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Day 227: CDS Maths

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

  1. Question 1

    Trigonometric Ratios and Identities. Asked once: CDS 2 2026

    48
    If A+B+C=πA + B + C = \pi (A, B, C > 0) and the angle C is obtuse, then which of the following is/are correct ? I. sin⁡A⋅sin⁡B<1\sin A \cdot \sin B < 1 II. tan⁡A⋅tan⁡B>1\tan A \cdot \tan B > 1 Select the answer using the code given below :

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  2. Question 2

    Algebraic Identities and Simplification. Asked once: CDS 2 2026

    11
    If 1x+k+1x+2k+1x+5k=1k\frac{1}{x + k} + \frac{1}{x + 2k} + \frac{1}{x + 5k} = \frac{1}{k}, then what is the solution of the equation ?

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  3. Question 3

    Averages. Asked once: CDS 1 2025

    3
    If the average of 64, 69, 72, 75, xx lies between 62 and 76 (excluding 62 and 76), then what is the number of possible integer values of xx ?

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  4. Question 4 (case study, 3 parts)

    Circles. Asked once: CDS 2 2026

    For the next three (03) items that follow : The centre O of a circle inside a triangle ABC is at a distance of 13 cm from each of the vertices of the triangle. The diameter of the circle is 10 cm and the circle touches only two sides of the triangle, AB and AC.
    81
    If x is the perimeter, in cm, of the triangle, then which one of the following is correct ?

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    82
    If y is the area in cm2\text{cm}^2 of the triangle, then which one of the following is correct ?

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    83
    Consider the following statements : I. ∠ABC\angle ABC lies between 60∘60^\circ and 90∘90^\circ. II. If z is the distance in cm from the centre O of the circle to the midpoint of BC, then 7 cm<z<8 cm7 \text{ cm} < z < 8 \text{ cm}. Which of the statements given above is/are correct ?

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  5. Question 5 (case study, 3 parts)

    Data Interpretation. Asked once: CDS 1 2025

    Consider the following for the next three (03) items that follow : Circulation figures (in thousands) of different newspapers (A, B, C, D, E) for five years are given below :
    YearABCDE
    2019201015820
    20201212181212
    20212414171415
    2022261016159
    20232216141611
    93
    In which of the given years was the circulation of the newspaper D close to its average circulation over all the years ?

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    94
    In which of the years from 2019 to 2022 was the circulation of the newspaper D close to the average circulation of all the newspapers in that year ?

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    95
    How many cases are there in which average of the circulation for an individual newspaper was more than the average of the circulation of all the newspapers ?

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