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Number System

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 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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  2. Question 2

    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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  3. Question 3

    This type asked 8 times: CDS 2 2016, CDS 1 2019, CDS 2 2019, CDS 2 2020, CDS 1 2021, CDS 1 2023, CDS 2 2025, CDS 1 2026. This one: CDS 1 2026 See all 8 of this type

    30
    What is the digit in the unit place of the number 11×33×55×77×991^1 \times 3^3 \times 5^5 \times 7^7 \times 9^9 ?

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  4. Question 4

    This type asked 8 times: CDS 1 2017, CDS 2 2019, CDS 2 2020, CDS 1 2021, CDS 2 2021, CDS 1 2023, CDS 2 2024, CDS 1 2025. This one: CDS 1 2025 See all 8 of this type

    5
    Let pp be the remainder when 7847^{84} is divided by 342 and qq be the remainder when 7847^{84} is divided by 344. What is (p−q)(p - q) equal to ?

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  5. Question 5

    This type asked 7 times: CDS 1 2018, CDS 1 2019, CDS 2 2019, CDS 2 2021, CDS 1 2023, CDS 1 2025, CDS 1 2026. This one: CDS 1 2026 See all 7 of this type

    5
    Let P=55×1515×2525×3535P = 5^5 \times 15^{15} \times 25^{25} \times 35^{35} and Q=1010×2020×3030×4040Q = 10^{10} \times 20^{20} \times 30^{30} \times 40^{40}. What is the number of consecutive zeros at the end of the sum (P+Q)(P + Q) ?

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  6. Question 6

    This type asked 7 times: CDS 2 2016, CDS 2 2019, CDS 1 2021, CDS 1 2022, CDS 1 2023, CDS 2 2024, CDS 2 2025. This one: CDS 2 2025 See all 7 of this type

    11
    What is the remainder when (1725+1925)(17^{25}+19^{25}) is divided by 18?

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  7. Question 7

    This type asked 6 times: CDS 1 2018, CDS 2 2018, CDS 1 2020, CDS 1 2022, CDS 1 2023, CDS 2 2026. This one: CDS 2 2026 See all 6 of this type

    1
    Two positive integers x and y are in the ratio 17 : 19. If the LCM of the two numbers is 1615, then what is x+yx + y equal to ?

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  8. Question 8

    This type asked 5 times: CDS 2 2016, CDS 1 2018, CDS 1 2020, CDS 1 2022, CDS 1 2026. This one: CDS 1 2026 See all 5 of this type

    21
    2727−940−37927^{27} - 9^{40} - 3^{79} is divisible by how many natural numbers less than 10 ?

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  9. Question 9

    This type asked 5 times: CDS 2 2016, CDS 1 2017, CDS 1 2022, CDS 1 2023, CDS 1 2026. This one: CDS 1 2026 See all 5 of this type

    31
    Let P=N2P = N^2 where N is an odd integer. What is the remainder when P is divided by 8 ?

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  10. Question 10

    This type asked 5 times: CDS 2 2018, CDS 1 2023, CDS 2 2024, CDS 1 2025, CDS 2 2025. This one: CDS 2 2025 See all 5 of this type

    30
    A number NN is such that when divided by 4, 6, 7 or 9, it leaves 3 as remainder. What is the smallest 4-digit number that satisfies this property?

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