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Day 313: CDS Maths

5 questions (7 parts). Try each one first, then open its answer.

  1. Question 1

    Mensuration 2D. Asked once: CDS 2 2022

    90
    Two rectangles are of same area equal to 480 square cm. They differ in lengths by 6 cm and breadths by 4 cm. What is the difference in their perimeters ?

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  2. Question 2 (case study, 3 parts)

    Mensuration 3D. Asked once: CDS 2 2019

    Consider the following for the next three (03) items : A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular cone is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder.
    91
    What is the ratio of the volume of the sphere to that of the cone ?

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    92
    What is the ratio of the volume of the cube to that of the cylinder ?

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    93
    Consider the following statements : 1. The surface area of the sphere is 5\sqrt{5} times the curved surface area of the cone. 2. The surface area of the cube is equal to the curved surface area of the cylinder. Which of the above statements is/are correct ?

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  3. Question 3

    Number System. Asked once: CDS 1 2023

    31
    Let a, b, c and d be four positive integers such that a+b+c+d=200a + b + c + d = 200. If S=(−1)a+(−1)b+(−1)c+(−1)dS = (-1)^a + (-1)^b + (-1)^c + (-1)^d, then what is the number of possible values of S?

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  4. Question 4

    Quadratic Equations. Asked once: CDS 1 2018

    75
    The length of a line segment AB is 2 cm. It is divided into two parts at a point C such that AC2=AB×CBAC^2 = AB \times CB. What is the length of CB ?

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  5. Question 5

    Surds, Indices and Simplification. Asked once: CDS 1 2017

    11
    If x=t1t−1x = t^{\frac{1}{t-1}} and y=ttt−1y = t^{\frac{t}{t-1}}, t>0t > 0, t≠1t \ne 1, then what is the relation between xx and yy ?

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