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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।

MathematicsRiya claims that \(0.101001000100001\ldots\) is rational because only the digits 0 and 1 occur in it. Which is the correct refutation of her claim?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsIf r is an irrational number and q is a rational number, which of the following expressions will always be irrational?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsIf \(r\) is a rational number and \(x\) is an irrational number, which of the following statements is always true?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsLet \(p\) be a rational number and \(x\) be an irrational number. Which of the following statements is always true?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsLet \(a\) be a non-zero rational number and \(b\) be an irrational number. Which of the following statements is always true?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsWhich of the following statements is necessarily true?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsA student claims that the product of two irrational numbers is always irrational. Which of the following examples disproves this claim?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsA student claims that every non-terminating decimal is irrational. Which of the following examples disproves the claim?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsLet \(x\) be an irrational number and \(q\) be a non-zero rational number. Which of the following statements is always true?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsWhich of the following numbers is rational despite containing square-root signs?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsWhich of the following decimal expansions identifies a real number as irrational?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsNidhi says that the number \(0.101001000100001\ldots\) is rational because its decimal expansion contains only 0 and 1. Which statement correctly explains Nidhi's error?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsLet \(r\) be an irrational number and \(q\) be a non-zero rational number. Which of the following statements is always true?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsIf \(x\) is an irrational number and \(r\) is a rational number, which of the following expressions will be irrational in every case?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsWhere \(q\) is any rational number, which of the following expressions is guaranteed to be irrational?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsA student claims that \(3+\sqrt{2}\) is a rational number. Which argument proves the student's claim wrong?Class 9Number SystemsIrrational numbersLevel 14Expert MathematicsIf \(r\) is an irrational number and \(q\) is a rational number, which of the following statements is always true?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsSuppose \(x\) is an irrational number and \(q\) is a non-zero rational number. Which statement about \(qx\) is always true?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsIf \(x\) is an irrational number, which of the following expressions is not necessarily irrational?Class 9Number SystemsIrrational numbersLevel 13Expert MathematicsA student claims that the product of two irrational numbers is always irrational. Which of the following examples disproves the claim?Class 9Number SystemsIrrational numbersLevel 13Expert