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Day 11: CDS Maths

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

  1. Question 1

    Heights and Distances. This type asked 5 times: CDS 2 2016, CDS 1 2017, CDS 2 2021, CDS 2 2024, CDS 1 2026. This one: CDS 1 2026 See all 5 of this type

    45
    Two persons are on diametrically opposite sides of a tower. They measure the angles of elevation of the top of the tower as 30∘30^\circ and 60∘60^\circ respectively. If the height of the tower is 100 m, what is the approximate distance between the two persons ?

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  2. Question 2

    Mensuration 3D. This type asked 5 times: CDS 2 2017, CDS 1 2021, CDS 1 2022, CDS 2 2023, CDS 1 2026. This one: CDS 1 2026 See all 5 of this type

    58
    A sphere of diameter 14 cm is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is 14 cm. If the sphere is completely submerged in water, then how much will the level of water rise ?

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  3. Question 3

    Number System. This type asked 5 times: CDS 2 2016, CDS 1 2018, CDS 1 2020, CDS 1 2022, CDS 1 2026. This one: CDS 1 2026 See all 5 of this type

    21
    2727−940−37927^{27} - 9^{40} - 3^{79} is divisible by how many natural numbers less than 10 ?

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  4. Question 4

    Number System. This type asked 5 times: CDS 2 2016, CDS 1 2017, CDS 1 2022, CDS 1 2023, CDS 1 2026. This one: CDS 1 2026 See all 5 of this type

    31
    Let P=N2P = N^2 where N is an odd integer. What is the remainder when P is divided by 8 ?

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  5. Question 5

    Polynomials. This type asked 5 times: CDS 2 2017, CDS 1 2020, CDS 1 2021, CDS 2 2022, CDS 1 2026. This one: CDS 1 2026 See all 5 of this type

    6
    If (x−5)(x - 5) is the HCF of x2−x−px^2 - x - p and x2−qx−10x^2 - qx - 10, then what is the value of (p+q)(p + q) ?

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