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Day 223: CDS Maths

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

  1. Question 1

    Inequalities. Asked once: CDS 2 2025

    2
    Consider the following in respect of a positive real number xx : I. x+1x>1x+\frac{1}{x}>1 II. (x+1x)2>2\left(x+\frac{1}{x}\right)^2>2 III. (x+1x)4>9\left(x+\frac{1}{x}\right)^4>9 Which of the above are correct?

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  2. Question 2 (case study, 2 parts)

    Linear Equations. Asked once: CDS 2 2023

    The total monthly electricity bill for a house consists of the sum of two parts, one part is proportional to number of rooms and the other part is proportional to number of units consumed. Rs. 400 is the monthly electricity bill for a house with 8 rooms and consuming 240 units and Rs. 320 is the monthly electricity bill for a house with 6 rooms and consuming 200 units.
    45
    What is the monthly electricity bill for a house with m rooms and consuming n units ?

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    46
    What is the monthly electricity bill for a house with 7 rooms consuming 300 units ?

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  3. Question 3

    Lines, Angles and Polygons. Asked once: CDS 2 2025

    70
    Consider the following angles : I. 4∘4^\circ II. 5∘5^\circ III. 6∘6^\circ IV. 8∘8^\circ How many of the above can be the exterior angle of a regular polygon?

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  4. Question 4

    Logarithms. Asked once: CDS 2 2026

    8
    Consider the following statements in respect of common logarithms : I. The logarithm of a number greater than 100 but less than 1000 lies between 2 and 3. II. The logarithm of a positive number less than unity is negative. Which of the statements given above is/are correct ?

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  5. Question 5

    Mensuration 2D. Asked once: CDS 2 2026

    72
    PQRS is a square. M is a point on PS such that PM : MS = 2 : 1 and N is a point on SR such that SN : NR = 1 : 2. If the area of triangle MQN is 10 square units, then what is the perimeter of the square ?

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