Question : If $\frac14\text{ of }\frac45+\frac95\text{ of }\frac{17}{3}-\frac{3}{10}=p$, then what is the value of $p$?

Option 1: $\frac{127}{5}$

Option 2: $\frac{177}{5}$

Option 3: $\frac{255}{2}$

Option 4: $\frac{51}{2}$

Question : What is the value of $\frac{\frac{5}{3} \text { of } \frac{1}{4} \times \frac{24}{5}-\frac{1}{5} \text { of } \frac{25}{8} \times \frac{24}{5}}{\frac{5}{12} \text { of } \frac{3}{4} \times \frac{4}{3}+\frac{3}{4} \text { of } \frac{12}{5} \times \frac{5}{6}}$?

Option 1: $-\frac{24}{23}$

Option 2: $-\frac{12}{23}$

Option 3: $-\frac{25}{46}$

Option 4: $-\frac{28}{23}$

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 $3x+\frac{1}{5x}=7$, then what is the value of $\frac{5x}{(15x^{2}+15x+1)}?$

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

Option 2: $\frac{1}{10}$

Option 3: $\frac{2}{5}$

Option 4: $10$

Question : If $3 \tan \theta=4$, then what is the value of $7 \sin \theta-2 \cos \theta$?

Option 1: $\frac{12}{5}$

Option 2: $4$

Option 3: $\frac{22}{5}$

Option 4: $\frac{17}{5}$

Question : If $x+\frac{1}{x}=3$, then the value of $\frac{3x^{2}-4x+3}{x^{2}-x+1}$ is:

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

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

Option 3: $\frac{5}{2}$

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