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Day 297: 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 2023

    16
    If x(a−b+aba−b)=y(a+b−aba+b)x\left(a - b + \dfrac{ab}{a - b}\right) = y\left(a + b - \dfrac{ab}{a + b}\right) and x+y=2a3x + y = 2a^3, then what is x−yx - y equal to ?

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  2. Question 2

    Circles. Asked once: CDS 1 2018

    100
    In the figure given below, two equal chords cut at point P. If AB = CD = 10 cm, OC = 13 cm (O is the centre of the circle) and PB = 3 cm, then what is the length of OP ?

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  3. Question 3

    Linear Equations. Asked once: CDS 1 2018

    7
    If 65x−33y=9765x - 33y = 97 and 33x−65y=133x - 65y = 1, then what is xyxy equal to?

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  4. Question 4 (case study, 2 parts)

    Mensuration 2D. Asked once: CDS 1 2024

    Consider the following for the next two (02) items that follow : In a pie-diagram (with radius 7 cm), the central angles of the sectors are in the ratio 2 : 3 : 7 : 5 : 1. (Take π=227\pi = \frac{22}{7})
    71
    If P is the area of the smallest sector and Q is the area of the largest sector, then what is P + Q equal to ?

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    72
    If p is the perimeter of the smallest sector, then what is the value of 9p ?

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  5. Question 5

    Mensuration 3D. Asked once: CDS 2 2021

    74
    ABCABC is a triangle right-angled at BB with AB=8AB = 8 cm and BC=6BC = 6 cm. It is made to revolve about its side BCBC. What is the approximate total surface area of the cone so formed ? (take π=227\pi = \frac{22}{7})

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