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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।

MathematicsA student assumes that \(\sqrt{2}=\frac{a}{b}\), where \(a\) and \(b\) are coprime integers. On proceeding with the proof, the student finds that both \(a\) and \(b\) are even. What decisive conclusion follows?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsA calculator displays \(\sqrt{3}\) as 1.7320508. Which conclusion is correct based on this display?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsWhat caution is necessary while proving the irrationality of √2 and √3?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsWhich option shows the correct cause-effect relation used in the proof of \(\sqrt{3}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsIf \(\sqrt{3}=\frac{p}{q}\) is assumed, where \(p\) and \(q\) are coprime integers, which conclusion produces the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsA student believes that any number with an infinite decimal expansion must be irrational. Which example disproves this statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsA student says that \(\sqrt{3}\) is irrational because its decimal expansion does not terminate. Which step correctly turns this into a rigorous proof?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsIn the proof of (\sqrt{3}), if both (p) and (q) become divisible by (3), what happens to the lowest form of (\frac{p}{q})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsWhich of the following statements is essential for proving the irrationality of \(\sqrt{3}\) by the contradiction method?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsIf a student writes (p=3q) directly from (p^2=3q^2) in the proof of (\sqrt{3}), what is the mistake?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsIf a student writes (a=2b) from (a^2=2b^2) in the proof of (\sqrt{2}), what is the mistake?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsWhich option gives the correct middle objective in the proof of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsWhich option gives the correct middle objective in the proof of (\sqrt{2})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsWhich option correctly describes the role of (p) and (q) in the proof of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsWhich option correctly describes the role of (m) and (n) in the proof of (\sqrt{2})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsA student assumes that \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. On squaring, the student gets \(p^2=2q^2\). Which conclusion proves that this assumption is invalid?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsIf assuming √2 is rational gives a contradiction, which assumption is proved false?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsA student says that if \(\sqrt{2}=\frac{p}{q}\), then both \(p\) and \(q\) may be even. Why is this statement incorrect in the proof that \(\sqrt{2}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsWhile proving the irrationality of \(\sqrt{3}\) by contradiction, suppose \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime. What is the first conclusion obtained from \(3q^2=p^2\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium MathematicsIn the proof of √3, what does p = 3k show?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Medium