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Day 3: CDS Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Averages. This type asked 7 times: CDS 2 2016, CDS 2 2018, CDS 2 2019, CDS 2 2020, CDS 2 2022, CDS 2 2024, CDS 2 2026. This one: CDS 2 2026 See all 7 of this type

    92
    The average weekly wages of male employees in a company is Rs. 4,200 and that of females is Rs. 3,200. If the average weekly wage of all employees is Rs. 4,000, then what is the ratio of male to female employees ?

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  2. Question 2

    Polynomials. This type asked 7 times: CDS 1 2017, CDS 2 2017, CDS 2 2018, CDS 2 2020, CDS 2 2022, CDS 1 2026, CDS 2 2026. This one: CDS 2 2026 See all 7 of this type

    20
    The LCM and HCF of two polynomials p(x)p(x) and q(x)q(x) are (x+k)2(x2−7x+6)(x + k)^2 (x^2 - 7x + 6) and (x+k)(x + k) respectively. If [x3+(2k−1)x2+k(k−2)x−k2][x^3 + (2k - 1)x^2 + k(k - 2)x - k^2] is one of the polynomials, then which of the following statements is/are correct ? I. The other polynomial is (x+k)(x−6)(x + k)(x - 6) where k≠−6k \ne -6. II. (x+k)(x + k) cannot be the HCF if k=−6k = -6. Select the answer using the code given below :

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  3. Question 3

    Trigonometric Ratios and Identities. This type asked 7 times: CDS 2 2016, CDS 1 2018, CDS 2 2020, CDS 1 2025, CDS 2 2025, CDS 1 2026, CDS 2 2026. This one: CDS 2 2026 See all 7 of this type

    49
    If (cos⁡35∘+cos⁡55∘)=p(\cos 35^\circ + \cos 55^\circ) = p, then what is sin⁡35∘⋅cos⁡35∘\sin 35^\circ \cdot \cos 35^\circ equal to ?

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  4. Question 4

    Number System. This type asked 7 times: CDS 1 2018, CDS 1 2019, CDS 2 2019, CDS 2 2021, CDS 1 2023, CDS 1 2025, CDS 1 2026. This one: CDS 1 2026 See all 7 of this type

    5
    Let P=55×1515×2525×3535P = 5^5 \times 15^{15} \times 25^{25} \times 35^{35} and Q=1010×2020×3030×4040Q = 10^{10} \times 20^{20} \times 30^{30} \times 40^{40}. What is the number of consecutive zeros at the end of the sum (P+Q)(P + Q) ?

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  5. Question 5

    Polynomials. This type asked 7 times: CDS 1 2017, CDS 2 2017, CDS 1 2018, CDS 1 2021, CDS 2 2021, CDS 2 2025, CDS 1 2026. This one: CDS 1 2026 See all 7 of this type

    8
    Which of the following expressions can divide both the polynomials x3+2x2−5x+2x^3 + 2x^2 - 5x + 2 and x3+4x2+x−6x^3 + 4x^2 + x - 6 exactly ? I. x−1x - 1 II. x+1x + 1 III. x+2x + 2 Select the correct answer using the code given below :

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