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Day 88: CDS Maths

5 questions (6 parts). Try each one first, then open its answer.

  1. Question 1

    Number System. Asked once: CDS 2 2024 (same type asked 8 times) See all 8 of this type

    4
    What is the remainder when 111222+222333+333444111^{222} + 222^{333} + 333^{444} is divided by 5 ?

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  2. Question 2

    Averages. Asked once: CDS 2 2022 (same type asked 7 times) See all 7 of this type

    64
    Consider the following table in respect of students of 4 schools who appeared in a test :
    SchoolNumber of studentsAverage marks in the test
    I6060
    II5080
    III5040
    IVx50
    If the average marks of the students of all four schools are 58, then how many students appeared from School-IV ?

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  3. Question 3

    Polynomials. Asked once: CDS 2 2022 (same type asked 7 times) See all 7 of this type

    26
    Let p(x)=x4+x2+1p(x) = x^4 + x^2 + 1, q(x)=x4−2x3+3x2−2x+1q(x) = x^4 - 2x^3 + 3x^2 - 2x + 1. If GCD of p(x)p(x) and q(x)q(x) is x2−x+1x^2 - x + 1, then what is their LCM ?

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  4. Question 4 (case study, 2 parts)

    Trigonometric Ratios and Identities. Asked once: CDS 1 2026 (same type asked 7 times) See all 7 of this type

    For the next two (02) items that follow : Let 12(tan⁡θ+cot⁡θ)=2512(\tan\theta + \cot\theta) = 25, where 45∘<θ<90∘45^\circ < \theta < 90^\circ.
    91
    What is a value of (sin⁡θ−cos⁡θ)(\sin\theta - \cos\theta) ?

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    92
    What is a value of (cosec⁡θ+sec⁡θ)(\operatorname{cosec}\theta + \sec\theta) ?

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  5. Question 5

    Number System. Asked once: CDS 1 2025 (same type asked 7 times) See all 7 of this type

    37
    Given that 100×99×98×…×3×2×1100n\frac{100 \times 99 \times 98 \times \ldots \times 3 \times 2 \times 1}{100^n} is an integer. What is the largest value of n for which this is true ?

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