Geometry (Part-5)

Total Questions: 50

41. Two circles of diameters 16 cm and 20 cm are such that the distance between their centers is 13 cm. What is the length (in cm) of a common tangent to these circles that does not intersect the line joining the centers? [SSC CHSL 02/07/2024 (3rd Shift)]

Correct Answer: (b) √165
Solution:

42. If ∆ABC ~ ∆QRP; area of ∆ABC: area of ∆PQR = 9 : 4; AB = 18 cm and BC = 15 cm, then find the length of PR. [SSC CHSL 02/07/2024 (3rd Shift)]

Correct Answer: (c) 10 cm
Solution:

43. In ΔEFG, XY || FG, area of the quadrilateral XFGY = 44 m². If EX : XF = 2 : 3, then find the area of ∆EXY (in m²). [SSC CHSL 02/07/2024 (4th Shift)]

Correct Answer: (c) 8.38
Solution:

44. Two circles touch each other externally at M. PQ is a direct common tangent to the two circles, P and Q are points of contact and ∠MPQ = 38°. ∠MQP is: [SSC CHSL 03/07/2024 (2nd Shift)]

Correct Answer: (c) 52°
Solution:

45. In a right-angled triangle ABC such that ∠BAC = 90º and AD is perpendicular to BC. If the area of ∆ABC is 63 cm², area of ∆ACD = 7cm², and AC = 5 cm, then the length of BC is equal to: [SSC CHSL 03/07/2024 (2nd Shift)]

Correct Answer: (d) 15 cm
Solution:

46. A, B, C are three points such that AB = 11cm, BC = 13 cm and AC = 24cm. Number of circles passing through the points A, B, C is: [SSC CHSL 03/07/2024 (2nd Shift)]

Correct Answer: (a) 0
Solution:

If AB = 11cm, BC = 13cm, and AC = 24cm these three point A,B and C lie on a straight line
Since the points are collinear, the number of circles that can pass through all three points is 0.
No circle can be drawn through three collinear points

47. A circle of diameter 26 cm has two equal parallel chords of length 10 cm each, then the distance between the two chords is: [SSC CHSL 03/07/2024 (2nd Shift)]

Correct Answer: (b) 24 cm
Solution:

48. PQ is parallel to SR in a trapezium PQRS. It is given that PQ > SR and the diagonals PR and QS intersect at O. If PO = 3 x - 15, OQ = x + 9, OR = x - 5 and OS = 5 and x has two values x₁and x₂, then the value of (x₁²-x₂²) is: [SSC CHSL 03/07/2024 (3rd Shift)]

Correct Answer: (b) 11
Solution:

49. If the perimeters of two similar triangles are in the ratio of 4:7, and the sum of the areas is 195 cm², then what 1/3 is of the difference between the areas (in cm²) of the two triangles? [SSC CHSL 03/07/2024 (4th Shift)]

Correct Answer: (b) 33
Solution:

50. Two parallel chords of length 8 units each are 6 units away from each other in a circle. [SSC CHSL 03/07/2024 (4th Shift)]

What is the radius of the circle in units?

Correct Answer: (b) 5
Solution: