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 $\left (2a-1 \right )^{2}+\left (4b-3 \right)^{2}+\left (4c+5 \right)^{2}=0$, then the value of $\frac{a^{3}+b^{3}+c^{3}-3abc}{a^{2}+b^{2}+c^{2}}$ is:

Option 1: $1\tfrac{3}{8}$

Option 2: $2\tfrac{3}{8}$

Option 3: $3\tfrac{3}{8}$

Option 4: $0$

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 $a^2+b^2+c^2=ab+bc+ca$, then the value of $\frac{11a^4+13b^4+15c^4}{16a^2b^2+19b^2c^2+17c^2a^2}$ is:

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

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

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

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

Question : If $\small c+\frac{1}{c}=3$, then the value of $\left (c-3 \right )^{7}+\frac{1}{c^{7}}$ is:

Option 1: 2

Option 2: 0

Option 3: 3

Option 4: 1