Question : If $2 x+\frac{2}{x}=5$, then the value of $\left(x^3+\frac{1}{x^3}+2\right)$ will be:

Option 1: $\frac{81}{11}$

Option 2: $\frac{81}{7}$

Option 3: $\frac{71}{8}$

Option 4: $\frac{81}{8}$

Question : If $\left(3 y+\frac{3}{y}\right)=8$, then find the value of $\left(y^2+\frac{1}{y^2}\right)$.

Option 1: $5\frac{1}{9}$

Option 2: $4\frac{5}{6}$

Option 3: $7\frac{1}{9}$

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

Question : What is the value of $\left(\mathrm{k}+\frac{1}{\mathrm{k}}\right)\left(\mathrm{k}-\frac{1}{\mathrm{k}}\right)\left(\mathrm{k}^2+\frac{1}{\mathrm{k}^2}\right)\left(\mathrm{k}^4+\frac{1}{\mathrm{k}^4}\right)$?

Option 1: $\mathrm{k}^{16}+\frac{1}{\mathrm{k}^{16}}$

Option 2: $\mathrm{k}^{16}-\frac{1}{\mathrm{k}^{16}}$

Option 3: $\mathrm{k}^8-\frac{1}{\mathrm{k}^8}$

Option 4: $\mathrm{k}^8+\frac{1}{\mathrm{k}^8}$

Question : If $\left(4y-\frac{4}{y}\right)=11$, find the value of $\left(y^2+\frac{1}{y^2}\right)$.

Option 1: $7 \frac{9}{16}$

Option 2: $5 \frac{9}{16}$

Option 3: $9 \frac{11}{16}$

Option 4: $9 \frac{9}{16}$

Question : If $\left (a+b \right):\left (b+c \right):\left (c+a \right)= 6:7:8$ and $\left (a+b+c \right) = 14,$ then value of $c$ is:

Option 1: 6

Option 2: 7

Option 3: 8

Option 4: 14