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 : In $\Delta PQR,$ $\angle P : \angle Q : \angle R = 1: 3 : 5$, what is the value of $\angle R - \angle P$?

Option 1: $30^\circ$

Option 2: $80^\circ$

Option 3: $45^\circ$

Option 4: $60^\circ$

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 : If $\triangle$PQR is right-angled at Q, PQ = 12 cm and $\angle$PRQ = 30°, then what is the value of QR?

Option 1: $12\sqrt{3}$

Option 2: $12\sqrt2$

Option 3: $12$

Option 4: $24$

Question : ΔPQR is right angled at Q such that PQ = ( x - y ), QR = x, and PR = ( x + y ). S is a point on QR such that QS = PQ. The ratio QS : SR for any values of x and y is:

Option 1: 3 : 1

Option 2: 2 : 1

Option 3: 1 : 2

Option 4: 1 : 3