Question : If $a x+b y=1$ and $b x+a y=\frac{2 a b}{a^2+b^2}$, then the value of $x$ (in terms of $a$ and $b$) is:

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

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

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

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

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 $\frac{x}{y}=\frac{a+2}{a-2}$, then the value of $\frac{x^{2}-y^{2}}{x^{2}+y^{2}}$ is:

Option 1: $\frac{4a}{a^{2}+2}$

Option 2: $\frac{2a}{a^{2}+2}$

Option 3: $\frac{4a}{a^{2}+4}$

Option 4: $\frac{2a}{a^{2}+4}$

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 $\frac{x}{y}=\frac{4}{5}$, 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 $x=p+\frac{1}{p}$ and $y=p-\frac{1}{p}$, then the value of $x^{4}-2x^{2}y^{2}+y^{4}$ is:

Option 1: 24

Option 2: 4

Option 3: 16

Option 4: 8