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Inequalities

CDS Maths. Try each one first, then open its answer.

Top 10 CDS PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 3 times: CDS 1 2022, CDS 2 2022, CDS 1 2026. This one: CDS 1 2026 See all 3 of this type

    76
    A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question : Is rnr^n less than 1, where r is a real number and n is a natural number ? Statement-I : 0<r2<10 < r^2 < 1 Statement-II : 0<r3<20 < r^3 < 2 Which one of the following is correct in respect of the above Question and the Statements ?

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  2. Question 2

    Asked 2 times: CDS 2 2018*, CDS 2 2019 (* = numbers or wording changed that year) See all 2 times it was asked

    49
    For the inequation x2−7x+12>0x^2 - 7x + 12 > 0, which one of the following is correct ?

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  3. Question 3

    Asked once: CDS 2 2022 (same type asked 3 times) See all 3 of this type

    30
    Consider the question and two statements given below : Let x and y be two real numbers. Question : Is xy>0xy > 0 ? Statement-1 : x8y9<0x^8 y^9 < 0. Statement-2 : x9y10<0x^9 y^{10} < 0. Which one of the following is correct in respect of the question and the statements ?

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  4. Question 4

    Asked once: CDS 1 2022 (same type asked 3 times) See all 3 of this type

    41
    Consider a question and two statements : Question : Is 3x+2y3x + 2y positive? Statement-I : x3=−29.8x^3 = -29.8 Statement-II : y3=3xy^3 = 3x Which one of the following is correct in respect of the question and the statements?

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  5. Question 5

    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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  6. Question 6

    Asked once: CDS 2 2025

    3
    Let pp and qq be natural numbers such that q>pq>p. What is the largest value of pp such that q2−5p−4q^2-5p-4 is negative?

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  7. Question 7

    Asked once: CDS 2 2025

    59
    What is the solution of the inequalities 5x+3<8x−95x + 3 < 8x - 9 and 2x+20>5x+22x + 20 > 5x + 2 ?

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  8. Question 8

    Asked once: CDS 2 2021

    7
    If xx is a negative real number, then which of the following are not correct ? 1. There is some natural number kk such that kx>0kx>0 2. x2+x>0x^2+x>0 always 3. 2x<x<−x2x<x<-x 4. x2x^2 is always a rational number Select the correct answer using the code given below :

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  9. Question 9

    Asked once: CDS 2 2021

    27
    Consider the following inequalities : 1. a2−b2a2+b2>a−ba+b\dfrac{a^2-b^2}{a^2+b^2}>\dfrac{a-b}{a+b} where a>b>0a>b>0 2. a3+b3a2+b2>a2+b2a+b\dfrac{a^3+b^3}{a^2+b^2}>\dfrac{a^2+b^2}{a+b} only when a>b>0a>b>0 Which of the above is/are correct ?

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  10. Question 10

    Asked once: CDS 2 2018

    48
    The solution of linear inequalities x+y≥5x + y \ge 5 and x−y≤3x - y \le 3 lies

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