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NDA 2 2024 Maths, question 2

Topic: Algebra

Q2

Consider the following statements :

I. The set of all irrational numbers between 12\sqrt{12} and 15\sqrt{15} is an infinite set.

II. The set of all odd integers less than 10001000 is a finite set.

Which of the statements given above is/are correct?

  1. (a) I onlyCorrect answer
  2. (b) II only
  3. (c) Both I and II
  4. (d) Neither I nor II

Solution.

Answer: (a) I only

  1. Every nonempty real interval contains infinitely many irrational numbers, so I is true.
  2. Odd integers less than 1000 include −1, −3, −5, … without a lower bound.
  3. Hence II is false; it would become true if “positive odd integers” were specified.