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Number Systems

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

MathematicsRiya says that \(\sqrt{3}\) is rational because its decimal form is \(1.732\). Which statement correctly identifies the error in her claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsWhich statement gives both correct reason and conclusion in the proof of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsA student argues that if \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers, then \(p^2=3q^2\) proves only that \(p\) is divisible by 3. Identify the student's error.Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsWhich initial assumption is made to prove the irrationality of \(\sqrt{2}\) by the method of contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsIn the proof that \(\sqrt{3}\) is irrational, suppose \(\sqrt{3}=p/q\) is in lowest terms and squaring gives \(p^2=3q^2\). What correctly fixes a student's error that \(3\mid p^2\) does not imply \(3\mid p\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsBefore proving the irrationality of \(\sqrt{3}\) by contradiction, in what form must \(\frac{p}{q}\) be assumed?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsIf the rational assumption for (\sqrt{2}) were correct, what should be true about (\frac{m}{n})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsWhat is the combined conclusion of the proofs of (\sqrt{2}) and (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsWhile proving \(\sqrt{3}\) irrational by contradiction, suppose \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. What follows immediately from \(p^2=3q^2\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsWhy is the proof of \(\sqrt{2}\) valid without decimal expansion?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsIn the proof of (\sqrt{3}), if (p) is not divisible by (3), what conflict occurs with (p^2=3q^2)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsIf \(\sqrt{3}\) is assumed to be \(\frac{p}{q}\) in lowest terms, what conclusion follows from \(p^2=3q^2\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsIf (p) and (q) are coprime, which situation is impossible in the proof of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsWhy are p and q chosen coprime in √3 = p/q?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsSuppose a student writes \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime, while proving that \(\sqrt{3}\) is irrational. From \(p^2=3q^2\), which conclusion about \(p\) is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsWhich statement is used to move from p² to p in the proof of √3?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsA student says that since 5 is a rational number, \(5+\sqrt{3}\) must also be rational. Which statement correctly identifies the error in the argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsIn the proof of (\sqrt{3}), why is it incomplete to write directly from (p^2=3q^2) that (q) is divisible by (3)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsA student believes that the statement “If the square of an integer is divisible by 3, then the integer is also divisible by 3” is false. Which statement correctly removes this misconception?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsWhich option gives the correct order in the proof of irrationality of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium