Question : If $p=9, q=\sqrt{17}$, then the value of $(p^2-q^2)^{-\frac{1}{3}}$ is equal to:

Option 1: 4

Option 2: $\frac{1}{4}$

Option 3: 3

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

Question : If $\frac{1}{p}+\frac{1}{q}=\frac{1}{p+q}$, the value of $\left (p^{3}-q^{3}\right )$ is:

Option 1: $p - q$

Option 2: $pq$

Option 3: $1$

Option 4: $0$

Question : The value of $ \frac{(p-q)^3+(q-r)^3+(r-p)^3}{12(p-q)(q-r)(r-p)}$, where $p \neq q \neq r$, is equal to:

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

Option 2: $\frac{1}{3}$

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

Option 4: $\frac{1}{2}$

Question : If $p^2+q^2=7pq$, then the value of $\frac{p}{q}+\frac{q}{p}$ is equal to:

Option 1: 9

Option 2: 5

Option 3: 7

Option 4: 3

Question : If $P=7+4\sqrt3$ and $PQ=1$, then what is the value of $\frac{1}{P^{2}}+\frac{1}{Q^{2}}$?

Option 1: 196

Option 2: 194

Option 3: 206

Option 4: 182