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Day 1: CDS Maths

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

  1. Question 1

    Logarithms. 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

    Number System. This type asked 9 times: CDS 1 2018, CDS 2 2020, CDS 2 2021, CDS 2 2022, CDS 1 2023, CDS 2 2023, CDS 2 2025, CDS 1 2026, CDS 2 2026. This one: CDS 2 2026 See all 9 of this type

    23
    A number N consists of two digits. The digit in the tens place is 3 times the digit in the units place. The digits are reversed and the resulting number is denoted by R. If N×R=3627N \times R = 3627, then what is the product of the digits of the number N ?

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  3. Question 3

    Polynomials. This type asked 9 times: CDS 2 2020, CDS 1 2021, CDS 2 2022, CDS 2 2023, CDS 1 2024, CDS 2 2024, CDS 1 2025, CDS 2 2025, CDS 2 2026. This one: CDS 2 2026 See all 9 of this type

    18
    What is the HCF of x3+x2y−10xy2+8y3x^3 + x^2y - 10xy^2 + 8y^3 and x3+x2y−4xy2−4y3x^3 + x^2y - 4xy^2 - 4y^3 ?

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  4. Question 4

    Time and Work. This type asked 9 times: CDS 1 2017, CDS 2 2017, CDS 1 2018, CDS 2 2019, CDS 1 2020, CDS 1 2022, CDS 2 2022, CDS 1 2023, CDS 1 2026. This one: CDS 1 2026 See all 9 of this type

    9
    Eight men and 24 women can finish a piece of work in one day while 12 men and 18 women can also finish it in one day. What is the time taken by 24 men and 72 women to finish the work ?

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  5. Question 5

    Number System. This type asked 8 times: CDS 2 2018, CDS 2 2020, CDS 1 2022, CDS 2 2022, CDS 1 2023, CDS 2 2024, CDS 1 2025, CDS 1 2026. This one: CDS 1 2026 See all 8 of this type

    27
    What is the sum of all the divisors of 256 ?

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