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Day 23: CDS Maths

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

  1. Question 1

    Mensuration 2D. This type asked 4 times: CDS 2 2018, CDS 2 2019, CDS 2 2023, CDS 1 2024. This one: CDS 1 2024 See all 4 of this type

    40
    What is the area of the region between two concentric circles, if the length of a chord of the outer circle touching the inner circle at a particular point of its circumference is 14 cm ? (Take π=227\pi = \frac{22}{7})

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  2. Question 2

    Quadratic Equations. This type asked 4 times: CDS 2 2020, CDS 2 2021, CDS 2 2022, CDS 1 2024. This one: CDS 1 2024 See all 4 of this type

    14
    What is the greatest value of k for which 2x2−4x+k=02x^2 - 4x + k = 0 has real roots ?

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  3. Question 3

    Surds, Indices and Simplification. This type asked 4 times: CDS 1 2019, CDS 2 2019, CDS 1 2022, CDS 1 2024. This one: CDS 1 2024 See all 4 of this type

    36
    If 1a+1b+1c+1d+1e=421972\cfrac{1}{a + \cfrac{1}{b + \cfrac{1}{c + \cfrac{1}{d + \cfrac{1}{e}}}}} = \frac{421}{972}, then what is the value of a×b×c×d×ea \times b \times c \times d \times e ?

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  4. Question 4

    Algebraic Identities and Simplification. This type asked 4 times: CDS 1 2021, CDS 2 2021, CDS 2 2022, CDS 2 2023. This one: CDS 2 2023 See all 4 of this type

    74
    If p=a2(b−a)(c−a)p = \frac{a^2}{(b - a)(c - a)}, q=b2(c−b)(a−b)q = \frac{b^2}{(c - b)(a - b)}, r=c2(a−c)(b−c)r = \frac{c^2}{(a - c)(b - c)}, then what is (p+q+r)2(p + q + r)^2 equal to ?

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  5. Question 5

    Mensuration 3D. This type asked 4 times: CDS 1 2019, CDS 1 2021, CDS 1 2022, CDS 2 2023. This one: CDS 2 2023 See all 4 of this type

    65
    Three solid lead spheres of diameters 6 cm, 8 cm and 10 cm are melted together and recast as a solid sphere. What is the percentage diminution of the surface area as compared to the sum of the surface areas of the three spheres ?

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