Question : In $\triangle$ABC, $\angle$C = 90° and CD is perpendicular to AB at D. If $\frac{\text{AD}}{\text{BD}}=\sqrt{k}$, then $\frac{\text{AC}}{\text{BC}}$=?

Option 1: $\sqrt{k}$

Option 2: $\frac{1}{\sqrt{k}}$

Option 3: $\sqrt[4]{k}$

Option 4: $k$

Question : If $a, b, c$ are all non-zero and $a+b+c=0$, then find the value of $\frac{a^2}{b c}+\frac{b^2}{c a}+\frac{c^2}{ab}$.

Option 1: $3$

Option 2: $4$

Option 3: $1$

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

Question : If $a+b+c=0$, then the value of $\frac{a^2}{b c}+\frac{b^2}{c a}+\frac{c^2}{a b}$ is:

Option 1: 1

Option 2: 3

Option 3: - 1

Option 4: 0

Question : If $a+b+c=m$ and $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=0$, then the average of $a^{2}, b^{2},$ and $c^{2}$ is:

Option 1: $m^{2}$

Option 2: $\frac{m^{2}}{3}$

Option 3: $\frac{m^{2}}{9}$

Option 4: $\frac{m^{2}}{27}$

Question : If $A+\frac{1}{1+\frac{1}{2+\frac{1}{3}}}=\frac{9}{10}$, then the value of A is:

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

Option 2: $\frac{3}{10}$

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

Option 4: $\frac{1}{10}$