$

Option 3: $-\frac{8}{25}$

Option 4: $-\frac{3}{25}$

Question :  If $\sec\theta +\tan\theta = 3$, then what is the value of $\sec \theta-\tan \theta$?

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

Option 2: $6$

Option 3: $\frac{1}{6}$

Option 4: $\frac{1}{5}$

Question : The value of $3\frac{1}{2} - [2\frac{1}{4}+ 1\frac{1}{4} - \frac{1}{2}(1\frac{1}{2}-\frac{1}{3} -\frac{1}{6})]$ is:

Option 1: $\frac{1}{2}$

Option 2: $2\frac{1}{2}$

Option 3: $3\frac{1}{2}$

Option 4: $9\frac{1}{2}$