Question : What is the value of $\frac{4x^2+9y^2+12xy}{144}$?

Option 1: $(\frac{x}{3} + \frac{y}{4})^2$

Option 2: $(\frac{x}{3} + y)^2$

Option 3: $(\frac{x}{4} + \frac{y}{6})^2$

Option 4: $(\frac{x}{6} + \frac{y}{4})^2$

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 $\frac{x+1}{x-1}=\frac{a}{b}$ and $\frac{1-y}{1+y}=\frac{b}{a}$, then the value of $\frac{x-y}{1+xy}$ is:

Option 1: $\frac{2ab}{a^{2}-b^{2}}$

Option 2: $\frac{a^{2}-b^{2}}{2ab}$

Option 3: $\frac{a^{2}+b^{2}}{2ab}$

Option 4: $\frac{a^{2}-b^{2}}{ab}$

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

Option 1: $\sqrt{3}$

Option 2: $3\sqrt{3}$

Option 3: $16\sqrt{3}$

Option 4: $2\sqrt{3}$

Question : If $6^{x}=3^{y}=2^{z}$, then what is the value of $\frac{1}{y}+\frac{1}{z}-\frac{1}{x}$?

Option 1: 1

Option 2: 0

Option 3: 3

Option 4: 6