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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 p and q be rational numbers with q ≠ 0. If a student claims that \(\frac{p+\sqrt{2}}{q}\) is rational, which conclusion would follow from the claim?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsIf \(x\) is an irrational number, which of the following expressions will always be irrational?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsLet \(x\) be an irrational number and \(r\) be a rational number. Which of the following expressions must be irrational?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsA student says that \\(\frac{\sqrt{18}}{\sqrt{2}}\\) is irrational because it is the quotient of two irrational numbers. Which evaluation is correct?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsA student says, “The product of any two irrational numbers is always irrational.” Which is the correct evaluation of the statement?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsIf \(x\) is an irrational number, which of the following expressions will always be a rational number?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsIf \(x\) is an irrational number, which of the following numbers will always be irrational?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsA student says, “The sum of two irrational numbers can never be rational.” Which of the following pairs proves this statement wrong?Class 9Number SystemsIrrational numbersLevel 13Hard MathematicsA student says that the decimal number \(0.101001000100001\ldots\) is rational because it contains only the digits 0 and 1. Which statement correctly identifies the student's error?Class 9Number SystemsIrrational numbersLevel 15Medium MathematicsA student claims that every non-terminating decimal number is irrational. Which of the following numbers is a counterexample to the claim?Class 9Number SystemsIrrational numbersLevel 15Medium MathematicsA student says that every non-terminating decimal expansion is irrational. Which of the following numbers disproves the statement?Class 9Number SystemsIrrational numbersLevel 15Medium MathematicsA student says that every non-terminating decimal is irrational. Which example shows the error in this statement?Class 9Number SystemsIrrational numbersLevel 15Medium MathematicsReena says that the sum of two irrational numbers is always irrational. Which of the following examples correctly shows the error in her statement?Class 9Number SystemsIrrational numbersLevel 15Medium MathematicsA student says, “Every non-terminating decimal expansion is irrational.” Which of the following examples proves this statement wrong?Class 9Number SystemsIrrational numbersLevel 15Medium MathematicsReema says that the sum of two irrational numbers is always irrational. Which of the following examples proves her statement wrong?Class 9Number SystemsIrrational numbersLevel 15Medium MathematicsRahul says that every number with an infinite decimal expansion is irrational. Which of the following examples proves Rahul’s statement wrong?Class 9Number SystemsIrrational numbersLevel 15Medium MathematicsReema says that every non-terminating decimal is an irrational number. Which of the following examples shows the error in her statement?Class 9Number SystemsIrrational numbersLevel 15Medium MathematicsRiya says that \(\sqrt{n}\) is irrational for every natural number n. Which of the following examples proves her statement wrong?Class 9Number SystemsIrrational numbersLevel 15Medium MathematicsWhich statement correctly describes the decimal expansion of an irrational number?Class 9Number SystemsIrrational numbersLevel 14Medium MathematicsA student says, “The sum of two irrational numbers is always irrational.” Which of the following examples proves this statement wrong?Class 9Number SystemsIrrational numbersLevel 14Medium