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Day 203: CDS Maths

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

  1. Question 1

    Logarithms. Asked once: CDS 2 2016 (same type asked 4 times) See all 4 of this type

    28
    What are the roots of the equation 2x+2⋅27xx−1=92^{x+2} \cdot 27^{\frac{x}{x-1}} = 9 ?

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  2. Question 2

    Mensuration 3D. Asked once: CDS 2 2020 (same type asked 4 times) See all 4 of this type

    67
    How many solid lead balls each of diameter 2 mm can be made from a solid lead ball of radius 8 cm ?

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  3. Question 3

    Quadrilaterals. Asked once: CDS 2 2020 (same type asked 3 times) See all 3 of this type

    61
    In a quadrilateral ABCD, ∠B=90∘\angle B = 90^\circ and AB2+BC2+CD2−AD2=0AB^2 + BC^2 + CD^2 - AD^2 = 0, then what is ∠ACD\angle ACD equal to ?

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  4. Question 4

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

    62
    In a triangle ABC, AD is perpendicular on BC. If ∠BAC=90∘\angle BAC = 90^\circ, AB = c, BC = a, CA = b and AD = p, then which one of the following is correct ?

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  5. Question 5

    Algebraic Identities and Simplification. Asked once: CDS 1 2017 (same type asked 3 times) See all 3 of this type

    18
    If a3=335+b3a^3 = 335 + b^3 and a=5+ba = 5 + b, then what is the value of a+ba + b (given that a>0a > 0 and b>0b > 0) ?

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