Geometry (Part-6)

Total Questions: 50

31. A line from point A is drawn that is tangent to the circle at point B. A secant is also drawn from point A to the circle intersecting it at points C and D. If AB = 42 cm and AC = 21 cm, then what is the ratio between AB and CD? [SSC CHSL 10/07/2024 (2nd Shift)]

Correct Answer: (d) 2 : 3
Solution:

32. The sides AB and AC of △ABC are produced to points D and E, respectively. The bisectors of ∠CBD and ∠BCE meet at P. If ∠A = 72º, then the measure of ∠P is: [SSC CHSL 10/07/2024 (3rd Shift)]

Correct Answer: (b) 54°
Solution:

33. If three sides of a triangle are 6 cm, 8 cm and 10 cm, then the area of the triangle is: [SSC CHSL 09/07/2024 (4th Shift)]

Correct Answer: (a) 24 cm²
Solution:

34. Let ABCD be a quadrilateral and AC, BD be diagonals. The length of BD = 20 cm and the heights of the triangles ABD and BCD are, respectively, 6 cm, 8 cm. Find the area of the quadrilateral ABCD (in cm²). [SSC CHSL 10/07/2024 (3rd Shift)]

Correct Answer: (a) 140
Solution:

35. In ∆ABC, if AB = √3 units. BC = 1 unit and AC = 2 units, then ∠ACB is equal to: [SSC CHSL 10/07/2024 (4th Shift)]

Correct Answer: (c) 60°
Solution:

36. PBA and PDC are two secants. AD is the diameter of the circle with the centre at O. ∠A = 30º ∠P = 20º Find the measure of ∠DBC. [SSC CHSL 11/07/2024 (1st Shift)]

Correct Answer: (d) 40°
Solution:

37. What is the area of a quadrilateral ABCD. (shown below) in which sides AB and BC are equal, sides AD and CD are of lengths 5 cm and 13 cm, respectively, and side AD is perpendicular to the diagonal AC? [SSC CHSL 11/07/2024 (1st Shift)]

Correct Answer: (a) 78 cm²
Solution:

38. Find the altitude (in cm) from the vertex Q to side PR of triangle PQR with side lengths PQ = 40 cm, PR = 40 cm and QR = 60 cm. [SSC CHSL 11/07/2024 (1st Shift)]

Correct Answer: (c) 15√7
Solution:

39. Which of the following is NOT true regarding a circle? [SSC CHSL 11/07/2024 (2nd Shift)]

Correct Answer: (a) Given any three points in a plane, there is always a circle passing through these points
Solution:Option (a) is not true as ''There is no circle passing through any three points in any plane''.

40. ΔΑΒC~AEDF and area(∆ABC): area (∆EDF )=1 : 4. If AB = 7 cm, BC = 8 cm and CA = 9 cm, then DF is equal to: [SSC CHSL 11/07/2024 (3rd Shift)]

Correct Answer: (d) 16 cm
Solution: