Consider the following statements:

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

II. The set of all odd integers less than 1000 is a finite set.

Which of the statements given above is/are correct?

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NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. I only
  2. II only
  3. Both I and II
  4. Neither I nor II

Answer (Detailed Solution Below)

Option 1 : I only
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Detailed Solution

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Concept:

Properties of Irrational Numbers:

  • Between any two irrational numbers, there are an infinite number of irrational numbers.
  • The set of all irrational numbers between \( \sqrt{12} \) and \( \sqrt{15} \) is an infinite set.

Calculation:

Between any two irrational numbers, there are an infinite number of irrational numbers.

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

Also, the set of all odd integers less than 1000 is \( \{-5, -3, 1, 3, \dots, 999\} \), which is an infinite set.

Hence, Option (a) is correct.

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