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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. 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. If \(\sqrt{1+\frac{\sqrt{3}}{2}}- \sqrt{1-\frac{\sqrt{3}}{2}}= c\) , then the value of c is:

  2. If \(\frac{\sqrt{38-5\sqrt{3} } }{\sqrt{26+7\sqrt{3} } }= \frac{a+b\sqrt{3} }{23} \) , b > 0, then the value of (b – a) is:

  3. If \( \frac{5}{4{\sqrt 2 }} + \frac{{3 + 2\sqrt 2 }}{{3 - 2\sqrt 2 }} - \frac{{3 - 2\sqrt 2 }}{{3 + 2\sqrt 2 }} = a + b\sqrt 2 \) , then what is the value of (3a + 4b)?

  4. If \(\frac {8 + 2\sqrt 3}{3\sqrt 3 + 5} = a\sqrt 3 - b,\)  then the value of a + b is equal to:

  5. If \(\frac{\sqrt{26-7\sqrt{3} } }{\sqrt{14+5\sqrt{3} } } = \frac{b+a\sqrt{3} }{11}\) , b > 0, then what is the value of  \(\sqrt{(b-a)} \)  ?

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