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Day 178: CDS Maths

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

  1. Question 1

    Number System. Asked once: CDS 1 2019 (same type asked 3 times) See all 3 of this type

    96
    What is the sum of all integer values of nn for which n2+19n+92n^2 + 19n + 92 is a perfect square ?

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  2. Question 2

    Sets. Asked once: CDS 2 2018 (same type asked 3 times) See all 3 of this type

    38
    In a class of 60 boys, there are 45 boys who play chess and 30 boys who play carrom. If every boy of the class plays at least one of the two games, then how many boys play carrom only ?

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  3. Question 3

    Time, Speed and Distance. Asked once: CDS 1 2018 (same type asked 3 times) See all 3 of this type

    40
    A passenger train and a goods train are running in the same direction on parallel railway tracks. If the passenger train now takes three times as long to pass the goods train, as when they are running in opposite directions, then what is the ratio of the speed of the passenger train to that of the goods train? (Assume that the trains run at uniform speeds)

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  4. Question 4

    Trigonometric Ratios and Identities. Asked once: CDS 1 2022 (same type asked 3 times) See all 3 of this type

    47
    If cos⁡(x+y)=0\cos(x + y) = 0 and sin⁡(x−y)=12\sin(x - y) = \frac{1}{2}, where x,y∈[0,π2]x, y \in \left[0, \frac{\pi}{2}\right], then what is the value of cot⁡(2x−y)\cot(2x - y)?

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  5. Question 5

    Mensuration 2D. Asked once: CDS 2 2018 (same type asked 3 times) See all 3 of this type

    93
    In the figure given below, ABCD is the diameter of a circle of radius 9 cm. The lengths AB, BC and CD are equal. Semicircles are drawn on AB and BD as diameters as shown in the figure. What is the area of the shaded region ?

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