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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।

MathematicsIn the proof of (\sqrt{3}), if (u) is not divisible by (3), what conflict occurs from (u^2=3v^2)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIn the proof that \(\sqrt{3}\) is irrational, suppose \(\frac{p}{q}\) is in lowest terms and \(p^2=3q^2\) is obtained. Which fact is needed to establish the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsSuppose \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime positive integers. After obtaining \(p^2=2q^2\), which conclusion correctly advances the proof?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIf \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers, is assumed, which conclusion creates a contradiction in the proof?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsWhich of the following numbers must be irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsWhile proving the irrationality of \(\sqrt{3}\), a student assumes \(\sqrt{3}=\frac{a}{b}\), where \(a\) and \(b\) are coprime. The student obtains \(a^2=3b^2\). Which conclusion is correct for proceeding with the proof?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIn a proof by contradiction that \(\sqrt{2}\) is irrational, why must \(p\) and \(q\) be chosen coprime when assuming \(\sqrt{2}=\frac{p}{q}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIn which situation does the real contradiction in the proof of (\sqrt{2}) occur?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIf the square of a rational number is 3, what conclusion is obtained about its numerator and denominator in the proof that \(\sqrt{3}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsRiya assumes that \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. After concluding from \(p^2=3q^2\) that \(p\) is divisible by 3, which is the correct next statement to obtain a contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIf (\sqrt{3}=\frac{u}{v}) is assumed in lowest form and (u^2=3v^2) is obtained, why is it correct to write (u=3k)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsFor a positive integer \(n\), which statement correctly identifies when \(\sqrt{n}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIf a proof assumes √3 rational and finally gets both p and q divisible by 3, with which initial condition is the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsA student assumes \(\sqrt{3}=\frac{a}{b}\), where \(a,b\) are coprime positive integers. From \(a^2=3b^2\), the student concludes that 3 divides \(a\). Which rule justifies this conclusion?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsLet \(p\) and \(q\) be coprime positive integers. In a proof by contradiction for the irrationality of \(\sqrt{3}\), if \(3\mid p^2\), which conclusion is necessary?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsWhich option gives the correct conclusion and its basis for the proof of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsWhile proving the irrationality of \(\sqrt{3}\) by contradiction, assume \(\sqrt{3}=p/q\), where \(p\) and \(q\) are coprime. Which conclusion produces a contradiction to this assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsIn the proof of √3, if a student stops after proving only p is divisible by 3, what is the error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsIn the proof of \(\sqrt{2}\), if a student ends the proof after only writing \(a\) is even, what is the error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard MathematicsWhich option best describes the role of (3) in the proof of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard