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Day 222: CDS Maths

5 questions (10 parts). Try each one first, then open its answer.

  1. Question 1

    Algebraic Identities and Simplification. Asked once: CDS 2 2026

    5
    If 12b+2c+12c+2a=1a+b\frac{1}{2b + 2c} + \frac{1}{2c + 2a} = \frac{1}{a + b}, then what is a2+b2+c2a^2 + b^2 + c^2 equal to ?

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  2. Question 2

    Averages. Asked once: CDS 1 2026

    37
    All possible groups of 3 distinct numbers from among A, B, C, D and E are formed. If the aggregate of sums of numbers of each group is 120, then what is the arithmetic mean of A, B, C, D and E ?

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  3. Question 3 (case study, 3 parts)

    Circles. Asked once: CDS 2 2026

    For the next three (03) items that follow : A circle with centre O passes through the vertex A of an equilateral triangle ABC and touches BC at its midpoint M. The circle cuts AB at D and AC at E.
    84
    What is AD : DB equal to ?

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    85
    If x is the area of the circle and y is the area of the triangle such that z=(xy)2z = \left(\dfrac{x}{y}\right)^2, then which one of the following is correct ?

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    86
    What is the ratio of the area of the triangle ADO to the area of the quadrilateral BDOM ?

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  4. Question 4 (case study, 3 parts)

    Data Interpretation. Asked once: CDS 1 2025

    Consider the following for the next three (03) items that follow : Study the following Pie Charts : Chart-I : Number of houses : 1,20,000 Chart-II : Population : 21,00,000 Chart-III : Number of families : 3,60,000
    96
    On an average, how many persons live in every pucca house ?

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    97
    If 5000 more Kutcha houses are built, then what will be approximate change in angle for Kutcha houses in Pie Chart-I ?

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    98
    If 300 families from the “Houseless” category shift into Kutcha houses, what will be the average number of families in every Kutcha house ?

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  5. Question 5 (case study, 2 parts)

    Heights and Distances. Asked once: CDS 2 2023

    AB is a straight road leading to the foot P of a tower of height h. Q is at distance x from P and R is at a distance y from Q (R is farther from P than Q; R, Q are on the same side). The angle of elevation of the top of the tower at Q is twice of that at R. (Use the formula tan⁡2θ=2tan⁡θ1−tan⁡2θ\tan 2\theta = \frac{2\tan\theta}{1 - \tan^2\theta})
    33
    Which one of the following is correct ?

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    34
    Which one of the following is correct ?

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