Geometry (Part-2)

Total Questions: 50

41. It is given that the area of a triangle is A. The values of its perimeter, inradius, circumradius and the average of the lengths of the medians are respectively p, r, R and d. The ratio A : p is equal to [SSC CHSL 10/07/2019 (Afternoon)]

Correct Answer: (b)
Solution:

42. A regular hexagon is inscribed in a circle. What is the ratio of the area of the circle to that of its portion not covered by the hexagon? [SSC CHSL 10/07/2019 (Morning)]

Correct Answer: (a)
Solution:

43. In a stadium an athlete is running on a circular path with uniform speed during a practice session. The angle covered by him during one second is found to be 10º by a coach observing him from the centre of the circular track. What would be the measure of angle (in degrees) described by the athlete by an observer standing on the circle? [SSC CHSL 09/07/2019 (Evening)]

Correct Answer: (a) 5
Solution:

44. The circumcentre, incentre, orthocentre and the centroid of a triangle are one and the same point. The triangle must be: [SSC CHSL 09/07/2019 (Evening)]

Correct Answer: (d) equilateral
Solution:Equilateral Triangle (only in equilateral triangle all converge at a point)

45. There is a polygon of 11 sides. How many triangles can be drawn by only using the vertices of the polygon? [SSC CHSL 08/07/2019 (Afternoon)]

Correct Answer: (a) 165
Solution:

46. In a circle with centre O, AB is a diameter. Points C, D and E are on the circle on one side of AB such that ABEDC is a pentagon. The sum of angles ACD and DEB is: [SSC CHSL 04/07/2019 (Morning)]

Correct Answer: (c) 270°
Solution:

47. In ∆ABC, D is a point on BC such that ∠BAD = 1/2 ∠ADC , ∠BAC = 87º and ∠C = 42º. What is the measure of angle ADB ? [SSC CHSL 04/07/2019 (Morning)]

Correct Answer: (d) 78°
Solution:

48. In a circle with centre O, A diameter AB and a chord CD intersect each other at E, AC and AD are joined. If ∠BOC = 48º and ∠AOD = 100°, then what is the measure of ∠CEB ? [SSC CHSL 03/07/2019 (Evening)]

Correct Answer: (b) 74º
Solution:

49. In ∆ABC, AD, the bisector of ∠A, meets BC at D. If BC = a, AC = b and AB = c, then BD-DC = [SSC CHSL 03/07/2019 (Afternoon)]

Correct Answer: (c)
Solution:

50. In a circle with centre O, ABDC is a cyclic quadrilateral with AB as a diameter of the circle. AC and BD produced meet at E. If ∠CED = 70º then what is the measure of ∠COD ? [SSC CHSL 03/07/2019 (Afternoon)]

Correct Answer: (d) 40º
Solution: