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Day 280: CDS Maths

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

  1. Question 1

    Trigonometric Ratios and Identities. Asked once: CDS 2 2024

    15
    What is the value of sin⁡2θcos⁡2θ(sec⁡2θ+cosec2θ)\sin^2\theta \cos^2\theta (\sec^2\theta + \mathrm{cosec}^2\theta) equal to ?

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  2. Question 2 (case study, 2 parts)

    Algebraic Identities and Simplification. Asked once: CDS 2 2023

    Let (x−a)(x−b)(x−ma)(x−mb)=(x+a)(x+b)(x+ma)(x+mb)\frac{(x-a)(x-b)}{(x-ma)(x-mb)} = \frac{(x+a)(x+b)}{(x+ma)(x+mb)}; m,a,b>0m, a, b > 0.
    43
    What is x2+abx2+m2ab\frac{x^2 + ab}{x^2 + m^2ab} equal to ?

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    44
    What is x equal to ?

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  3. Question 3

    Circles. Asked once: CDS 2 2019

    88
    Consider the following statements : 1. The number of circles that can be drawn through three non-collinear points is infinity. 2. Angle formed in minor segment of a circle is acute. Which of the above statements is/are correct ?

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  4. Question 4

    Data Interpretation. Asked once: CDS 2 2017

    96
    Which one of the following is not correct ? The proportion of various items in a pie diagram is proportional to the

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  5. Question 5

    Heights and Distances. Asked once: CDS 2 2017

    54
    A man, standing at a point X on the bank XY of a river that cannot be crossed, observes a tower to be Nα∘EN \alpha^\circ E on the opposite parallel bank. He then walks 200 m along the bank to the point Y towards East, and finds the tower to be Nβ∘WN \beta^\circ W. From these observations, the breadth of the river will be (Given that tan⁡α∘=2\tan \alpha^\circ = 2 and tan⁡β∘=0.5\tan \beta^\circ = 0.5)

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