Geometry (Part-6)

Total Questions: 50

41. Let C be a circle with center O and PQ be the diameter of C. Let AB be a chord on C. If ∠QOB = 40°, ∠AOP = 80°, then find ∠AOB. [SSC CHSL 11/07/2024 (3rd Shift)]

Correct Answer: (d) 60°
Solution:

42. If L is the midpoint of side BC of ∆ABC and the area of ∆ABL is 15 cm², then the area (in sq cm) of ∆ABC is: [SSC CHSL 11/07/2024 (4th Shift)]

Correct Answer: (c) 30
Solution:

43. A right angled triangle of area 600 m² is to be made such that the hypotenuse is double the base. For the triangle, the hypotenuse is ________ more than the base. [SSC CHSL 11/07/2024 (4th Shift)]

Correct Answer: (a) 26.32 m
Solution:

44. From an external point A, tangents AP and AQ are drawn to a circle with centre O. If ∠APQ = 40°, then find ∠POQ. [SSC CPO 27/06/2024 (1st Shift)]

Correct Answer: (d) 80°
Solution:

45. What is the length of the arc of a circle whose radius is 35 cm and whose arc subtends an angle of 72° at the centre of the circle? [SSC CPO 27/06/2024 (2nd Shift)]

Correct Answer: (b) 44 cm
Solution:

46. In a ∆ABC, angle BAC = 30° and angle BCA = 60°. If AC = 13 cm and AB = 12 cm, then BC is equal to: [SSC CPO 27/06/2024 (3rd Shift)]

Correct Answer: (b) 5 cm
Solution:

47. Triangle DEF is an equilateral triangle with a side length of 12 cm. If point G is the mid-point of side DE, what is the length (in cm) of side FG? [SSC CPO 27/06/2024 (3rd Shift)]

Correct Answer: (b) 6√3
Solution:

48. Which of the following statements is/are correct? [SSC CPO 28/06/2024 (1st Shift)]

A. A triangle can have all angles less than 60°.
B. A triangle can have one obtuse angle.
C. A triangle can have two right angles.
D. A triangle can have two acute angles.

Correct Answer: (b) B and D
Solution:

B and D
A triangle can have two acute angles and a triangle can have one obtuse angle also.

49. If one angle of triangle PQR is greater than the sum of the other two, the triangle PQR will be: [SSC CPO 29/06/2024 (1st Shift)]

Correct Answer: (a) obtuse angle
Solution:An obtuse triangle is a triangle with one angle greater than 90º.

50. Taking any three of the line segments out of segments of length 2 cm, 5 cm, 7 cm and 8 cm, the number of triangles that can be formed is: [SSC CPO 29/06/2024 (2nd Shift)]

Correct Answer: (a) 2
Solution: