Geometry (Part-12)

Total Questions: 50

21. S and T are points on the sides PQ and PR, respectively, of ∆PQR such that PS × PR = PQ x PT. If ∠Q = 96º and ∠PST = ∠PRQ + 34°, then ∠QPR =? [SSC CGL Tier II (29/01/2022)]

1. (a) 26°
2. (b) 24°
3. (c) 22°
4. (d) 25°

Correct Answer: (c) 22°

Solution:

22. O is a point in the interior of ∆ABC such that OA = 12 cm, OC = 9cm, ∠AOB = ∠BOC = ∠COA and ∠ABC = 60º. What is the length (in cm) of OB? [SSC CGL Tier II (29/01/2022)]

1. (a) 6√2
2. (b) 6√3
3. (c) 4√3
4. (d) 4√6

Correct Answer: (b) 6√3

Solution:

23. ABCD is a quadrilateral in which AB || DC. E and F are the midpoints of the diagonals AC and BD, respectively. If AB = 18 cm and CD = 6cm, then EF = ? [SSC CGL Tier II (29/01/2022)]

1. (a) 12
2. (b) 9
3. (c) 6
4. (d) 8

Correct Answer: (c) 6

Solution:

24. A₁ and A₂ are two regular polygons. The sum of all the interior angles of A₁, is 1080°. Each interior angle of A₂ exceeds its exterior angle by 132°. The sum of the number of sides A₁ and A₂ is: [SSC CGL Tier II (03/02/2022)]

1. (a) 21
2. (b) 22
3. (c) 23
4. (d) 24

Correct Answer: (c) 23

Solution:

25. ABCD is a cyclic quadrilateral. Sides AB and DC, when produced, meet at E and sides AD and BC when produced, meet at F. If ∠ADC = 76º and ∠AED = 55º then ∠AFB is equal to: [SSC CGL Tier II (03/02/2022)]

1. (a) 34°
2. (b) 26°
3. (c) 29°
4. (d) 27°

Correct Answer: (d) 27°

Solution:

26. In ∆ABC, D and E are points on the sides BC and AB, respectively, such that ∠ACB = ∠DEB. If AB = 12 cm, BE = 5 cm and BD : CD = 1 : 2 then BC is equal to: [SSC CGL Tier II (03/02/2022)]

1. (a) 8√3 cm
2. (b) 5√5 cm
3. (c) 6√5 cm
4. (d) 6√3 cm

Correct Answer: (c) 6√5 cm

Solution:

27. In a square ABCD, diagonals AC and BD intersect at O. The angle bisector of ∠CAB meets BD and BC at F and G. respectively. OF : CG is equal to: [SSC CGL Tier II (03/02/2022)]

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

Correct Answer: (a) 1 : 2

Solution:

28. In ΔΑΒC, ∠A = 50º, BE and CF are perpendiculars on AC and AB at E and F, respectively. BE and CF intersect at H. The bisectors of ∠HBC and ∠HCB intersect at P. ∠BPC is equal to: [SSC CGL Tier II (03/02/2022)]

1. (a) 155°
2. (b) 100°
3. (c) 115°
4. (d) 120°

Correct Answer: (a) 155°

Solution:

29. In equilateral ∆ABC, D and E are points on the sides AB and AC, respectively, such that AD = CE, BE and CD intersect at F. The measure (in degrees) of ∠CFB is: [SSC CGL Tier II (03/02/2022)]

1. (a) 120°
2. (b) 135°
3. (c) 125°
4. (d) 105°

Correct Answer: (a) 120°

Solution:

30. In ∆ABC, D is a point on BC such that ∠ADB = 2∠DAC, ∠BAC = 70° and ∠B = 56°. What is the measure of ∠ADC? [SSC CGL Tier II (03/02/2022)]

1. (a) 72°
2. (b) 54°
3. (c) 74°
4. (d) 81°

Correct Answer: (a) 72°

Solution:

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