Question : Circum-centre of $\triangle PQR$ is O. If $\angle QPR=55^{\circ}$ and $\angle QRP=75^{\circ}$, What is the value (in degree) of $\angle OPR$?

Option 1: 45°

Option 2: 40°

Option 3: 65°

Option 4: 70°

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 $\triangle \mathrm{ABC}, \angle \mathrm{A}=68^{\circ}$. If I is the incentre of the triangle, then the measure of $\angle B I C$ is:

Option 1: 124°

Option 2: 68°

Option 3: 148°

Option 4: 54°

Question : Internal bisectors of $\angle$ B and $\angle$ C of $\triangle$ ABC meet at O. If $\angle$ BAC = $80^{\circ}$, then the value of $\angle$ BOC is:

Option 1: $120^{\circ}$

Option 2: $140^{\circ}$

Option 3: $110^{\circ}$

Option 4: $130^{\circ}$

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: $24$