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Consider the following statements:

I. The set of all irrational numbers between  and  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 and 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 and is an infinite set.

Also, the set of all odd integers less than 1000 is , which is an infinite set.

Hence, Option (a) is correct.

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