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

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 : If $6^{x}=3^{y}=2^{z}$, then what is the value of $\frac{1}{y}+\frac{1}{z}-\frac{1}{x}$?

Option 1: 1

Option 2: 0

Option 3: 3

Option 4: 6

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 $x^2+\frac{1}{x^2}=7$, then what is the value of $x^3+\frac{1}{x^3}$?

Option 1: 9

Option 2: 18

Option 3: 27

Option 4: 36