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Day 319: CDS Maths

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

  1. Question 1

    Trigonometric Ratios and Identities. Asked once: CDS 1 2022

    57
    Consider the following : 1. sec⁡2θ+cosec⁡2θ=tan⁡θ+cot⁡θ\sqrt{\sec^2\theta + \operatorname{cosec}^2\theta} = \tan\theta + \cot\theta, where 0<θ<90∘0 < \theta < 90^\circ 2. tan⁡2θ+cot⁡2θ+4=sec⁡θ+cosec⁡θ\sqrt{\tan^2\theta + \cot^2\theta + 4} = \sec\theta + \operatorname{cosec}\theta, where 0<θ<90∘0 < \theta < 90^\circ Which of the above is/are an identity/identities?

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  2. Question 2

    Algebraic Identities and Simplification. Asked once: CDS 2 2021

    25
    If xb+c−a=yb−c−a=za+b−c=k\dfrac{x}{b+c-a}=\dfrac{y}{b-c-a}=\dfrac{z}{a+b-c}=k, then what is x2+y2+z2−2xy−2yz+2zxx^2+y^2+z^2-2xy-2yz+2zx equal to ?

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  3. Question 3

    Mensuration 2D. Asked once: CDS 1 2022

    68
    A square sheet is formed by joining nn identical square sheets of same size. If the length of the diagonal of the bigger square sheet so formed is mm, then what is the side length of a smaller square sheet?

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  4. Question 4

    Mensuration 3D. Asked once: CDS 1 2019

    26
    A hollow right circular cylindrical vessel of volume VV whose diameter is equal to its height, is completely filled with water. A heavy sphere of maximum possible volume is then completely immersed in the vessel. What volume of water remains in the vessel ?

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  5. Question 5

    Number System. Asked once: CDS 2 2022

    20
    The value of a 2-digit number is 5 times the sum of the digits. What is the product of the digits ?

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