Question : Chords AC and BD of a circle with centre O, intersect at right angles at E. If $\angle OAB=25^{\circ}$, then the value of $\angle EBC$ is:

Option 1: $30^{\circ}$

Option 2: $25^{\circ}$

Option 3: $20^{\circ}$

Option 4: $15^{\circ}$

Question : A polygon has 54 diagonals. The number of sides in the polygon is:

Option 1: 7

Option 2: 9

Option 3: 12

Option 4: 15

Question : $2(\sin 1^{\circ}× \sec 89^{\circ} ) + 3 (\cos 11^{\circ} × \operatorname{cosec} 79^{\circ}) + 5 (\tan 21^{\circ} × \tan 69^{\circ})$ = ?

Option 1: 11

Option 2: 12

Option 3: 20

Option 4: 10

Question : PQR is a triangle. The bisectors of the internal angle $\angle Q$ and external angle $\angle R$ intersect at S. If $\angle QSR=40^{\circ}$, then $\angle P$ is:

Option 1: $40^{\circ}$

Option 2: $60^{\circ}$

Option 3: $80^{\circ}$

Option 4: $30^{\circ}$

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: $60^\circ$