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 $\triangle$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 : In $\Delta$PQR, $\angle$P : $\angle$Q : $\angle$R = 2 : 2 : 5. A line parallel to QR is drawn which touches PQ and PR at A and B respectively. What is the value of $\angle$PBA – $\angle$PAB?

Option 1: 60º

Option 2: 30º

Option 3: 20º

Option 4: 50º

Question : The sides $P Q$ and $P R$ of $\triangle P Q R$ are produced to points $S$ and $T$, respectively. The bisectors of $\angle S Q R$ and $\angle T R Q$ meet at $\mathrm{U}$. If $\angle \mathrm{QUR}=59^{\circ}$, then the measure of $\angle \mathrm{P}$ is:

Option 1: 31^o

Option 2: 62^o

Option 3: 41^o

Option 4: 49^o

Question : $\triangle$ PQR circumscribes a circle with centre O and radius r cm such that $\angle$ PQR = $90^{\circ}$. If PQ = 3 cm, QR = 4 cm, then the value of r is:

Option 1: 2

Option 2: 1.5

Option 3: 2.5

Option 4: 1