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Day 103: CDS Maths

5 questions (6 parts). Try each one first, then open its answer.

  1. Question 1

    Algebraic Identities and Simplification. Asked once: CDS 2 2023 (same type asked 4 times) See all 4 of this type

    69
    What is x2−y2−z2−2yzx2+y2−z2+2xy+x2−y2−z2−2yzx2−y2+z2−2xz\frac{x^2 - y^2 - z^2 - 2yz}{x^2 + y^2 - z^2 + 2xy} + \frac{x^2 - y^2 - z^2 - 2yz}{x^2 - y^2 + z^2 - 2xz} equal to ?

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  2. Question 2

    Mensuration 2D. Asked once: CDS 1 2025 (same type asked 4 times) See all 4 of this type

    17
    The adjacent sides of a parallelogram are 10 cm and 8 cm and the angle between them is 150∘150^\circ. What is the area of the parallelogram ?

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  3. Question 3

    Mensuration 2D. Asked once: CDS 1 2020 (same type asked 4 times) See all 4 of this type

    86
    What is the area of the largest square plate cut from a circular disk of radius one unit ?

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  4. Question 4 (case study, 2 parts)

    Mensuration 3D. Asked once: CDS 1 2025 (same type asked 4 times) See all 4 of this type

    The angle at the vertex of a conical body is 120∘120^\circ.
    69
    What is the ratio of the radius of the conical body to its slant height ?

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    70
    If the sum of slant height, height and radius is (9+33)(9 + 3\sqrt{3}) cm, then what is the volume of the cone ?

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  5. Question 5

    Percentage, Profit and Loss. Asked once: CDS 1 2024 (same type asked 4 times) See all 4 of this type

    5
    A person bought a book at 3/4th3/4^{\text{th}} of its listed price and sold it at 50% more than its listed price. What is the percentage of gain in the transaction ?

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