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

MathematicsWhich option best describes the role of (2) in the proof of (\sqrt{2})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsA student says that the decimal expansion of \(\sqrt{3}\) is 1.732... and does not terminate; therefore, \(\sqrt{3}\) is irrational. What is the main error in the student's reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsIn the proof of (\sqrt{2}), if both (a,b) are even, why can (\frac{a}{b}) be called reducible?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsSuppose \(r=\sqrt{2}+\sqrt{3}\) is a rational number. Which conclusion from this assumption proves by contradiction that \(\sqrt{2}+\sqrt{3}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsIf an answer writes √2 = a/b but does not mention gcd(a,b) = 1, what is the best comment?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsIn the proof of (\sqrt{3}), which skipped step would prevent the final contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsIf \(\sqrt{3}=\frac{p}{q}\) is assumed to be in lowest terms and \(p^2=3q^2\) is obtained, which conclusion is necessary to establish the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsWhich option correctly distinguishes (q\neq0) and the coprime condition in the proof of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsIf \(\sqrt{3}=\frac{p}{q}\) is assumed in lowest terms to prove irrationality, which statement establishes the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsWhich of the following conclusions about radicals is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsWhile proving the irrationality of \(\sqrt{3}\) by contradiction, suppose \(\sqrt{3}=\frac{p}{q}\) is in lowest terms. What conclusion about \(p\) follows from \(p^2=3q^2\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsWhich option gives the deeper prime-factor reason for irrationality of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsWhich option states the correct hidden principle used in the proof of (\sqrt{2})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsWhich statement is sufficient to reject the rational assumption in the proof of (√3)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsWhich statement is sufficient to reject the rational assumption in the proof of (\sqrt{2})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsIn the proof by contradiction that \(\sqrt{3}\) is irrational, if \(p\) and \(q\) are coprime and \(p^2=3q^2\), which conclusion follows immediately?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsA student claims that \(5+\sqrt{3}\) is rational because 5 is rational. Which is the correct refutation of this claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsWhich option gives the correct comparative analysis of the proofs of (\sqrt{2}) and (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsFor a positive integer \(n\), which of the following statements is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsIn the proof of √2, which option correctly distinguishes an ordinary rational form from the proof-ready form?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard