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Day 338: CDS Maths

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

  1. Question 1

    Algebraic Identities and Simplification. Asked once: CDS 2 2016

    4
    If x2=y+zx^2 = y + z, y2=z+xy^2 = z + x and z2=x+yz^2 = x + y, then what is the value of 1x+1+1y+1+1z+1\frac{1}{x+1} + \frac{1}{y+1} + \frac{1}{z+1} ?

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  2. Question 2

    Mensuration 2D. Asked once: CDS 1 2019

    42
    If ll is the length of the median of an equilateral triangle, then what is its area ?

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  3. Question 3

    Mensuration 3D. Asked once: CDS 2 2016

    50
    A building is in the form of a cylinder surmounted by a hemispherical dome on the diameter of the cylinder. The height of the building is three times the radius of the base of the cylinder. The building contains 67121 m367\frac{1}{21}\ \text{m}^3 of air. What is the height of the building ?

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  4. Question 4

    Number System. Asked once: CDS 2 2019

    34
    A prime number contains the digit X at unit's place. How many such digits of X are possible ?

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  5. Question 5

    Triangles. Asked once: CDS 2 2018

    99
    In the figure given below, ABC is an equilateral triangle with each side of length 30 cm. XY is parallel to BC, XP is parallel to AC and YQ is parallel to AB. If XY + XP + YQ is 40 cm, then the value of PQ is

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