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Day 104: CDS Maths

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

  1. Question 1

    Polynomials. Asked once: CDS 1 2019 (same type asked 4 times) See all 4 of this type

    97
    What is the LCM of the polynomials x3+3x2+3x+1x^3 + 3x^2 + 3x + 1, x3+5x2+5x+4x^3 + 5x^2 + 5x + 4 and x2+5x+4x^2 + 5x + 4 ?

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  2. Question 2

    Ratio, Proportion and Variation. Asked once: CDS 2 2023 (same type asked 4 times) See all 4 of this type

    67
    Three glasses P, Q and R have capacities in the ratio 1 : 2 : 3. All these glasses are completely filled with mixtures of milk and water. The ratio of milk to water in P is 1 : 2, in Q it is 2 : 3 and in R it is 3 : 1. If the content of all three glasses are put into a bigger container, what will be the ratio of milk to water in the container ?

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  3. Question 3

    Surds, Indices and Simplification. Asked once: CDS 2 2022 (same type asked 4 times) See all 4 of this type

    4
    If x+20+x−1x+20−x−1=73\frac{\sqrt{x + 20} + \sqrt{x - 1}}{\sqrt{x + 20} - \sqrt{x - 1}} = \frac{7}{3}, then what is the value of (x+20)(x−1)\sqrt{(x + 20)(x - 1)} ?

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  4. Question 4

    Surds, Indices and Simplification. Asked once: CDS 2 2023 (same type asked 4 times) See all 4 of this type

    15
    If 3x−1+33−x=63^{x - 1} + 3^{3 - x} = 6, then what is 2x−1+23−x2^{x - 1} + 2^{3 - x} equal to ?

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  5. Question 5

    Trigonometric Ratios and Identities. Asked once: CDS 2 2024 (same type asked 4 times) See all 4 of this type

    17
    If cosec θ−cot⁡θ=m\mathrm{cosec}\,\theta - \cot\theta = m and sec⁡θ−tan⁡θ=n\sec\theta - \tan\theta = n, then what is cosec θ+sec⁡θ\mathrm{cosec}\,\theta + \sec\theta equal to ?

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