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Logarithms

CDS Maths. Try each one first, then open its answer.

Top 10 CDS PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 9 times: CDS 2 2016, CDS 1 2017, CDS 2 2018, CDS 1 2019, CDS 2 2019, CDS 1 2020, CDS 2 2023, CDS 2 2025, CDS 2 2026. This one: CDS 2 2026 See all 9 of this type

    9
    What is the number of zeros immediately after the decimal point in (0.5)1000(0.5)^{1000} ? (Given that log⁡102=0.30103\log_{10} 2 = 0.30103)

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  2. Question 2

    Asked 7 times: CDS 2 2016*, CDS 1 2017*, CDS 1 2019*, CDS 2 2019*, CDS 1 2020*, CDS 2 2023*, CDS 2 2025 (* = numbers or wording changed that year) See all 7 times it was asked

    10
    If log⁡102=0.301\log_{10}2=0.301 and log⁡103=0.477\log_{10}3=0.477, then what is the number of digits in the expansion of 606060^{60}?

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  3. Question 3

    This type asked 4 times: CDS 2 2017, CDS 2 2018, CDS 1 2021, CDS 1 2026. This one: CDS 1 2026 See all 4 of this type

    29
    If log⁡10(80)=p\log_{10}(80) = p, log⁡10(45)=q\log_{10}(45) = q and log⁡10(216)=r\log_{10}(216) = r, then what is log⁡10(384)\log_{10}(384) equal to ?

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  4. Question 4

    This type asked 4 times: CDS 2 2016, CDS 2 2020, CDS 1 2021, CDS 2 2021. This one: CDS 2 2021 See all 4 of this type

    20
    If 5x−1=(2.5)log⁡1055^{x-1}=(2.5)^{\log_{10}5}, then what is the value of xx ?

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  5. Question 5

    This type asked 2 times: CDS 2 2022, CDS 2 2025. This one: CDS 2 2025 See all 2 of this type

    37
    If α\alpha and β\beta are the roots of the equation log⁡10[998+x2−18x+76]=3\log_{10}\left[998 + \sqrt{x^2 - 18x + 76}\right] = 3 then what is (α−β)2(\alpha - \beta)^2 equal to?

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  6. Question 6

    Asked once: CDS 1 2021 (same type asked 4 times) See all 4 of this type

    41
    What is log⁡1031.25\log_{10} 31.25 equal to?

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  7. Question 7

    Asked once: CDS 1 2021 (same type asked 4 times) See all 4 of this type

    45
    If 5x−3=85^{x-3} = 8, then what is xx equal to?

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  8. Question 8

    Asked once: CDS 2 2022 (same type asked 2 times) See all 2 of this type

    24
    If log⁡10[995+x2−12x+60]=3\log_{10}\left[995 + \sqrt{x^2 - 12x + 60}\right] = 3, then what is the sum of the roots of the equation ?

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  9. Question 9

    Asked once: CDS 2 2018 (same type asked 4 times) See all 4 of this type

    14
    If log⁡102=0.3010\log_{10} 2 = 0.3010 and log⁡103=0.4771\log_{10} 3 = 0.4771, then the value of log⁡100(0.72)\log_{100} (0.72) is equal to

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  10. Question 10

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

    43
    If 63−4x 4x+5=86^{3 - 4x}\, 4^{x + 5} = 8 (Given log⁡102=0.301\log_{10} 2 = 0.301 and log⁡103=0.477\log_{10} 3 = 0.477), then which one of the following is correct ?

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