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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।

MathematicsLet \(x\) be an irrational number and \(r\) be a rational number. Which of the following expressions is always irrational?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsLet \(x\) be an irrational number and \(r\) be a non-zero rational number. Which of the following expressions must be irrational?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsLet \(x\) be an irrational number and \(r\) be a rational number. Which of the following expressions will always be irrational?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsWhich of the following statements correctly identifies the decimal expansion of an irrational number?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsWhich of the following statements is necessarily true for every irrational number \(x\)?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsIf \(x\) is an irrational number and \(r\) is a non-zero rational number, which of the following statements is always true?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsIf \(x\) is an irrational number and \(r\) is a non-zero rational number, which statement about \(rx\) is always true?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsIf r is a non-zero irrational number and q is a non-zero rational number, which of the following statements is always true?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsA student says, “Every number with a non-terminating decimal expansion is irrational.” Which of the following numbers proves this statement wrong?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsLet \(a\) be an irrational number and \(r\) be a non-zero rational number. Which of the following statements is always true?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsRiya says that the quotient of two irrational numbers is always irrational. Which of the following examples proves her statement wrong?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsLet \(x\) be a non-zero irrational number, and let \(a\) and \(b\) be rational numbers, where \(b\ne0\). Which of the following expressions is always irrational?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsLet \(r\) be a rational number and \(x\) be an irrational number. Which of the following conclusions is always true?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsA student claims that the sum of any two irrational numbers is always irrational. Which of the following examples proves the claim wrong?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsA student claims that the sum of two irrational numbers is always irrational. Which of the following expressions is a counterexample to the claim?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsA student has written the following conclusions about irrational numbers. Which conclusion is always correct?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsWhich of the following statements correctly describes the relationship between rational and irrational numbers?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsWhich condition on two irrational numbers guarantees that their sum is rational?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsIf \(x\) is an irrational number and \(r\ne 0\) is a rational number, which of the following statements is always true?Class 9Number SystemsIrrational numbersLevel 15Hard MathematicsIf \(a\) is an irrational number and \(b\) is a non-zero rational number, which statement about \(a+b\) is always true?Class 9Number SystemsIrrational numbersLevel 15Hard