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Day 7: CDS Maths

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

  1. Question 1

    Trigonometric Ratios and Identities. This type asked 6 times: CDS 2 2016, CDS 1 2019, CDS 2 2019, CDS 2 2021, CDS 1 2022, CDS 1 2023. This one: CDS 1 2023 See all 6 of this type

    51
    What is the value of cos⁡232∘+cos⁡258∘sec⁡250∘−cot⁡240∘+4tan⁡13∘tan⁡37∘tan⁡53∘tan⁡77∘\frac{\cos^2 32^\circ + \cos^2 58^\circ}{\sec^2 50^\circ - \cot^2 40^\circ} + 4\tan 13^\circ \tan 37^\circ \tan 53^\circ \tan 77^\circ ?

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  2. Question 2

    Circles. This type asked 5 times: CDS 2 2016, CDS 1 2022, CDS 2 2023, CDS 2 2025, CDS 2 2026. This one: CDS 2 2026 See all 5 of this type

    57
    The chord of a circle is 20 cm and the height of the minor segment is 5 cm. What is the diameter of the circle ?

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  3. Question 3

    Heights and Distances. This type asked 5 times: CDS 2 2016, CDS 1 2022, CDS 1 2023, CDS 1 2026, CDS 2 2026. This one: CDS 2 2026 See all 5 of this type

    44
    A person walking along a straight road observes that at two consecutive kilometer-stones the angles of elevation of a hill in front of him are 30∘30^\circ and 60∘60^\circ respectively. What is the height of the hill ?

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  4. Question 4

    Mensuration 2D. 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

    Mensuration 2D. 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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