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Day 304: 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 2023

    71
    Which of the following is/are identity/identities ? 1. sin⁡3θ+cos⁡3θsin⁡θ+cos⁡θ+sin⁡θcos⁡θ=1\frac{\sin^3 \theta + \cos^3 \theta}{\sin \theta + \cos \theta} + \sin \theta \cos \theta = 1; 0<θ<π20 < \theta < \frac{\pi}{2} 2. 1−sin⁡6θ=cos⁡2θ(cos⁡4θ+3sin⁡2θ)1 - \sin^6 \theta = \cos^2 \theta (\cos^4 \theta + 3 \sin^2 \theta) Select the correct answer using the code given below :

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  2. Question 2

    Algebraic Identities and Simplification. Asked once: CDS 2 2022

    9
    Consider the following statements : 1. (ab+bc+ca)(ab + bc + ca) is a factor of a2(b−c)3+b2(c−a)3+c2(a−b)3a^2(b - c)^3 + b^2(c - a)^3 + c^2(a - b)^3. 2. (a+b+c)(a + b + c) is a factor of a2(b−c)3+b2(c−a)3+c2(a−b)3a^2(b - c)^3 + b^2(c - a)^3 + c^2(a - b)^3. Which of the statements given above is/are correct ?

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  3. Question 3 (case study, 2 parts)

    Mensuration 2D. Asked once: CDS 1 2023

    Consider the following for the next two (02) items that follow : In the following figure, a rectangle ABCD is inscribed in a circle of radius r. Given ∠DAE=30∘\angle DAE = 30^\circ and ∠ACD=30∘\angle ACD = 30^\circ.
    97
    What is the ratio of the area of the circle to the area of the rectangle ?

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    98
    What is the area of △AEC\triangle AEC ?

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  4. Question 4

    Mensuration 3D. Asked once: CDS 2 2020

    66
    If H, C and V are respectively the height, curved surface area and volume of a cone, then what is 3πVH3+9V23 \pi V H^3 + 9 V^2 equal to ?

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  5. Question 5

    Number System. Asked once: CDS 1 2024

    26
    The expression 555777+777555555^{777} + 777^{555} is divisible by which of the following ? 1. 2 2. 3 3. 37 Select the correct answer using the code given below :

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