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Day 66: CDS Maths

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

  1. Question 1

    Logarithms. This type asked 2 times: CDS 2 2022, CDS 2 2025. This one: CDS 2 2025 See all 2 of this type

    37
    If α\alpha and β\beta are the roots of the equation log⁡10[998+x2−18x+76]=3\log_{10}\left[998 + \sqrt{x^2 - 18x + 76}\right] = 3 then what is (α−β)2(\alpha - \beta)^2 equal to?

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  2. Question 2

    Number System. This type asked 2 times: CDS 1 2023, CDS 2 2025. This one: CDS 2 2025 See all 2 of this type

    17
    Let x=n(n+1)(n+2)x=n(n+1)(n+2), where nn is an even natural number. Which of the following statements is/are correct? I. xx is always divisible by 48. II. x2x^2 is always divisible by 144. Select the answer using the code given below.

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  3. Question 3

    Percentage, Profit and Loss. This type asked 2 times: CDS 2 2020, CDS 2 2025. This one: CDS 2 2025 See all 2 of this type

    53
    There are two employees XX and YY. XX's salary is first increased by 12% and then decreased by 10%, and YY's salary is first increased by 10% and then decreased by 12%. If their salaries at present are equal, then what was the ratio of initial salary of XX to initial salary of YY?

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  4. Question 4

    Polynomials. This type asked 2 times: CDS 1 2020, CDS 2 2025. This one: CDS 2 2025 See all 2 of this type

    1
    Let p(x)p(x) be a polynomial. When p(x)p(x) is divided by (x−1)(x-1), it leaves 2 as the remainder. When p(x)p(x) is divided by (x−2)(x-2), it leaves 1 as the remainder. What is the remainder when p(x)p(x) is divided by (x−1)(x−2)(x-1)(x-2)?

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  5. Question 5

    Quadrilaterals. This type asked 2 times: CDS 1 2024, CDS 2 2025. This one: CDS 2 2025 See all 2 of this type

    88
    A Question is given followed by two Statements I and II. Consider the Question and the Statements. Question : In a quadrilateral ABCD, AB=6AB = 6 units, BC=18BC = 18 units, CD=6CD = 6 units, DA=9DA = 9 units. What is the length of diagonal BD? Statement-I : The length of BD is an integer greater than 13. Statement-II : The length of BD is an even integer. Which one of the following is correct in respect of the above Question and the Statements?

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