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 : In $\triangle A B C, \mathrm{BD} \perp \mathrm{AC}$ at $\mathrm{D}$. $\mathrm{E}$ is a point on $\mathrm{BC}$ such that $\angle B E A=x^{\circ}$. If $\angle E A C=46^{\circ}$ and $\angle E B D=60^{\circ}$, then the value of $x$ is:

Option 1: 72°

Option 2: 78°

Option 3: 68°

Option 4: 76°

Question : PQR is an equilateral triangle inscribed in a circle. S is any point on the arc QR. Measure of $\frac{1}{2} \angle \mathrm{PSQ}$ is:

Option 1: 20°

Option 2: 15°

Option 3: 30°

Option 4: 60°

Question : $\triangle \mathrm{ABC}$ and $\triangle \mathrm{DEF}$ are two triangles such that $\triangle \mathrm{ABC} \cong \triangle \mathrm{FDE}$. If AB = 5 cm, $\angle$B = 40° and $\angle$A = 80°, then which of the following options is true?

Option 1: DF = 5 cm, $\angle$E = 60°

Option 2: DE = 5 cm, $\angle$F = 60°

Option 3:  DE = 5 cm, $\angle$D = 60°

Option 4: DE = 5 cm, $\angle$E = 60°

Question : If $\triangle ABC$ is right-angled at B, AB = 30 units and $\angle ACB=60°$, what is the value of AC?

Option 1: $20$ units

Option 2: $20\sqrt3$ units

Option 3: $40$ units

Option 4: $60$ units