Geometry (Part-4)

Total Questions: 50

11. ∆ABC and ∆RPQ are congruent, then the side of ∆ABC that corresponds to PQ is: [SSC CGL 11/09/2024 (2nd Shift)]

Correct Answer: (d) BC
Solution:

12. In a ∆ABC, if 1/2 ∠A + ∠B + ∠C = 120°, then the value of 1/2 ∠A is: [SSC CGL 11/09/2024 (3rd Shift)]

Correct Answer: (d) 30°
Solution:

13. P and Q are centres of two circles whose radii are 7 cm and 3 cm, respectively. If the direct common tangents to the circles meet PQ extended at A, then A divides PQ ______ . [SSC CGL 11/09/2024 (3rd Shift)]

Correct Answer: (c) externally in the ratio 7:3
Solution:

14. Consider a triangle PQR, right angled at R, in which PQ = 29 units, QR = 21 units and ∠PQR = θ. Find the value of cos²θ - sin²θ. [SSC CGL 11/09/2024 (3rd Shift)]

Correct Answer: (d)
Solution:

15. In ∆ABC, two medians AD and BE intersect at G at right angles. If AD = 12 cm and BE = 9 cm, then the length of AB is equal to: [SSC CGL 11/09/2024 (3rd Shift)]

Correct Answer: (d) 10 cm
Solution:

16. In a triangle PQR, S is a point on the side QR such that PS⊥QR, then which of the following options is true? [SSC CGL 12/09/2024 (1st Shift)]

Correct Answer: (b) PR² + QS² = PQ² + SR²
Solution:

17. In triangles ABC and DEF, AB = FD and ∠A = ∠D. The two triangles are congruent by SAS criterion if : [SSC CGL 12/09/2024 (1st Shift)]

Correct Answer: (d) AC = DE
Solution:

18. The measures of the three angles of a triangle are in the ratio 17:13:15. Find the positive difference between the greatest and the smallest of these three angles. [SSC CGL 12/09/2024 (1st Shift)]

Correct Answer: (a) 16°
Solution:

19. In triangle ABC, the length of side BC is 2 cm less than twice the length of side AB. The length of side AC exceeds the length of side AB by 10 cm. The perimeter of the triangle is 40 cm. Determine the length (in cm) of the smallest side of the triangle. [SSC CGL 12/09/2024 (2nd Shift)]

Correct Answer: (d) 8
Solution:

20. In ∆DEF, the bisector of ∠D intersects side EF at point N. If DE = 36 cm, DF = 40 cm and EF = 38 cm, then the length (in cm) of NF is ________ . [SSC CGL 12/09/2024 (2nd Shift)]

Correct Answer: (b) 20
Solution: