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Misconception Analysis

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

MathematicsA student says that \(\sqrt{3}\) is rational because 1.732 is a terminating decimal. What is the error in the student's reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Easy MathematicsA student says, “\(\sqrt{3}=\frac{6}{\sqrt{12}}\), so \(\sqrt{3}\) is rational.” What is the error in the argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Easy MathematicsA student claims that \(\sqrt{2}\) is rational because \(1.414=\frac{1414}{1000}\). What is the main error in the argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Easy MathematicsA student calls the number 0.101001000100001… rational because it contains only the digits 0 and 1. Why is the student’s conclusion incorrect?Class 9Number SystemsIrrational numbersExpert MathematicsA student claims that every non-terminating decimal is irrational. Which of the following examples disproves the claim?Class 9Number SystemsIrrational numbersExpert 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 numbersExpert 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 numbersHard 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 numbersHard 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 numbersMedium MathematicsRina says, “\(\sqrt{18}\) is rational because 18 is an integer.” Which option correctly identifies her error?Class 9Number SystemsIrrational numbersMedium MathematicsA student claims that the number 0.101001000100001... is rational because it contains only the digits 0 and 1. Which statement correctly corrects the student's claim?Class 9Number SystemsIrrational numbersMedium 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 numbersMedium MathematicsA student says that \(4+\sqrt{3}\) is rational because 4 is rational. What is the error in the student's conclusion?Class 9Number SystemsIrrational numbersMedium MathematicsA student says that \(0.101001000100001\ldots\) is a rational number because it contains only the digits 0 and 1. What is the correct evaluation of the student's statement?Class 9Number SystemsIrrational numbersMedium MathematicsA student claims that \(0.999\ldots\) is less than \(1\) because all its finite decimal forms, such as \(0.9\) and \(0.99\), are less than \(1\). Which is the correct evaluation of this claim?Class 9Number SystemsDecimal representationExpert MathematicsReema says that \(0.\overline{27}\) is irrational because its decimal expansion is non-terminating. Which statement best explains Reema’s error?Class 9Number SystemsDecimal representationHard MathematicsRiya says, “If the denominator of a fraction in simplest form has a prime factor other than 2 or 5, then its decimal expansion repeats from immediately after the decimal point.” Which fraction below proves Riya’s statement wrong?Class 9Number SystemsDecimal representationHard MathematicsA student says that \(0.101001000100001\ldots\) is a recurring decimal because 0 and 1 appear repeatedly in it. Which is the correct evaluation of the statement?Class 9Number SystemsDecimal representationMedium MathematicsA student says that \(0.101001000100001\ldots\) is rational because it contains only the digits 0 and 1. Which statement correctly explains the student's error?Class 9Number SystemsDecimal representationMedium MathematicsA student claims that every non-terminating decimal expansion is irrational. Which example proves the claim wrong?Class 9Number SystemsDecimal representationMedium