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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।

MathematicsIf the square of an integer is divisible by 3, which conclusion about the integer must be true?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsWhile proving the irrationality of \(\sqrt{3}\) by contradiction, if \(\sqrt{3}=\frac{p}{q}\) is assumed to be in lowest terms, which conclusion about \(p\) and \(q\) produces the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsWhich of the following statements is an essential part of the proof by contradiction that \(\sqrt{2}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIn a proof that \(\sqrt{3}\) is irrational, a student writes: “If \(3\mid p^2\), we can conclude only that \(p^2=3k\).” What is the correct correction needed to continue the argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsWhat is the most exam-useful caution in the proofs of √2 and √3?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsWhich option correctly pairs the conclusion and basis of the proof of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIf \(\sqrt{3}=\frac{p}{q}\) is assumed in lowest terms to prove its irrationality, which fact produces the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIf a student stops after proving only (u) divisible by (3) in the proof of (\sqrt{3}), what is the main error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIf a student stops after proving only (x) even in the proof of (\sqrt{2}), what is the main error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsWhich statement is an essential basis of the proof by contradiction that \(\sqrt{2}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsWhich option best states the role of (2) in the proof of (\sqrt{2})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIn the contradiction proof that √3 is irrational, \(p^2=3q^2\) gives \(3\mid p^2\). Which fact is used to conclude that \(3\mid p\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIf both \(x,y\) are even, why is \(\frac{x}{y}\) considered reducible?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsWhile proving the irrationality of \(\sqrt{3}\) by contradiction, what conclusion about \(p\) is drawn from \(p^2=3q^2\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIf a proof writes (\sqrt{2}=\frac{x}{y}) but does not state lowest form, what is the biggest weakness?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIn a proof by contradiction that \(\sqrt{2}\) is irrational, suppose \(\sqrt{2}=\frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers. Which final condition contradicts this assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsWhich skipped step would make the proof of \(\sqrt{2}\) incomplete?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsWhat is the correct difference between the roles of (v\neq0) and (\gcd(u,v)=1) in the proof of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsWhat is the correct difference between the roles of (y\neq0) and (\gcd(x,y)=1) in the proof of (\sqrt{2})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIf u and v are coprime and both are proved divisible by 3, what contradiction about gcd(u,v) follows?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard