Geometry (Part-4)

Total Questions: 50

41. If we extend a chord infinitely on both sides, then the chord becomes a________ . [SSC CGL 18/09/2024 (3rd Shift)]

Correct Answer: (c) secant
Solution:If we extend a chord infinitely on both sides, then the chord becomes a secant.

42. P, Q and R are the three angles of a triangle. If P - Q = 20º and Q - R = 26º then ∠P is equal to: [SSC CGL 19/09/2024 (1st Shift)]

Correct Answer: (d) 82°
Solution:

43. PQ and RS are common tangents to two circles intersecting at A and B. A and B, when produced on both sides, meet the tangents PQ and RS at X and Y, respectively. If AB = 3 cm and XY = 5cm then PQ is_________ . [SSC CGL 19/09/2024 (2nd Shift)]

Correct Answer: (d) 4 cm
Solution:

44. A quadrilateral PQRS is inscribed in a circle of centre O, such that PQ is a diameter and ∠PSR = 120º Find the value of ∠QPR. [SSC CGL 19/09/2024 (2nd Shift)]

Correct Answer: (a) 30°
Solution:

45. ∆ABC and ∆DEF are two triangles such that ∆ABC ≅ ∆FDE. If AB = 17 cm, angle B = 52º and ∠A = 95º, then which of the following options is true ? [SSC CGL 19/09/2024 (2nd Shift)]

Correct Answer: (b) DF = 17cm, ∠E = 33º
Solution:

46. In a kite ABCD, longer diagonal BD is drawn. If ∠ABD = 54º and ∠ADB = 50º, then what is the measure (in degrees) of the ∠DCB? [SSC CGL 19/09/2024 (3rd Shift)]

Correct Answer: (b) 76
Solution:

47. In ∆PQR, if PT is the median, then which of the following is correct? [SSC CGL 19/09/2024 (3rd Shift)]

Correct Answer: (b) PQ² + PR² = 2(PT² + QT²)
Solution:

48. In the following sets, which set represents the sides of a right-angled triangle? [SSC CGL 23/09/2024 (1st Shift)]

Correct Answer: (d) {5, 12, 13}
Solution:

We know that in a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.
After checking all options one by one, only option (d) satisfies
(5, 12, 13)
⇒ 5² + 12² = 13²
⇒ 25 + 144 = 169 ⇒ LHS, RHS

49. Which of the following are the angles of a scalene triangle? [SSC CGL 23/09/2024 (1st Shift)]

Correct Answer: (a) 60°, 30° and 90°
Solution:

We know that a scalene triangle has three angles of different measurments.
So, 60º, 30º, and 90º
Only, option (a) is the correct answer because in this option all angles are different.

50. The distance between the longest chord and the centre of a circle is: [SSC CGL 23/09/2024 (2nd Shift)]

Correct Answer: (a) Equal to zero unit
Solution:We know the longest chord of the circle is also called the diameter of the circle.
So, the distance between the longest chord and center of the circle = 0 unit.