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Day 244: CDS Maths

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

  1. Question 1

    Linear Equations. Asked once: CDS 2 2022

    8
    If three times the greater of two numbers is divided by the smaller number, the quotient will be 6 and the remainder will be 6. If five times the smaller number is divided by the greater number, the quotient will be 2 and the remainder will be 3. What is the difference between the numbers ?

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  2. Question 2

    Lines, Angles and Polygons. Asked once: CDS 1 2020

    95
    Angles are shown in the given figure. What is value of ∠1+∠2+∠3+∠4+∠5+∠6+∠7+∠8\angle 1 + \angle 2 + \angle 3 + \angle 4 + \angle 5 + \angle 6 + \angle 7 + \angle 8?

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  3. Question 3

    Logarithms. Asked once: CDS 1 2023

    33
    Consider the following statements : 1. log⁡1050\log_{10} 50 is a rational number. 2. log⁡10010\log_{100} 10 is an irrational number. Which of the statements given above is/are correct?

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  4. Question 4

    Mensuration 2D. Asked once: CDS 2 2024

    84
    The area of the circle circumscribing three identical circles touching each other is π(2+3)23\frac{\pi\left(2 + \sqrt{3}\right)^2}{3} square cm. What is the radius of one of the smaller circles ?

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  5. Question 5 (case study, 2 parts)

    Mensuration 3D. Asked once: CDS 1 2025

    A pot is made from a hollow sphere of inner radius 20 cm by cutting its upper portion horizontally. The height of the pot is 30 cm.
    59
    What is the inner radius of the circular opening of the pot so formed ?

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    60
    What is the angle made by the line joining the centre of the sphere and any point on the rim of the circular opening with a vertical line passing through the centre ?

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