PYQ Vault

Mensuration 2D

CDS Maths. Try each one first, then open its answer.

Top 10 CDS 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 8 times: CDS 2 2016, CDS 2 2017, CDS 2 2018, CDS 1 2019, CDS 2 2020, CDS 2 2022, CDS 2 2024, CDS 2 2025. This one: CDS 2 2025 See all 8 of this type

    75
    The sides of a triangle are 11 cm, 60 cm and 61 cm. What is the area of the triangle formed by joining the mid-points of the sides of the triangle?

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  2. Question 2

    This type asked 6 times: CDS 2 2017, CDS 1 2019, CDS 1 2020, CDS 2 2020, CDS 2 2023, CDS 2 2025. This one: CDS 2 2025 See all 6 of this type

    76
    A pendulum swings through an angle of 30∘30^\circ and its end describes an arc of length 55 cm. What is the length of the pendulum? (Take π=22/7\pi = 22/7)

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  3. Question 3

    This type asked 6 times: CDS 1 2017, CDS 1 2018, CDS 1 2019, CDS 1 2021, CDS 1 2022, CDS 2 2025. This one: CDS 2 2025 See all 6 of this type

    79
    A wire is in the form of an equilateral triangle with an area of 36336\sqrt{3} cm2^2. If it is changed into a semicircle, then what is its radius?

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  4. Question 4

    This type asked 5 times: CDS 2 2020, CDS 2 2021, CDS 2 2022, CDS 1 2024, CDS 2 2026. This one: CDS 2 2026 See all 5 of this type

    53
    A chord of a circle makes an angle of 90∘90^\circ at the centre of the circle. If the area of the major segment is k times the area of the minor segment, then what is the value of k ? (Take π=227\pi = \frac{22}{7})

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  5. Question 5

    This type asked 5 times: CDS 1 2020, CDS 2 2020, CDS 2 2021, CDS 1 2022, CDS 2 2026. This one: CDS 2 2026 See all 5 of this type

    52
    The area of a rhombus is 720 cm2\text{cm}^2 and the sum of its diagonals is 98 cm. What is the perimeter of the rhombus ?

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  6. Question 6

    This type asked 5 times: CDS 1 2019, CDS 1 2020, CDS 1 2021, CDS 1 2023, CDS 1 2025. This one: CDS 1 2025 See all 5 of this type

    84
    An arc AB of a circle subtends an angle x radian at the centre O. If the area of the sector AOB is equal to half of the square of length of arc AB, then what is x equal to ?

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  7. Question 7

    This type asked 5 times: CDS 2 2016, CDS 2 2018, CDS 1 2019, CDS 1 2020, CDS 2 2020. This one: CDS 2 2020 See all 5 of this type

    79
    If the perimeter of a circle and a square are equal, then what is the ratio of the area of the circle to that of the square ?

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  8. Question 8

    Asked 4 times: CDS 2 2016*, CDS 2 2017*, CDS 2 2018*, CDS 2 2024 (* = numbers or wording changed that year) See all 4 times it was asked

    50
    What is the area of a triangle having sides 4, 4 and 6 units ?

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  9. Question 9

    This type asked 4 times: CDS 2 2018, CDS 2 2022, CDS 1 2025, CDS 1 2026. This one: CDS 1 2026 See all 4 of this type

    71
    A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question : A circle is inscribed in the equilateral triangle Δ\Delta. What is the radius of the circle ? Statement-I : Area of Δ\Delta is equal to 16316\sqrt{3} cm2\text{cm}^2. Statement-II : Perimeter of Δ\Delta is 24 cm. Which one of the following is correct in respect of the above Question and the Statements ?

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  10. Question 10

    This type asked 4 times: CDS 1 2022, CDS 2 2024, CDS 1 2025, CDS 2 2025. This one: CDS 2 2025 See all 4 of this type

    71
    In a triangle ABCABC, ∠A=30∘\angle A = 30^\circ, AB=7AB = 7 cm and AC=12AC = 12 cm. What is the area of the triangle ABCABC?

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