Geometry

Total Questions: 50

21. The median AD of a triangle ABC is produced and a perpendicular CF is dropped on it. BE is perpendicular to AD. If BC = 34 cm and DF = 8 cm, what is the length (in cm) of BE? [Graduate Level 20/06/2024 (Shift-3)]

1. (a) 17
2. (b) 9
3. (c) 15
4. (d) 19

Correct Answer: (c) 15

Solution:

22. How many times does the hour hand and minute hand of a clock coincide in half a day? [Higher Secondary 20/06/2024 (Shift-2)]

1. (a) 55
2. (b) 22
3. (c) 11
4. (d) 44

Correct Answer: (c) 11

Solution:

23. If a transversal intersects two parallel lines, and the difference between two interior angles on the same side of the transversal is 40°, then find the smallest angle among the interior angles. [SSC CHSL Tier II (10/01/2024)]

1. (a) 70°
2. (b) 50°
3. (c) 40°
4. (d) 60°

Correct Answer: (a) 70°

Solution:

24. Which of the following statements is NOT true? [SSC CHSL Tier II (02/11/2023)]

1. (a)
2. (b)
3. (c)
4. (d)

Correct Answer: (d)

Solution:

25. △PQR is right angled at Q such that PQ = (x-y), QR = x and PR = (x+y). S is a point on QR such that QS = PQ. The ratio QS : SR for any values of x and y is : [SSC CPO 05/10/2023 (3rd Shift)]

1. (a) 1 : 3
2. (b) 1 : 2
3. (c) 2 : 1
4. (d) 3 : 1

Correct Answer: (d) 3 : 1

Solution:

26. Two circles with centres P and Q of radii 6 cm and 4 cm, respectively, touch each other internally. If the perpendicular bisector of PQ meets the bigger circle in A and B, then the value of AB is: [SSC CPO 05/10/2023 (2nd Shift)]

1. (a) √35 cm
2. (b) √5 cm
3. (c) 2√5 cm
4. (d) 2√35 cm

Correct Answer: (d) 2√35 cm

Solution:

27. Two circles of radius 13 cm and 15 cm intersect each other at points A and B. If the length of the common chord is 12 cm, then what is the distance between their centers? [SSC CPO 03/10/2023 (1st Shift)]

1. (a)
2. (b)
3. (c)
4. (d)

Correct Answer: (d)

Solution:

28. M is the mid-point of side QR of a parallelogram PQRS (P being on the top left hand, followed by other points going clockwise). The line SM is drawn intersecting PQ produced at T. What is the length (in terms of the length of SR) of PT? [SSC CHSL 10/08/2023 (1st Shift)]

1. (a)
2. (b)
3. (c)
4. (d)

Correct Answer: (c)

Solution:

29. Two circles with diameters 50 cm and 58 cm, respectively, intersect each other at points A and B, such that the length of the common chord is 40 cm. Find the distance (in cm) between the centres of these two circles. [SSC CHSL 08/08/2023 (3rd Shift)]

1. (a) 34
2. (b) 37
3. (c) 36
4. (d) 35

Correct Answer: (c) 36

Solution:

30. PQ is a chord of a circle. The tangent XR at X on the circle cuts PQ produced at R. If XR = 12cm PQ = x cm, QR = x -2 cm, then x (in cm) is: [SSC CHSL 04/08/2023 (3rd Shift)]

1. (a) 7
2. (b) 6
3. (c) 10
4. (d) 14

Correct Answer: (c) 10

Solution:

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