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Day 237: CDS Maths

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

  1. Question 1

    Time, Speed and Distance. Asked once: CDS 1 2026

    16
    A train P starts from station X for station Y and another train Q starts from station Y for station X at the same time. After passing each other, P takes 4 hours to reach Y and Q takes 1 hour to reach X. If the average speed of P is 60 km/h, then what is the average speed of Q ?

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  2. Question 2 (case study, 2 parts)

    Triangles. Asked once: CDS 2 2026

    For the next two (02) items that follow : PQR is a triangle such that QP = QR = 15 cm and PR = 18 cm. PN, QM and RT are the altitudes of the triangle which intersect at O.
    89
    What is QT : QO equal to ?

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    90
    What is the ratio of QO to OM ?

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  3. Question 3

    Trigonometric Ratios and Identities. Asked once: CDS 1 2026

    42
    For 0<θ<π20 < \theta < \frac{\pi}{2}, consider the following : I. (tan⁡4θ+tan⁡6θ)(cot⁡4θ+cot⁡6θ)=sec⁡2θ cosec2θ(\tan^4\theta + \tan^6\theta)(\cot^4\theta + \cot^6\theta) = \sec^2\theta\,\mathrm{cosec}^2\theta II. tan⁡θ+sin⁡θtan⁡θ−sin⁡θ=cot⁡2θ(sec⁡θ+1)2\frac{\tan\theta + \sin\theta}{\tan\theta - \sin\theta} = \cot^2\theta(\sec\theta + 1)^2 Which of the above is/are identities ?

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  4. Question 4

    Algebraic Identities and Simplification. Asked once: CDS 2 2025

    40
    What is xx−y+yy−z+zz−xx+yx−y+y+zy−z+z+xz−x+3\cfrac{\frac{x}{x-y} + \frac{y}{y-z} + \frac{z}{z-x}}{\frac{x+y}{x-y} + \frac{y+z}{y-z} + \frac{z+x}{z-x} + 3} equal to?

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  5. Question 5

    Averages. Asked once: CDS 2 2024

    67
    A question is given followed by two statements I and II. Consider the Question and the Statements and mark the correct option. Question : The largest of five different integers is 8 and least is 2. What is the average of these integers ? Statement-I : The sum of all the 5 integers is a multiple of 5 Statement-II : The number of odd integers is odd Which one of the following is correct in respect of the above Question and the Statements ?

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