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Day 2: CDS Maths

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

  1. Question 1

    Number System. 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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  2. Question 2

    Mensuration 2D. This type asked 8 times: CDS 2 2016, CDS 2 2017, CDS 2 2018, CDS 1 2019, CDS 2 2020, CDS 2 2022, CDS 2 2024, CDS 2 2025. This one: CDS 2 2025 See all 8 of this type

    75
    The sides of a triangle are 11 cm, 60 cm and 61 cm. What is the area of the triangle formed by joining the mid-points of the sides of the triangle?

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  3. Question 3

    Trigonometric Ratios and Identities. This type asked 8 times: CDS 2 2017, CDS 2 2018, CDS 2 2019, CDS 1 2020, CDS 2 2021, CDS 2 2022, CDS 1 2023, CDS 2 2025. This one: CDS 2 2025 See all 8 of this type

    35
    If cot⁡θ=7\cot\theta = \sqrt{7}, then what is cosec2θ−sec⁡2θcosec2θ+sec⁡2θ\dfrac{\mathrm{cosec}^2\theta - \sec^2\theta}{\mathrm{cosec}^2\theta + \sec^2\theta} equal to?

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  4. Question 4

    Number System. 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

    Logarithms. 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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