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Mensuration 2D

SSC CGL Quant. Try each one first, then open its answer.

Top 10 SSC CGL PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 13 times: 17 Jul 2023 S3, 17 Jul 2023 S4, 18 Jul 2023 S4, 19 Jul 2023 S3, 26 Jul 2023 S2, 17 Sep 2024 S1, 19 Sep 2024 S3, 14 Sep 2025 S1, 14 Sep 2025 S3, 15 Sep 2025 S2, 23 Sep 2025 S3, 24 Sep 2025 S2, 26 Sep 2025 S1. This one: 26 Sep 2025 S1 See all 13 of this type

    57
    A sector of radius 14 cm has an area of 154 cm2154\text{ cm}^2. Find the angle of the sector.

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  2. Question 2

    This type asked 12 times: 17 Jul 2023 S2, 19 Jul 2023 S1, 21 Jul 2023 S4, 12 Sep 2024 S3, 13 Sep 2024 S1, 17 Sep 2024 S1, 26 Sep 2024 S2, 12 Sep 2025 S2, 15 Sep 2025 S3, 17 Sep 2025 S2, 23 Sep 2025 S1, 26 Sep 2025 S3. This one: 26 Sep 2025 S3 See all 12 of this type

    56
    The angle subtended by an arc at the center is 72∘72^\circ, and its length is 22 cm. Find the radius of the circle.

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  3. Question 3

    This type asked 8 times: 17 Jul 2023 S4, 20 Jul 2023 S1, 21 Jul 2023 S3, 25 Jul 2023 S3, 9 Sep 2024 S2, 12 Sep 2024 S2, 13 Sep 2024 S3, 18 Sep 2024 S3. This one: 18 Sep 2024 S3 See all 8 of this type

    69
    Find the area (in cm2\text{cm}^2) of the sector, where the radius of the circle is 24 cm and length of the arc is 7 cm.

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  4. Question 4

    Asked 7 times: 12 Sep 2025 S3*, 13 Sep 2025 S3*, 14 Sep 2025 S2*, 17 Sep 2025 S1*, 17 Sep 2025 S3*, 18 Sep 2025 S2*, 19 Sep 2025 S1* (* = numbers or wording changed that year) See all 7 times it was asked

    67
    A sector of a circle has a central angle of 60∘60^\circ and a radius of 9 cm. Another sector of the same circle has a central angle of π3\frac{\pi}{3} radians. What is the ratio of the area of the first sector to the area of the second sector?

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  5. Question 5

    This type asked 7 times: 14 Sep 2025 S2, 15 Sep 2025 S1, 15 Sep 2025 S2, 16 Sep 2025 S1, 16 Sep 2025 S2, 20 Sep 2025 S1, 26 Sep 2025 S3. This one: 26 Sep 2025 S3 See all 7 of this type

    73
    What is the area of the segment formed by a chord in a circle of radius 10 cm, if the angle subtended at the center is 90∘90^\circ?

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  6. Question 6

    This type asked 7 times: 27 Jul 2023 S3, 9 Sep 2024 S3, 12 Sep 2024 S3, 13 Sep 2024 S1, 17 Sep 2024 S3, 18 Sep 2024 S1, 25 Sep 2024 S2. This one: 25 Sep 2024 S2 See all 7 of this type

    58
    A circular arc whose radius is 14 cm, makes an angle of 45∘45^\circ at the centre. Find the perimeter (in cm) of the sector. (Use π=227)\left(\text{Use } \pi = \frac{22}{7}\right)

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  7. Question 7

    Asked 6 times: 17 Jul 2023 S3*, 17 Jul 2023 S4*, 19 Jul 2023 S3*, 14 Sep 2025 S3*, 23 Sep 2025 S3*, 24 Sep 2025 S2 (* = numbers or wording changed that year) See all 6 times it was asked

    69
    A sector of a circle having a radius of 10 cm and has a central angle of 3π4\frac{3\pi}{4} radians. What is the area of the sector?

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  8. Question 8

    This type asked 6 times: 12 Sep 2025 S3, 13 Sep 2025 S3, 16 Sep 2025 S1, 18 Sep 2025 S3, 22 Sep 2025 S1, 23 Sep 2025 S3. This one: 23 Sep 2025 S3 See all 6 of this type

    59
    The ratio of areas of two regular polygons with same number of sides is 4:9. What is the ratio of their side lengths?

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  9. Question 9

    This type asked 6 times: 12 Sep 2025 S1, 12 Sep 2025 S2, 13 Sep 2025 S2, 14 Sep 2025 S1, 14 Sep 2025 S3, 16 Sep 2025 S2. This one: 16 Sep 2025 S2 See all 6 of this type

    68
    A circular fountain with a radius of 7 m is encircled by a grass bed that is 3.5 m wide. Determine the ratio of the area of the grass bed to the area of the fountain.

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  10. Question 10

    This type asked 5 times: 19 Sep 2025 S2, 21 Sep 2025 S1, 21 Sep 2025 S3, 23 Sep 2025 S1, 24 Sep 2025 S2. This one: 24 Sep 2025 S2 See all 5 of this type

    60
    A regular hexagonal nut has outer side 6 cm and inner hollow side 3 cm. What is the material approximate area in the cross-section?

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