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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 statement is correct about the decimal expansion of \(\sqrt{3}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsFor a square with an area of 2 cm², Aarav says, “Since the area is a rational number, the perimeter of the square must also be rational.” Which is the correct evaluation of Aarav’s statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Expert MathematicsIn the proof of (\sqrt{2}), if (a,b) are assumed coprime and later (a=2r) and (b=2s) are obtained, which conclusion is most precise?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsIn irrationality of (\sqrt{3}), which assumption is rejected by the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsA student assumes that \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. After obtaining \(p^2=3q^2\), the student says, “\(p\) is divisible by 3, but \(q\) need not be divisible by 3.” Which statement correctly identifies the error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsWhat is the most important exam caution in the proofs of √2 and √3?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIf (p,q) are assumed divisible by (3) from the start in the proof of (\sqrt{3}), what is the mistake?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsIf both (a,b) are assumed even from the beginning while proving (\sqrt{2}), what is the mistake?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsWhile proving the irrationality of \(\sqrt{2}\) by contradiction, assume that \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. Which conclusion makes this assumption impossible?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsIf \(\sqrt{3}=\frac{p}{q}\) is assumed to be in lowest terms, where \(p\) and \(q\) are coprime integers, which statement produces the contradiction in the proof of its irrationality?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsSuppose \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. Which property is used to infer \(3\mid p\) from \(3\mid p^2\) in the proof?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsSuppose \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. Which contradiction follows from this assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsIn a proof by contradiction that √2 is irrational, a student assumes √2 = a/b, where a and b are coprime positive integers. From 2b² = a², the student concludes that a is even. Which is the correct basis for this conclusion?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsWhy must \(p/q\) be taken in lowest terms in the standard proof by contradiction that \(\sqrt{3}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsHow would the decimal expansion of \(\sqrt{2}\) be classified?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsWhich divisibility rule is crucial in the proof by contradiction that \(\sqrt{3}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsA student assumes that \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers, and on squaring obtains \(p^2=2q^2\). Which reasoning correctly proves irrationality?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsIf a student tries to prove irrationality of √2 by writing its decimal value, what is the correct evaluation?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsWhy must \(\sqrt{3}=\frac{p}{q}\) be assumed to be in lowest terms while proving the irrationality of \(\sqrt{3}\) by contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Expert MathematicsWhat problem appears when a² = 2b² is viewed through prime factors in the proof of √2?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Hard