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Day 199: CDS Maths

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

  1. Question 1

    Algebraic Identities and Simplification. Asked once: CDS 2 2020 (same type asked 4 times) See all 4 of this type

    34
    What is the value of a2+aca2c−c3−a2−c2a2c+2ac2+c3−2ca2−c2+3a+c\dfrac{a^2 + ac}{a^2c - c^3} - \dfrac{a^2 - c^2}{a^2c + 2ac^2 + c^3} - \dfrac{2c}{a^2 - c^2} + \dfrac{3}{a + c} ?

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  2. Question 2

    Mensuration 2D. Asked once: CDS 1 2018 (same type asked 4 times) See all 4 of this type

    91
    What is the area of the largest circular disc cut from a square of side 2π\dfrac{2}{\sqrt{\pi}} units ?

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  3. Question 3

    Mensuration 3D. Asked once: CDS 2 2017 (same type asked 4 times) See all 4 of this type

    72
    The vertical angle of a right circular cone is π2\frac{\pi}{2} and the slant height is 2 r\sqrt{2}\,r cm. What is the volume of the cone in cubic cm ?

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  4. Question 4

    Percentage, Profit and Loss. Asked once: CDS 2 2016 (same type asked 4 times) See all 4 of this type

    23
    A shopkeeper increases the cost price of an item by 20% and offers a discount of 10% on this marked price. What is his percentage gain ?

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  5. Question 5

    Surds, Indices and Simplification. Asked once: CDS 1 2021 (same type asked 4 times) See all 4 of this type

    10
    What is the value of xx, if b+b2−2bxb−b2−2bx=a\frac{b + \sqrt{b^2 - 2bx}}{b - \sqrt{b^2 - 2bx}} = a?

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