Geometry

 

1. The sum of the interior angles of a polygon is 1620°. The number of sides of the polygon are

   •  9
   •  11
   •  15
   •  12

2. A cyclic parallelogram having unequal adjacent sides is necessarily a :

   •  square
   •  rectangle
   •  rhombus
   •  trapezium

3. If the angles of a triangle are in the ratio 5 : 3 : 2, then the triangle could be :

   •  obtuse
   •  acute
   •  right
   •  isosceles

4. If one of the diagonals of a rhombus is equal to its side, then the diagonals of the rhombus are in the ratio:

   •  
   •  
   •  3 : 1
   •  2 : 1

5. In the given figure, ∠ ABC and ∠ DEF are two angles such that BA ⊥ ED and EF ⊥ BC, then find value of ∠ ABC + ∠ DEF.
   

   •  120°
   •  180°
   •  150°
   •  210°

6. In the given figure given below, E is the mid-point of AB and F is the midpoint of AD. if the area of FAEC is 13, what is the area of ABCD?
   

   •  19.5
   •  26
   •  39
   •  21

7. Give that segment AB and CD are parallel, if lines ℓ, m and n intersect at point O. Find the ratio of θ to ∠ODS
   

   •  2 : 3
   •  3 : 2
   •  3 : 4
   •  Data insufficient

8. AB ⊥ BC and BD ⊥ AC. CE bisects the angle C. ∠A = 30°. Then, what is ∠CED?
   

   •  30°
   •  60°
   •  45°
   •  65°

9. In triangle ABC, angle B is a right angle. If (AC) is 6 cm, and D is the mid – point of side AC. The length of BD is
   

   •  4 cm
   •  
   •  3 cm
   •  3 . 5 cm

10. ABCD is a square of area 4, which is divided into four non overlapping triangles as shown in the fig. Then the sum of the perimeters of the triangles is
    

    •  
    •  
    •  
    •  

11. The sides of a quadrilateral are extended to make the angles as shown below :
    
    What is the value of x?

    •  100
    •  90
    •  80
    •  75

12. Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side is

    •  1/2
    •  2/3
    •  1/4
    •  3/4

13. If two parallel lines are cut by two distinct transversals, then the quadrilateral formed by these four lines will always be a :

    •  parallelogram
    •  rhombus
    •  square
    •  trapezium

14. In the following figure, find ∠ADC.
    

    •  55°
    •  27.5°
    •  60°
    •  30°

15. In a triangle ABC, the internal bisector of the angle A meets BC at D. If AB = 4, AC = 3 and ∠A = 60°, then the length of AD is

    •  
    •  
    •  
    •  

16. In the figure AG = 9, AB = 12, AH = 6, Find HC.
    

    •  18
    •  12
    •  16
    •  6

17. In ∆ABC, DE || BC and AD/DB = 3/5. If AC = 5.6 cm, find AE.
    

    •  2.1 cm
    •  3.1 cm
    •  1.2 cm
    •  2.3 cm

18. In the given fig. AB || QR, find the length of PB.
    

    •  3 cm
    •  2 cm
    •  4 cm
    •  6 cm

19. In a triangle ABC, the lengths of the sides AB, AC and BC are 3, 5 and 6 cm, respectively. If a point D on BC is drawn such that the line AD bisects the angle A internally, then what is the length of BD?

    •  2 cm
    •  2.25 cm
    •  2.5 cm
    •  3 cm

20. The number of tangents that can be drawn to two non-intersecting circles is :

    •  4
    •  3
    •  2
    •  1