Mensuration · SSC CGL previous year questions

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2025 151 questions

Q712025 · 15 Sept 2025 · Shift 1
A right triangle has sides 3, 4, and 5. A smaller triangle is drawn inside it with its vertices on the sides of the larger triangle, such that it is similar to the larger triangle. If its perimeter is 6, what is its area?
1. A.1.5
2. B.2.4
3. C.3
4. D.6
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Answer: A
Q742025 · 15 Sept 2025 · Shift 1
There are two parallel chords measuring 16 cm and 12 cm, both situated on the same side of the centre of a circle. The space between the two chords is 2 cm. What is the radius of the circle?
1. A.8 cm
2. B.10 cm
3. C.12 cm
4. D.15 cm
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Answer: B
Q752025 · 15 Sept 2025 · Shift 1
What is the area of the segment formed by a chord in a circle of radius 12 cm, if the angle subtended at the centre is 150°?
1. A.60π − 36
2. B.36π − 36
3. C.60π − 72
4. D.36π − 72
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Answer: A
Q662025 · 15 Sept 2025 · Shift 2
A right circular cone has radius of 7 cm and a height of 24 cm. A sphere is placed inside the cone such that it touches the base and the slanted surface of the cone. Find the radius of this inscribed sphere.
1. A.5.25 cm
2. B.4.86 cm
3. C.3.82 cm
4. D.6.24 cm
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Answer: A
Q672025 · 15 Sept 2025 · Shift 2
If the perimeter of a regular octagon is 80 cm, what is the side length?
1. A.10 cm
2. B.8 cm
3. C.12 cm
4. D.6 cm
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Answer: A
Q682025 · 15 Sept 2025 · Shift 2
A circular wheel is divided into 8 equal sectors. If the area of one sector is 45 cm², what is the radius of the wheel?
1. A.8.6 cm
2. B.6.5 cm
3. C.10.7 cm
4. D.7.5 cm
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Answer: C
Q692025 · 15 Sept 2025 · Shift 2
If the lateral surface area of a prism is 240 cm² and height is 8 cm, what is the perimeter of the base?
1. A.30 cm
2. B.24 cm
3. C.36 cm
4. D.40 cm
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Answer: A
Q722025 · 15 Sept 2025 · Shift 2
If two circles are touching internally, how many common tangents do they have?
1. A.0
2. B.1
3. C.2
4. D.3
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Answer: B
Q742025 · 15 Sept 2025 · Shift 2
A sector of a circle with radius 6 cm has a central angle of 60°. What is the area of the corresponding segment?
1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4
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Answer: B
Q702025 · 15 Sept 2025 · Shift 3
The cost of fencing a circular ground at ₹120/m is ₹3,768. Find the radius of the ground.
1. A.5 m
2. B.10 m
3. C.15 m
4. D.20 m
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Answer: A
Q712025 · 15 Sept 2025 · Shift 3
A circular logo of radius 14 cm is fitted perfectly inside a square plaque. Find the area of unused square space around the circle.
1. A.168.25 cm²
2. B.56.78 cm²
3. C.161.54 cm²
4. D.64.26 cm²
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Answer: A
Q712025 · 14 Sept 2025 · Shift 1
A sector of a circle having a radius 14 cm has area 154 cm². Find the angle of the sector.
1. A.90°
2. B.120°
3. C.150°
4. D.180°
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Answer: A
Q702025 · 14 Sept 2025 · Shift 2
A cone is such that the area of its base equals its lateral surface area. If radius is r, find the slant height l.
1. A.r
2. B.2r
3. C.3r
4. D.4r
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Answer: A
Q712025 · 14 Sept 2025 · Shift 2
A square field of side 28 m has a circular pond in the center. If the area of the pond is 616 m², what is the area of the remaining field?
1. A.148 m²
2. B.168 m²
3. C.678 m²
4. D.682 m²
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Answer: B
Q662025 · 14 Sept 2025 · Shift 3
A circular path of 3 m width runs around a circular park with radius 8 m. What is the area of the path?
1. A.179.07 m²
2. B.131.09 m²
3. C.138.02 m²
4. D.144.05 m²
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Answer: A
Q692025 · 14 Sept 2025 · Shift 3
A sector of a circle has a radius of 10 cm and a central angle of $\frac{π}{6}$ radians. What is the area of the sector?
1. A.26.18 cm²
2. B.8.33 cm²
3. C.10.47 cm²
4. D.12.5 cm²
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Answer: A
Q742025 · 14 Sept 2025 · Shift 3
The diameter of a circle measures 25 cm. What is the maximum length of a chord in this circle?
1. A.12 cm
2. B.25 cm
3. C.50 cm
4. D.100 cm
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Answer: B
Q662025 · 13 Sept 2025 · Shift 1
The area of a sector of a circle with radius 7 cm and central angle 90° is:
1. A.38.48 cm²
2. B.35.2 cm²
3. C.40.5 cm²
4. D.42.62 cm²
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Answer: A
Q682025 · 13 Sept 2025 · Shift 1
What is the area of a sector with a central angle of 120° and radius 8 cm?
1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4
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Answer: A
Q722025 · 13 Sept 2025 · Shift 2
A circular pond is surrounded by a path 2 m wide. If the total area (pond + path) is 616 m² and the pond area is 452.16 m², what is the radius of the pond?
1. A.10 m
2. B.11 m
3. C.12 m
4. D.13 m
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Answer: C
Q722025 · 13 Sept 2025 · Shift 3
If the base of a prism is a regular hexagon of side 6 cm and the height is 10 cm, what is its volume?
1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4
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Answer: D
Q732025 · 13 Sept 2025 · Shift 3
Three concentric circles are designed as part of a target practice board. Their diameters form an arithmetic progression. If the smallest circle has a circumference of 6π cm and the largest circle has a circumference of 14π cm, what is the circumference of the middle circle?
1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4
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Answer: B
Q662025 · 12 Sept 2025 · Shift 2
A circular park having a radius of 14 m. If a 1.5 m wide path is built around it, what is the approximate area of the path?
1. A.139 m²
2. B.135 m²
3. C.142 m²
4. D.150 m²
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Answer: A
Q692025 · 12 Sept 2025 · Shift 2
What is the central angle of a sector with an arc length of 10 cm in a circle of radius 5 cm?
1. A.6 radians
2. B.3 radians
3. C.2 radians
4. D.4 radians
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Answer: C
Q692025 · 12 Sept 2025 · Shift 3
A right circular cone has a radius of 7 cm and height of 24 cm. What is the slant height?
1. A.25 cm
2. B.30 cm
3. C.35 cm
4. D.40 cm
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Answer: A