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Day 39: CDS Maths

5 questions (7 parts). Try each one first, then open its answer.

  1. Question 1

    Sequence and Series. This type asked 3 times: CDS 1 2018, CDS 2 2020, CDS 1 2024. This one: CDS 1 2024 See all 3 of this type

    28
    The sum of two positive numbers is 40. If the GM of these two numbers is lower than their AM by 20%, then what is the difference between the two numbers ?

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  2. Question 2

    Sequence and Series. This type asked 3 times: CDS 2 2016, CDS 1 2021, CDS 1 2024. This one: CDS 1 2024 See all 3 of this type

    35
    What is 312×22+522×32+732×42+…\frac{3}{1^2 \times 2^2} + \frac{5}{2^2 \times 3^2} + \frac{7}{3^2 \times 4^2} + \ldots equal to ?

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  3. Question 3

    Statistics. This type asked 3 times: CDS 2 2016, CDS 2 2018, CDS 1 2024. This one: CDS 1 2024 See all 3 of this type

    15
    Consider the following data : 110, 41, 43, 95, 127, 99, 61, 92, 71, 93, 110, 36. If 93 is replaced by 94, then consider the following statements : 1. The difference between new median and old median is 1. 2. The difference between new mean and old mean is less than 0.1. 3. The difference between new mode and old mode is zero. Which of the statements given above are correct ?

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  4. Question 4 (case study, 3 parts)

    Time, Speed and Distance. This type asked 3 times: CDS 1 2017, CDS 2 2022, CDS 1 2024. This one: CDS 1 2024 See all 3 of this type

    Consider the following for the next three (03) items that follow : Two trains A and B started from stations P and Q respectively towards each other. Train A started at 7 p.m. at a speed of 60 km/hr and train B started at 4 a.m. (next day) at a speed of 90 km/hr. The distance between the two stations P and Q is 800 km.
    73
    How far from station Q will the two trains meet ?

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    74
    At what time will the two trains meet ?

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    75
    If the lengths of the two trains A and B are 400 m and 500 m respectively, then what is the time taken by them to cross each other ?

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  5. Question 5

    Algebraic Identities and Simplification. This type asked 3 times: CDS 1 2020, CDS 1 2021, CDS 2 2023. This one: CDS 2 2023 See all 3 of this type

    83
    If a,b,c,x,y,za, b, c, x, y, z are real numbers such that (a+b+c)2−3(ab+bc+ca)+3(x2+y2+z2)=0(a + b + c)^2 - 3(ab + bc + ca) + 3(x^2 + y^2 + z^2) = 0, then which one of the following is correct ?

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