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Day 21: CDS Maths

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

  1. Question 1

    Quadratic Equations. This type asked 4 times: CDS 2 2018, CDS 1 2019, CDS 2 2024, CDS 1 2025. This one: CDS 1 2025 See all 4 of this type

    1
    A real number M is squared to give the value N. What is the minimum value of (M+N)(M + N) ?

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  2. Question 2

    Quadratic Equations. This type asked 4 times: CDS 2 2016, CDS 1 2019, CDS 1 2022, CDS 1 2025. This one: CDS 1 2025 See all 4 of this type

    79
    If p (≠0)p\,(\ne 0) and q (≠0)q\,(\ne 0) are the roots of the equation x2+px+q=0x^2 + px + q = 0, then what is p2+q2p^2 + q^2 equal to ?

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  3. Question 3

    Surds, Indices and Simplification. This type asked 4 times: CDS 2 2017, CDS 2 2019, CDS 1 2020, CDS 1 2025. This one: CDS 1 2025 See all 4 of this type

    77
    If p=0.09‾p = 0.0\overline{9}, then what is the value of 70p2+43p−570p^2 + 43p - 5 ?

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  4. Question 4

    Time, Speed and Distance. This type asked 4 times: CDS 2 2016, CDS 1 2020, CDS 1 2021, CDS 1 2025. This one: CDS 1 2025 See all 4 of this type

    46
    Travelling at 3/5th3/5^{\text{th}} of his usual speed, a man is late by 20 minutes. What is the usual time if he travels with his usual speed ?

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  5. Question 5

    Averages. This type asked 4 times: CDS 2 2016, CDS 1 2017, CDS 2 2020, CDS 2 2024. This one: CDS 2 2024 See all 4 of this type

    21
    The arithmetic mean of nn numbers is MM. If the sum of first (n−1)(n - 1) terms is kk, then what is the nnth number ?

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