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: $\frac{5}{3}$

Question : If $\frac{x}{y}=\frac{4}{5}$, then the value of $(\frac{4}{7}+\frac{2y–x}{2y+x})$ is:

Option 1: $\frac{3}{7}$

Option 2: $1\frac{1}{7}$

Option 3: $1$

Option 4: $2$

Question : If $x+\frac{2}{x}=1$, then the value of $\frac{x^2+7x+2}{x^2+13x+2}$ is:

Option 1: $\frac{5}{7}$

Option 2: $\frac{3}{7}$

Option 3: $\frac{4}{7}$

Option 4: $\frac{2}{7}$

Question : If $3 \operatorname{cosec} A=7$, then what is the value of $\cos A \tan A$?

Option 1: $\frac{2 \sqrt{10}}{7}$

Option 2: $\frac{3}{7}$

Option 3: $\frac{4}{7}$

Option 4: $\frac{\sqrt{10}}{7}$

Question : If $\sin \theta-\cos \theta=\frac{1}{5}$, then find the value of $\sin \theta+\cos \theta$.

Option 1: $\frac{5}{7}$

Option 2: $\frac{7}{5}$

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

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