Geometry (Part-10)

Total Questions: 50

11. Find the length of the arc if the angle at the centre of the circle of radius 7 units is 60°. [SSC CHSL 20/03/2023 (3rd Shift)]

Correct Answer: (c) 22/3 units
Solution:

12. In triangle XYZ, ∠Y is the smallest angle and ∠Y = 25 degree. If the ratio of the angle is 20:11:5. then what is the largest angle of ∆XYZ? [SSC CHSL 21/03/2023 (1st Shift)]

Correct Answer: (d) 100°
Solution:

13. Distance of a chord RS from the centre is 20 cm, If the length of this chord is 30 cm, then what will be the diameter of this circle? (in cm) [SSC CHSL 21/03/2023 (3rd Shift)]

Correct Answer: (d) 50
Solution:

14. A, B, C are three points such that AB = 9cm, BC = 11 cm and AC = 20 cm. The number of circles passing through points A, B, C is: [SSC CGL Tier II (02/03/2023)]

Correct Answer: (b) 0
Solution:

Rules for formation of triangle = sum of any two sides must be greater than the third side.
Here, AB + BC = AC
So, no triangle can be formed. and Thus no circle will be passed from the given points A, B, and C.

15. In ∆PQR, PQ QR and O is an interior point of ∆PQR such that ∠OPR= ∠ORP. Consider the following statements:  [SSC CGL Tier II (02/03/2023)]

(i) ∆POR is an isosceles triangle.
(ii) O is the centroid of ∆PQR.
(iii) ∆PQO is congruent to ∆RQO.
Which of the above statements are correct?

Correct Answer: (b) Only (i) and (iii))
Solution:

16. ABCD is a cyclic quadrilateral and BC is a diameter of the related circle on which A and D also lie. ∠BCA = 19° and ∠CAD  = 32°. What is the measure of ∠ACD? [SSC CGL Tier II (03/03/2023)]

Correct Answer: (d) 39°
Solution:

17. If the external angle of a regular polygon is 18°, then the number of diagonals in this polygon is: [SSC CGL Tier II (03/03/2023)]

Correct Answer: (c) 170
Solution:

18. If ∆ABC is right angled at B, AB = 12 cm and ∠CAB = 60°, determine the length of BC. [SSC CGL Tier II (06/03/2023)]

Correct Answer: (d) 12√3 cm
Solution:

19. Find the number of diagonals of a regular polygon, sum of whose interior angles is 2700°. [SSC CGL Tier II (06/03/2023)]

Correct Answer: (b) 119
Solution:

20. PQRS is a cyclic quadrilateral. If ∠P is three times of ∠R and ∠S is four times of ∠Q, then the sum of ∠S + ∠R will be: [SSC CGL Tier II (07/03/2023)]

Correct Answer: (d) 189°
Solution: