PYQ Vault

Day 269: CDS Maths

5 questions (6 parts). Try each one first, then open its answer.

  1. Question 1

    Mensuration 2D. Asked once: CDS 2 2024

    83
    In a rectangle ABCDABCD, ACAC is one of the diagonals. If AC+AB=3ADAC + AB = 3AD and AC−AD=4AC - AD = 4 units, then what is the area of the triangle ?

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  2. Question 2 (case study, 2 parts)

    Mensuration 3D. Asked once: CDS 2 2023

    A right conical cap just covers two spheres placed one above the other on a table such that it touches both the spheres. Let r be the radius of the smaller sphere and R be the radius of the bigger sphere. Let 2θ2\theta be the vertical angle of the cone.
    39
    What is the height of the cone ?

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    40
    What is the radius of the base of the cone ?

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  3. Question 3

    Number System. Asked once: CDS 1 2025

    9
    Consider a 2-digit number N. Let P be the product of the digits of the number. If P is added to square of the digit in the tens place of N, we get 84. If P is added to the square of the digit in the unit place of N, we get 60. What is the value of P+NP + N ?

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  4. Question 4

    Percentage, Profit and Loss. Asked once: CDS 1 2019

    21
    A trader sells two computers at the same price, making a profit of 30% on one and a loss of 30% on the other. What is the net loss or profit percentage on the transaction ?

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  5. Question 5

    Polynomials. Asked once: CDS 2 2023

    17
    Which one of the following is a factor of 33x3+22y3−18xy+663\sqrt{3}x^3 + 2\sqrt{2}y^3 - 18xy + 6\sqrt{6} ?

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