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 : 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 : The measure of three angles of a quadrilateral are in the ratio 1 : 2 : 3. If the sum of these three measures is equal to the measure of the fourth angle, then find the smallest angle.

Option 1: $30^\circ$

Option 2: $40^\circ$

Option 3: $60^\circ$

Option 4: $50^\circ$

Question : In a triangle ABC, if $\angle B=90^{\circ}, \angle C=45^{\circ}$ and AC = 4 cm, then the value of BC is:

Option 1: $\sqrt{2} \mathrm{~cm}$

Option 2: $4 \mathrm{~cm}$

Option 3: $2 \sqrt{2} \mathrm{~cm}$

Option 4: $4 \sqrt{2} \mathrm{~cm}$

Question : In $\triangle$ ABC, $\angle$ C = 90$^{\circ}$. M and N are the midpoints of sides AB and AC, respectively. CM and BN intersect each other at D and $\angle$ BDC = 90$^{\circ}$. If BC = 8 cm, then the length of BN is:

Option 1: $6 \sqrt{3} {~cm}$

Option 2: $6 \sqrt{6} {~cm}$

Option 3: $4 \sqrt{6} {~cm}$

Option 4: $8 \sqrt{3} {~cm}$