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Day 281: CDS Maths

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

  1. Question 1

    Linear Equations. Asked once: CDS 1 2020

    11
    A two-digit number is 9 more than four times of the number obtained by interchanging its digits. If the product of digits in the two-digit number is 8, then what is the number ?

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  2. Question 2

    Logarithms. Asked once: CDS 1 2017

    16
    What is the solution of the equation xlog⁡10(103)+log⁡103=log⁡10(2+3x)+xx \log_{10} \left( \dfrac{10}{3} \right) + \log_{10} 3 = \log_{10} (2 + 3^x) + x ?

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  3. Question 3 (case study, 3 parts)

    Mensuration 2D. Asked once: CDS 1 2024

    Consider the following for the next three (03) items that follow : A triangle CEF is drawn inside a square ABCD as shown in the figure given below. Given : CF = 8 cm, EF = 6 cm and CE = 10 cm.
    76
    What is the area of the square ?

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    77
    What is tan⁡α+tan⁡β\tan \alpha + \tan \beta equal to ?

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    78
    What is the area of triangle CDE ?

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  4. Question 4

    Mensuration 3D. Asked once: CDS 1 2022

    85
    The length, breadth and height of a cuboid are in the ratio 27:8:127 : 8 : 1. The cuboid is melted and recast into a cube. If pp is the surface area of the cuboid and qq is the surface area of the cube, then what is p/qp/q equal to?

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  5. Question 5

    Number System. Asked once: CDS 2 2024

    75
    The difference of 1031−510^{31} - 5 and 1030+p10^{30} + p is divisible by 3 where pp is a digit. How many values of pp are possible ?

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