Geometry (Part-6)

Total Questions: 50

11. AB is parallel to DC in a trapezium ABCD. It is given that AB > DC and the diagonals AC and BD intersect at O. If AO = 3x - 15 OB = x + 9 OC = x - 5 and OD = 5, and x has two values x₁ and x₂, then the value of (x₁² + x₂²) is: [SSC CHSL 05/07/2024 (1st Shift)]

1. (a) 45
2. (b) 56
3. (c) 61
4. (d) 73

Correct Answer: (c) 61

Solution:

12. In triangle XYZ, XY = YZ and m angle X = 78º. Find the value of m angle Y. [SSC CHSL 05/07/2024 (1st Shift)]

1. (a) 24º
2. (b) 39°
3. (c) 34°
4. (d) 28°

Correct Answer: (a) 24º

Solution:

13. Two parallel chords are drawn in a circle of radius 25 cm. The distance between the two chords is 27 cm. If the length of one chord is 48 cm, then length of the other chord is equal to: [SSC CHSL 05/07/2024 (3rd Shift)]

1. (a) 42 cm
2. (b) 48 cm
3. (c) 30cm
4. (d) 36 cm

Correct Answer: (c) 30cm

Solution:

14. In a triangle ABC, BD is perpendicular to AC. E is a point on BC such that angle BEA = x°. If angle EAC = 38° and angle EBD = 40°, then the value of x is: [SSC CHSL 05/07/2024 (3rd Shift)]

1. (a) 88
2. (b) 82
3. (c) 48
4. (d) 96

Correct Answer: (a) 88

Solution:

15. If the angle of the sector with radius 7 cm is 120° then find the length of arc (in cm). (Use π = 22/7) [SSC CHSL 05/07/2024 (3rd Shift)]

1. (a) 67/3
2. (b) 22/3
3. (c) 47/3
4. (d) 44/3

Correct Answer: (d) 44/3

Solution:

16. Let ABC be a triangle such that ∠ABC = 70º and ∠ACB = 50º. Let O be the incentre of the triangle. Find ∠BOC. [SSC CHSL 05/07/2024 (4th Shift)]

1. (a) 120º
2. (b) 130°
3. (c) 100°
4. (d) 60°

Correct Answer: (a) 120º

Solution:

17. Let C be a circle with center O and AB be a chord of C such that the length of AB is equal to the radius of C. Let D be any point on major arc of AB. Find ∠AOB and ∠ADB, respectively. [SSC CHSL 08/07/2024 (1st Shift)]

1. (b) 90°; 60°
2. (c) 120°; 100°
3. (d) 100°; 80°
4. (a) 60°; 30°

Correct Answer: (a) 60°; 30°

Solution:

18. Two circles have radii of 27 cm and 36 cm. The distance between their centres is 45 cm. What is the length (in cm) of their common chord? [SSC CHSL 08/07/2024 (2nd Shift)]

1. (a) 47.5 cm
2. (b) 37.2 cm
3. (c) 40.5 cm
4. (d) 43.2 cm

Correct Answer: (d) 43.2 cm

Solution:

19. Find the altitude (in cm) of side MT of triangle MNT with side MN = 36 cm, MT = 36 cm and NT = 48 cm. [SSC CHSL 08/07/2024 (3rd Shift)]

1. (a) 18√3
2. (b) 16√5
3. (c) 12√5
4. (d) 24√3

Correct Answer: (b) 16√5

Solution:

20. Side BC of a ∆ABC is extended upto D such that CD = AC. If ∠BAD = 118º and ∠ACB = 80º, then the value of ∠ABC is equal to: [SSC CHSL 08/07/2024 (4th Shift)]

1. (a) 36°
2. (b) 27°
3. (c) 22°
4. (d) 32°

Correct Answer: (c) 22°

Solution:

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