Q2 / 120 · NDA 2024 (Phase 2) · Mathematics

Consider the following statements : A. The set of all irrational numbers between $\sqrt{12}$ and $\sqrt{15}$ is an infinite set. B. The set of all odd integers less than 1000 is a finite set. Which of the statements given above is/are correct?

  • Correct answer
    A
    A only
  • B
    B only
  • C
    Both A and B
  • D
    Neither A nor B

Solution

Since between any two irrational numbers, infinite number of irrational numbers are there. Hence, the set of all irrational numbers between $\sqrt{12}$ and $\sqrt{15}$ is having infinite number of elements. $\because$ Set of all odd integers less than 1000 is $\{\ldots . .-5,-3$, $1,3, \ldots . .999\}$ which is an infinite set.

Hence, the correct answer is option: 'A'.

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