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Day 322: CDS Maths

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

  1. Question 1

    Algebraic Identities and Simplification. Asked once: CDS 2 2021

    40
    If 2x−3y−7=02x-3y-7=0, then what is the value of 8x3−36x2y+54xy2−27y3−3408x^3-36x^2y+54xy^2-27y^3-340 ?

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  2. Question 2

    Mensuration 2D. Asked once: CDS 2 2021

    63
    Let pp be the area of a square XX and qq be the area of the square formed on the diagonal of the square XX. What is the value of pq\frac{p}{q} ?

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  3. Question 3

    Mensuration 3D. Asked once: CDS 2 2018

    78
    A semi-circular plate is rolled up to form a conical surface. The angle between the generator and the axis of the cone is

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  4. Question 4 (case study, 2 parts)

    Number System. Asked once: CDS 2 2021

    Consider the following for the next two (02) items that follow : Collect all the sequences of five consecutive integers such that their product is equal to one of these integers. Let XX be the collection of all possible such sequences. Let PP be the smallest integer and QQ be the largest integer occurring in these sequences.
    99
    How many such sequences of five consecutive integers are possible ?

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    100
    What is the arithmetic mean of PP and QQ ?

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  5. Question 5

    Quadratic Equations. Asked once: CDS 2 2016

    8
    In the quadratic equation x2+ax+b=0x^2 + ax + b = 0, aa and bb can take any value from the set {1,2,3,4}\{1, 2, 3, 4\}. How many pairs of values of aa and bb are possible in order that the quadratic equation has real roots ?

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