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Day 224: CDS Maths

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

  1. Question 1

    Mensuration 3D. Asked once: CDS 2 2026

    66
    A thin metallic sheet, 1.92 m2\text{m}^2 in area, is cut into two equal pieces. One piece is used to make a hollow cube of volume P (in m3\text{m}^3) and the other is used to make a hollow cuboid of volume Q (in m3\text{m}^3) with dimensions in the ratio 4 : 2 : 1. If no sheet is wasted, which one of the following is correct ?

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  2. Question 2

    Number System. Asked once: CDS 2 2026

    7
    A number is formed by three digits, each less by unity than the digit that follows it. If 15 is added to the number, then the sum is 30 times the sum of the digits of the number. What is the product of the digits of the number ?

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  3. Question 3

    Percentage, Profit and Loss. Asked once: CDS 1 2026

    32
    A reduction of 10% in the price of sugar enables a person to buy 6.2 kg more for Rs. 2790. What is the reduced price per kilogram ?

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  4. Question 4

    Polynomials. Asked once: CDS 2 2026

    12
    Consider the polynomial p(x)=x5+2x4+x3−x2−2x−1p(x) = x^5 + 2x^4 + x^3 - x^2 - 2x - 1 : I. x2+2x+1x^2 + 2x + 1 is a factor of p(x)p(x). II. x2+x+1x^2 + x + 1 divides p(x)p(x). Which of the statements given above is/are correct ?

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  5. Question 5

    Quadratic Equations. Asked once: CDS 2 2026

    4
    Suppose p and q are positive integers where q is not a perfect square. If 1p+q\frac{1}{p + \sqrt{q}} is a root of a quadratic equation having integer coefficients, then which of the following statements is/are correct ? I. The sum of the roots is 2p times the product of the roots. II. The sum of the reciprocals of the roots is equal to 2p. Select the answer using the code given below :

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