Question : If $\mathrm{p}=7+4 \sqrt{3}$, then what is the value of $\frac{\mathrm{p}^6+\mathrm{p}^4+\mathrm{p}^2+1}{\mathrm{p}^3}$?

Option 1: 2617

Option 2: 2167

Option 3: 2716

Option 4: 2176

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

Option 1: 24

Option 2: 18

Option 3: 20

Option 4: 29

Question : If $\mathrm{k}+\frac{1}{\mathrm{k}}=4$, then what is the value of $\mathrm{k}^4+\frac{1}{\mathrm{k}^4}$ ?

Option 1: 410

Option 2: 192

Option 3: 212

Option 4: 194

Question : If $\mathrm{p}=\frac{\sqrt{2}+1}{\sqrt{2}-1}$ and $\mathrm{q}=\frac{\sqrt{2}-1}{\sqrt{2}+1}$ then, find the value of $\frac{\mathrm{p}^2}{\mathrm{q}}+\frac{\mathrm{q}^2}{\mathrm{p}}$.

Option 1: 200

Option 2: 196

Option 3: 198

Option 4: 188

Question : $\triangle \mathrm{XYZ} \sim \triangle \mathrm{GST}$ and $\mathrm{XY}: \mathrm{GS}=2: 3, \mathrm{XV}$ is the median to the side $\mathrm{YZ}$, and $\mathrm{GD}$ is the median to the side ST. The value of $\left(\frac{\mathrm{YV}}{\mathrm{SD}}\right)^2$ is:

Option 1: $\frac{4}{9}$

Option 2: $\frac{3}{5}$

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

Option 4: $\frac{2}{3}$