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Day 285: CDS Maths

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

  1. Question 1

    Logarithms. Asked once: CDS 2 2016

    1
    What is the solution of log⁡10[1−{1−(1−x2)−1}−1]−12=1\log_{10}\left[1 - \left\{1 - \left(1 - x^2\right)^{-1}\right\}^{-1}\right]^{-\frac{1}{2}} = 1 ?

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  2. Question 2 (case study, 2 parts)

    Mensuration 2D. Asked once: CDS 1 2024

    Consider the following for the next two (02) items that follow : ABCD is a circle with centre O and taking OC as a diameter, a circle is drawn as shown in the figure given below. Let OB = 7 cm. (Use π=227\pi = \frac{22}{7})
    79
    What is the area of the shaded region ?

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    80
    What is the ratio of the area of the shaded region to the area of the non-shaded region ?

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  3. Question 3

    Mensuration 3D. Asked once: CDS 1 2022

    84
    Water is trickling out of a completely filled cylindrical tank of height 1 m and diameter 2 m. Every second a spherical droplet of 1 cm radius trickles down from the bottom of the tank. The tank will be emptied in approximately

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  4. Question 4

    Number System. Asked once: CDS 2 2024

    24
    What is the sum of the largest and the smallest 4-digit numbers made by using single digit prime numbers (without repetition) ?

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  5. Question 5

    Percentage, Profit and Loss. Asked once: CDS 1 2017

    38
    If a%a\% of aa + b%b\% of bb = 2% of abab, then what percent of aa is bb ?

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