Question : In a $\triangle \mathrm{PQR}$ and $\triangle\mathrm{ABC}$, $\angle$P = $\angle$A and AC = PR. Which of the following conditions is true for $\triangle$PQR and $\triangle$ABC to be congruent?

Option 1: AB = PQ by SSS

Option 2: AB = PQ by SAS

Option 3: BC = QR by ASS

Option 4: $\angle$Q = $\angle$B by AAA

Question : In a $\triangle P Q R, \angle P: \angle Q: \angle R=3: 4: 8$. The shortest side and the longest side of the triangle, respectively, are:

Option 1: PQ and PR

Option 2: QR and PR

Option 3: PQ and QR

Option 4: QR and PQ

Question : Let $\triangle ABC \sim \triangle RPQ$ and $\frac{{area}(\triangle {ABC})}{{area}(\triangle {PQR})}=\frac{4}{9}$. If AB = 3 cm, BC = 4 cm and AC = 5 cm, then RP (in cm) is equal to:

Option 1: 6

Option 2: 5

Option 3: 4.5

Option 4: 12

Question : In $\triangle$PQR, $\angle$ PQR = $90^{\circ}$, PQ = 5 cm and QR = 12 cm. What is the radius (in cm) of the circumcircle of $\triangle$PQR?

Option 1: 6.5

Option 2: 7.5

Option 3: 13

Option 4: 15

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: $k$