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 : $\triangle \mathrm{ABC}$ 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 : In $\triangle$ABC and $\triangle$PQR, $\angle$B = $\angle$Q, $\angle$C = $\angle$R. M is the midpoint of side QR. If AB : PQ = 7 : 4, then $\frac{\text{area($\triangle$ ABC)}}{\text{area($\triangle$ PMR)}}$ is:

Option 1: $\frac{35}{8}$

Option 2: $\frac{49}{16}$

Option 3: $\frac{49}{8}$

Option 4: $\frac{35}{16}$

Question : Let ABC and PQR be two congruent triangles such that $\angle A = \angle P = 90^{\circ}$. If BC = 17 cm, PR = 8 cm, find AB (in cm).

Option 1: 12

Option 2: 15

Option 3: 14

Option 4: 9

Question : In $\triangle \mathrm{ABC}, \mathrm{BD} \perp \mathrm{AC}$ at D. E is a point on BC such that $\angle \mathrm{BEA}=x^{\circ}$. If $\angle \mathrm{EAC}=62^{\circ}$ and $\angle \mathrm{EBD}=60^{\circ}$, then the value of $x$ is:

Option 1: $92^\circ$

Option 2: $78^\circ$

Option 3: $76^\circ$

Option 4: $68^\circ$