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Day 24: CDS Maths

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

  1. Question 1

    Triangles. This type asked 4 times: CDS 2 2016, CDS 1 2017, CDS 1 2019, CDS 2 2023. This one: CDS 2 2023 See all 4 of this type

    56
    ABC is a triangle with sides AB = 41 cm, BC = 28 cm and CA = 15 cm. If D, E and F are the mid-points of AB, BC and CA respectively, then what is the area of the triangle DEF ?

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  2. Question 2

    Trigonometric Ratios and Identities. This type asked 4 times: CDS 2 2019, CDS 1 2020, CDS 2 2022, CDS 2 2023. This one: CDS 2 2023 See all 4 of this type

    25
    What is 3(sin⁡x−cos⁡x)4+6(sin⁡x+cos⁡x)2+4(sin⁡x)6+4(cos⁡x)63(\sin x - \cos x)^4 + 6(\sin x + \cos x)^2 + 4(\sin x)^6 + 4(\cos x)^6 equal to ?

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  3. Question 3

    Mensuration 3D. This type asked 4 times: CDS 2 2017, CDS 1 2021, CDS 1 2022, CDS 1 2023. This one: CDS 1 2023 See all 4 of this type

    86
    A square sheet of side length 44 cm is rolled along one of its sides to form a cylinder by making opposite edges just to touch each other. What is the volume of the cylinder ? (Take π=227\pi = \frac{22}{7})

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  4. Question 4

    Mensuration 3D. This type asked 4 times: CDS 1 2017, CDS 2 2019, CDS 2 2020, CDS 1 2023. This one: CDS 1 2023 See all 4 of this type

    58
    The surface area of a cube is increased by 25%. If p is the percentage increase in its length, then which one of the following is correct ?

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  5. Question 5

    Surds, Indices and Simplification. This type asked 4 times: CDS 2 2017, CDS 2 2019, CDS 2 2022, CDS 1 2023. This one: CDS 1 2023 See all 4 of this type

    25
    If x=4444…x = \sqrt{4\sqrt{4\sqrt{4\sqrt{4 \ldots}}}}, then what is the value of x?

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