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Day 5: CDS Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Time and Work. This type asked 6 times: CDS 1 2017, CDS 1 2018, CDS 2 2018, CDS 2 2020, CDS 1 2021, CDS 1 2026. This one: CDS 1 2026 See all 6 of this type

    15
    12 men working 8 hours a day can completely build a wall of length 100 m, breadth 20 cm and height 5 m in 10 days. How many days will 16 men working 10 hours a day require to build a wall of length 200 m, breadth 60 cm and height 5 m ?

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  2. Question 2

    Mensuration 2D. 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

    Mensuration 2D. 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

    Triangles. This type asked 6 times: CDS 1 2019, CDS 1 2021, CDS 1 2023, CDS 2 2023, CDS 1 2025, CDS 2 2025. This one: CDS 2 2025 See all 6 of this type

    72
    ABCABC is a triangle right angled at BB. DD is a point on ACAC such that BDBD is perpendicular to ACAC. If AB=pAB = p and BC=3pBC = \sqrt{3}p, then what is BDBD equal to?

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  5. Question 5

    Trigonometric Ratios and Identities. This type asked 6 times: CDS 2 2021, CDS 1 2022, CDS 1 2023, CDS 2 2023, CDS 1 2025, CDS 2 2025. This one: CDS 2 2025 See all 6 of this type

    33
    If 2tan⁡θ=sec⁡2θ−22\tan\theta = \sec^2\theta - 2, where 0<θ<π/20 < \theta < \pi/2, then what is cot⁡θ\cot\theta equal to?

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