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Day 253: CDS Maths

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

  1. Question 1 (case study, 2 parts)

    Trigonometric Ratios and Identities. Asked once: CDS 2 2025

    Let sin⁡αsin⁡β=423\dfrac{\sin\alpha}{\sin\beta} = \dfrac{4\sqrt{2}}{3} and cos⁡αcos⁡β=239\dfrac{\cos\alpha}{\cos\beta} = \dfrac{2\sqrt{3}}{9}.
    45
    What is tan⁡2α\tan^2\alpha equal to?

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    46
    What is tan⁡2β\tan^2\beta equal to?

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  2. Question 2

    Algebraic Identities and Simplification. Asked once: CDS 2 2025

    14
    If p+qq+r=r+ss+p\frac{p+q}{q+r}=\frac{r+s}{s+p}; (q+r)≠0(q+r)\ne 0, (s+p)≠0(s+p)\ne 0, then which one of the following is correct?

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  3. Question 3

    Averages. Asked once: CDS 1 2021

    95
    The marks obtained by 5 students are 21, 27, 19, 26, 32. Later on 5 grace marks are added to each student. What are the average marks of the revised marks of the students?

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  4. Question 4

    Circles. Asked once: CDS 1 2022

    61
    Consider the following statements : 1. If two chords ABAB and ACAC of a circle are equal, then the centre of the circle lies on the angle bisector of angle CABCAB. 2. If two concentric circles are intersected by a line at AA, BB, CC and DD respectively, then AC=BDAC = BD. Which of the above statements is/are correct?

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  5. Question 5 (case study, 4 parts)

    Data Interpretation. Asked once: CDS 1 2021

    For the next four (4) items, consider the following data with regard to different types (I, II, III, IV, V) of multivitamin tablets produced in a company (in lakhs) :
    YearIIIIIIIVV
    200016080709075
    200120015085160100
    200213535449585
    20032409512080120
    20041801108595115
    200521015010092110
    97
    Which product is produced least over the years 2000-2005?

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    98
    In which one of the following pairs of years, the difference in total number of tablets produced between them is minimum?

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    99
    The ratio of percentage drop in total production in 2004 compared to 2001 to that in 2000 compared to 2001, is

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    100
    In which year, the production of Type I is more than the sum of the production of Type III and Type IV?

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