Question : If $\left(y+\frac{1}{y}\right)=4$, then find the value of $\left(y^6+\frac{1}{y^6}\right)$.

Option 1: 2702

Option 2: 2704

Option 3: 4096

Option 4: 2706

Question : The simplified value of $\small \left (1-\frac{2xy}{x^{2}+y^{2}}\right )\div\left (\frac{x^{3}-y^{3}}{x-y}-3xy\right)$ is:

Option 1: $\frac{1}{x^{2}-y^{3}}$

Option 2: $\frac{1}{x^{2}+y^{2}}$

Option 3: $\frac{1}{x-y}$

Option 4: $\frac{1}{x+y}$

Question : The value of $\left(2 \frac{6}{7}\right.$ of $\left.4 \frac{1}{5} \div \frac{2}{3}\right) \times 5 \frac{1}{9} \div\left(\frac{3}{4} \times 2 \frac{2}{3}\right.$ of $\left.\frac{1}{2} \div \frac{1}{4}\right)$ is:

Option 1: 25

Option 2: 19

Option 3: 23

Option 4: 21

Question : The value of $\left(1 \frac{1}{3} \div 2 \frac{6}{7}\right.$ of $\left.5 \frac{3}{5}\right) \times\left(6 \frac{2}{5} \div 4 \frac{1}{2}\right.$ of $\left.5 \frac{1}{3}\right) \div\left(\frac{3}{4} \times 2 \frac{2}{3} \div \frac{5}{9}\right.$ of $\left.1 \frac{1}{5}\right)=k$, where $\mathrm{k}$ lies between:

Option 1: 0.07 and 0.08

Option 2: 0.007 and 0.008

Option 3: 0.0007 and 0.0008

Option 4: 0.7 and 0.8

Question : The value of $9 \div\left\{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{6} \div\left(\frac{3}{4}-\frac{1}{3}\right)\right.$ of $\left.\frac{2}{9}\right\}$ is:

Option 1: $\frac{540}{173}$

Option 2: $\frac{340}{173}$

Option 3: $\frac{480}{173}$

Option 4: $\frac{2540}{173}$