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Day 120: CDS Maths

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

  1. Question 1

    Time, Speed and Distance. Asked once: CDS 2 2022 (same type asked 3 times) See all 3 of this type

    16
    There are two stations X and Y, 1320 km apart. A train starts from station X at 6 a.m. and moves at an average speed of 60 km/hr. At 2 p.m. another train starts from Y towards X and moves at an average speed of 80 km/hr. When do they meet ?

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  2. Question 2

    Algebraic Identities and Simplification. Asked once: CDS 1 2021 (same type asked 3 times) See all 3 of this type

    3
    How many pairs of (x,y)(x, y) can be chosen from the set {2,3,6,8,9}\{2, 3, 6, 8, 9\} such that xy+yx=2\frac{x}{y} + \frac{y}{x} = 2, where x≠yx \ne y?

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  3. Question 3

    Time, Speed and Distance. Asked once: CDS 2 2019 (same type asked 3 times) See all 3 of this type

    11
    Radha and Hema are neighbours and study in the same school. Both of them use bicycles to go to the school. Radha's speed is 8 km/hr whereas Hema's speed is 10 km/hr. Hema takes 9 minutes less than Radha to reach the school. How far is the school from the locality of Radha and Hema ?

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  4. Question 4

    Trigonometric Ratios and Identities. Asked once: CDS 1 2017 (same type asked 3 times) See all 3 of this type

    61
    If xsin⁡θ=ycos⁡θ=2ztan⁡θ1−tan⁡2θx \sin \theta = y \cos \theta = \frac{2z \tan \theta}{1 - \tan^2 \theta}, then what is 4z2(x2+y2)4z^2 (x^2 + y^2) equal to ?

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  5. Question 5

    Trigonometric Ratios and Identities. Asked once: CDS 1 2018 (same type asked 3 times) See all 3 of this type

    60
    If sec⁡x cosec x=2\sec x \,\mathrm{cosec}\, x = 2, then what is tan⁡nx+cot⁡nx\tan^n x + \cot^n x equal to ?

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