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Question

The negative of a non-zero rational number is:

This question was previously asked in
RRB NTPC 2019 CBT 1 Question Paper (8-Mar-2021) (Shift 2)
The correct answer is
a rational number

To solve this question, we need to understand the properties of rational numbers and how negation affects them.

  1. A rational number is any number that can be expressed as the quotient or fraction \(\frac{p}{q}\), where \(p\) and \(q\) are integers and \(q \neq 0\).
  2. The negative of a rational number is simply the negation of that number. If we have a rational number \(\frac{p}{q}\), its negative would be \(-\frac{p}{q}\). Since the negation operation just changes the sign of the number, the result \(-\frac{p}{q}\) is still a fraction of integers, where the denominator is not zero, thus maintaining its identity as a rational number.
  3. Let's examine the options:
    • Surd: A surd is an irrational number that cannot be expressed as a simple fraction. Since the negative of a rational number is itself rational, this option is incorrect.
    • Zero: The negative of a non-zero rational number cannot be zero. Therefore, this option is incorrect.
    • A rational number: As shown, the negative of a rational number is itself a rational number. Thus, this is the correct option.
    • An irrational number: An irrational number cannot be expressed as a fraction of two integers. The negation of a rational number cannot become irrational, so this option is incorrect.
  4. Conclusion: The negative of a non-zero rational number is indeed a rational number. Therefore, the correct answer is "a rational number."
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Similar Questions

  1. $(\sqrt{5} + \sqrt{7})^2$ is a:
  2. An irrational number between 3 and 5 is:
  3. Which of the following rational number lies between $\frac{1}{4}$ and $\frac{1}{2}$.
  4. Which of the following rational number lies between 9.2 and 10.5?
  5. Express $-\frac{40}{56}$ as a rational number whose numerator is $-5$.
  6. The arrangement of rational numbers $-\frac{7}{10}, \frac{5}{-8}, \frac{2}{-3}$ in ascending order is:

Important Questions from Rational or Irrational Numbers

  1. Which of the following number is irrational?

  2. Which of the following numbers will have an irrational square root?

  3. What is the square root of 16 + 6√7?

  4. A non-terminating but recurring decimal is:

  5. Which of the following is false?

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