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Rational Numbers

Class 9 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsIf two irrational numbers \(a\) and \(b\) are such that \(a+b\) is rational, which conclusion about \(ab\) is correct?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsA student says that every non-terminating decimal number is irrational. Which of the following numbers shows the error in this statement?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsA student claims, “The sum of two irrational numbers is always irrational.” Which of the following pairs disproves this claim?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsA student claims that \(5-\sqrt{7}\) is a rational number. Which argument correctly proves that the claim is wrong?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsWhich of the following statements is always true about the sum of two irrational numbers?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsIn which option is the difference of two irrational numbers rational?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsIf \(p\) is an irrational number and \(q\) is a non-zero rational number, which of the following statements is always true?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsA student claims that \(\frac{\sqrt{18}}{\sqrt{2}}\) must be irrational because both the numerator and denominator are irrational. What is the correct conclusion?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsRavi claims that \(x=\frac{3+\sqrt{2}}{5}\) is rational because its denominator is 5. What is the error in Ravi’s claim?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsIn which option are both numbers irrational, but their sum is rational?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsReema claims that the product of two irrational numbers is always irrational. Which of the following examples disproves her claim?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsIf an irrational number is added to a rational number, what will the resulting number always be?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsA student claims that the quotient of any two irrational numbers is always irrational. Which of the following calculations conclusively proves the claim wrong?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsIf \(x\) is an irrational number and \(r\) is a rational number, which of the following will always be irrational?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsA student claims that the number 0.101001000100001... is rational because it contains only the digits 0 and 1. What is the correct evaluation of this claim?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsA student says that the product of any two irrational numbers is always irrational. Which option correctly evaluates this statement using a a a ?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsWhich of the following statements is always true, where a rational number may also be zero?Class 9Number SystemsIrrational numbersLevel 14Hard MathematicsRiya claims that the product of any two irrational numbers is always irrational. Which of the following pairs is a counterexample to her claim?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsLet \(x\) be an irrational number and \(r\) be a rational number. Which of the following statements is always true?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsWhich of the following decimal representations denotes an irrational number?Class 9Number SystemsIrrational numbersLevel 13Hard