PYQ Vault

Day 292: CDS Maths

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

  1. Question 1 (case study, 3 parts)

    Mensuration 2D. Asked once: CDS 1 2024

    Consider the following for the next three (03) items that follow : Two circles with centres at O1O_1 and O2O_2 touching each other are placed inside a rectangle of sides 9 cm and 8 cm as shown in the figure given below.
    96
    What is the sum of the areas of the two circles ?

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    97
    Which one of the following is correct in respect of angle θ\theta ?

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    98
    What is the area of the shaded region ?

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  2. Question 2 (case study, 3 parts)

    Mensuration 3D. Asked once: CDS 2 2021

    Consider the following for the next three (03) items that follow : A solid consisting of a right circular cone of radius xx and height 2x2x standing on a hemisphere of radius xx (take π=227\pi = \frac{22}{7})
    76
    The volume of the solid is equal to that of a

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    77
    What is the approximate total surface area of the solid ?

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    78
    The solid is placed upright in a right circular cylinder full of water such that it touches the bottom. If the internal radius of cylinder is xx and height is 3x3x, what is the approximate volume of water left in the cylinder ?

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  3. Question 3

    Number System. Asked once: CDS 2 2024

    97
    How many numbers of the form 2n−12^n - 1 and less than 2000 are prime ?

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  4. Question 4

    Polynomials. Asked once: CDS 2 2017

    18
    The product of the polynomials (x+2)(x + 2), (x−2)(x - 2), (x3−2x2+4x−8)(x^3 - 2x^2 + 4x - 8) and (x3+2x2+4x+8)(x^3 + 2x^2 + 4x + 8) is

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  5. Question 5

    Quadratic Equations. Asked once: CDS 2 2021

    9
    Which one of the following equations does not have real roots ?

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