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Day 84: CDS Maths

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

  1. Question 1

    Surds, Indices and Simplification. This type asked 2 times: CDS 2 2018, CDS 2 2019. This one: CDS 2 2019 See all 2 of this type

    47
    If ax=by=cza^x = b^y = c^z and b2=acb^2 = ac, then what is 1x+1z\frac{1}{x} + \frac{1}{z} equal to ?

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  2. Question 2

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

    89
    Consider the following inequalities in respect of any triangle ABC : 1. AC−AB<BCAC - AB < BC 2. BC−AC<ABBC - AC < AB 3. AB−BC<ACAB - BC < AC Which of the above are correct ?

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  3. Question 3

    Lines, Angles and Polygons. This type asked 2 times: CDS 1 2018, CDS 1 2019. This one: CDS 1 2019 See all 2 of this type

    27
    Three parallel lines xx, yy and zz are cut by two transversals mm and nn. Transversal mm cuts the lines xx, yy, zz at PP, QQ, RR respectively; and Transversal nn cuts the lines xx, yy, zz at LL, MM, NN respectively. If PQ=3PQ = 3 cm, QR=9QR = 9 cm and MN=10.5MN = 10.5 cm, then what is the length of LMLM ?

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  4. Question 4

    Ratio, Proportion and Variation. This type asked 2 times: CDS 2 2017, CDS 1 2019. This one: CDS 1 2019 See all 2 of this type

    25
    A stock of food grains is enough for 240 men for 48 days. How long will the same stock last for 160 men ?

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  5. Question 5

    Algebraic Identities and Simplification. This type asked 2 times: CDS 2 2017, CDS 2 2018. This one: CDS 2 2018 See all 2 of this type

    25
    If ab + bc + ca = 0, then the value of (b2−ca)(c2−ab)+(a2−bc)(c2−ab)+(a2−bc)(b2−ca)(a2−bc)(b2−ca)(c2−ab)\frac{(b^2 - ca)(c^2 - ab) + (a^2 - bc)(c^2 - ab) + (a^2 - bc)(b^2 - ca)}{(a^2 - bc)(b^2 - ca)(c^2 - ab)} is

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