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

Option 1: 64

Option 2: 66

Option 3: 62

Option 4: 60

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

Option 1: 64

Option 2: 62

Option 3: 60

Option 4: 66

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 $\tan \theta=\frac{8}{19}$, find the value of $\sec ^2 \theta$.

Option 1: $\frac{11}{19} \\$

Option 2: $1 \frac{8}{19} \\$

Option 3: $\frac{297}{361} \\$

Option 4: $1 \frac{64}{361}$

Question : Find the value of the given expression:
$\frac{(4\frac{1}{3}+3\frac{1}{3}\times 1\frac{4}{5}\div 3\frac{3}{4}\times (1\frac{1}{2}+1\frac{1}{3}))}{(\frac{2}{3}\div \frac{5}{6}\times \frac{2}{3})}$

Option 1: $11 \frac{3}{8}$

Option 2: $10\frac{1}{8}$

Option 3: $14\frac{3}{8}$

Option 4: $16\frac{5}{8}$

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