1). If every interior angle of regular octagon is \( \Large 135 ^{\circ} \), then find the external angle of it.
A). \( \Large 65 ^{\circ} \) 
B). \( \Large 75 ^{\circ} \) 
C). \( \Large 45 ^{\circ} \) 
D). \( \Large 55 ^{\circ} \) 

2). In a \( \Large \triangle ABC, \angle A : \angle B : \angle C = 2 : 4 : 3 \). The shortest side and the longest side of the triangles are respectively.
A). AC and AB 
B). AC and BC 
C). BC and AC 
D). AB and AC 

3). In a \( \Large \triangle \)ABC, \( \Large \angle A = 90 ^{\circ} \), \( \Large \angle C = 55 ^{\circ} \) and \( \Large \overline{AD}\perp\overline{BC} \), What is the value of \( \Large \angle BAD \)?
A). \( \Large 60 ^{\circ} \) 
B). \( \Large 45 ^{\circ} \) 
C). \( \Large 55 ^{\circ} \) 
D). \( \Large 35 ^{\circ} \) 

4). O is the circumcentre of the \( \Large \triangle \) ABC. If \( \Large \angle BAC \) = \( \Large 50 ^{\circ} \), then \( \Large \angle OBC \) is equal to
A). \( \Large 30 ^{\circ} \) 
B). \( \Large 60 ^{\circ} \) 
C). \( \Large 40 ^{\circ} \) 
D). \( \Large 50 ^{\circ} \) 

5). ABC is a right angled triangle such that AB = a  b, BC = a and CA = a + b. D is a point on BC such that BD = AB. The ratio of BD : DC for any value of a and b is given by
A). 3 ; 2 
B). 4 : 3 
C). 5 : 4 
D). 3 : 1 

6). ABC is a triangle, where BC = 2AB, \( \Large \angle B\) = \( \Large 30 ^{\circ} \) and \( \Large \angle A\) = \( \Large 90 ^{\circ} \). The magnitude of the side AC is
A). \( \Large \frac{2 BC}{3} \) 
B). \( \Large \frac{3 BC}{4} \) 
C). \( \Large \frac{BC}{\sqrt{3}} \) 
D). \( \Large \frac{\sqrt{3 BC}}{2} \) 

7). The bisectors BI and CI of \( \Large \angle B\) and \( \Large \angle C\) of \( \Large \triangle ABC\) meet in I. What is \( \Large \angle BIC\) equal to?
A). \( \Large 90 ^{\circ}  \frac{A}{4} \) 
B). \( \Large 90 ^{\circ} + \frac{A}{4} \) 
C). \( \Large 90 ^{\circ}  \frac{A}{2} \) 
D). \( \Large 90 ^{\circ} + \frac{A}{2} \) 

8). In the figure given below, \( \Large \angle PQR\) = \( \Large 90 ^{\circ} \) and QL is a median, PQ = 5 cm and QR = 12 cm. Then, QL is equal to
A). 5 cm 
B). 5.5 cm 
C). 6 cm 
D). 6.5 cm 

9). ABC and XYZ are two similar triangles with \( \Large \angle C\) = \( \Large \angle Z\), whose areas are respectively 32 and 60.5. If XY = 7.7 cm, then what is AB equal to?
A). 5.6 cm 
B). 5.8 cm 
C). 6.0 cm 
D). 6.2 cm 

10). ABC is a triangle right angled at A and a \( \Large \perp AD \) is drawn on the hypotenuse BC. What is BC.AD equal to?
A). AB.AC 
B). AB.AD 
C). CA.CD 
D). AD.DB 
