PYQ Vault

Day 248: CDS Maths

5 questions (9 parts). Try each one first, then open its answer.

  1. Question 1

    Algebraic Identities and Simplification. Asked once: CDS 2 2025

    27
    If (a−b)2+(b−c)2+(c−a)2=6(a-b)^2+(b-c)^2+(c-a)^2=6 and a2+b2+c2=29a^2+b^2+c^2=29, then what is (a+b+c)(a+b+c) equal to?

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  2. Question 2

    Averages. Asked once: CDS 1 2021

    94
    What is the arithmetic mean of the first ten composite numbers?

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  3. Question 3 (case study, 2 parts)

    Circles. Asked once: CDS 1 2023

    Consider the following for the next two (02) items that follow : In the following figure, a triangle ABC is inscribed in a circle with centre at O. Let ∠POA=x∘\angle POA = x^\circ and ∠OQB=y∘\angle OQB = y^\circ. Further, OB = BQ.
    99
    What is the relation between x and y ?

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    100
    If y=15y = 15, then what is ∠ACB\angle ACB equal to ?

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  4. Question 4 (case study, 4 parts)

    Data Interpretation. Asked once: CDS 2 2021

    Consider the following for the next four (04) items that follow : The following Pie-Charts show the percentage of different categories (AA, BB, CC, DD, EE and FF) of employees in a company in the year 2019 and 2020. The total number of employees was 4000 in 2019 and 5000 in 2020.
    91
    There are two categories of employees in 2019 whose total strength remained the same in 2020. What are these two categories ?

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    92
    In which one of the following categories of employees, the percentage change in number of employees in 2020 was maximum as compared to 2019 ?

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    93
    What was the percentage increase of category-EE employees in 2020 as compared to that in 2019 ?

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    94
    There are two categories of employees whose strength increased by same percentage in 2020. What are the two categories ?

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  5. Question 5

    Heights and Distances. Asked once: CDS 1 2021

    60
    A vertical tower standing at the corner of a rectangular field subtends angles of 60∘60^\circ and 45∘45^\circ at the two nearer corners. If θ\theta is the angle that the tower subtends at the farthest corner, then what is cot⁡θ\cot\theta equal to?

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