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Class 9 Mathematics

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

MathematicsJust before constructing √15 in a square root spiral, which length will already have been constructed?Class 9Number SystemsSquare root spiralEasy MathematicsIn constructing a square root spiral, which side of the previous right triangle is used as one side of the next triangle?Class 9Number SystemsSquare root spiralEasy MathematicsIn constructing a square root spiral, a student uses a hypotenuse of \(\sqrt{6}\) and draws a perpendicular side of 1 unit. Which number will the new hypotenuse represent?Class 9Number SystemsSquare root spiralEasy MathematicsIn a square root spiral, which segment is drawn at the end of the previous hypotenuse to form a new right triangle?Class 9Number SystemsSquare root spiralEasy MathematicsIf \(x=\sqrt{2}+\sqrt{3}\), which argument correctly disproves the assumption that \(x\) is rational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Expert MathematicsA student claims that if \(3p^2=q^2\), then \(p\) must be divisible by 3. What is the correct evaluation of the claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Expert MathematicsSuppose \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. Which statement correctly justifies the conclusion \(3\mid p\) from \(3\mid p^2\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Expert MathematicsIf \(\sqrt{3}=\frac{p}{q}\) is assumed to be in lowest terms and \(p^2=3q^2\) is obtained, which conclusion about \(p\) and \(q\) contradicts this assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Expert MathematicsIf \(\sqrt{3}=\frac{p}{q}\) is assumed to be in lowest terms and \(p^2=3q^2\) is obtained, which conclusion establishes the contradiction in this assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Expert MathematicsWhich of the following statements is correctly used in the proof that sqrt(3) is irrational in number systems?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Expert MathematicsIf a contradiction is obtained after assuming that √2 is rational, according to logic which conclusion is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Expert MathematicsIn a proof by contradiction, a student assumes \(\sqrt{3}=p/q\), where \(p\) and \(q\) are coprime. After obtaining \(p^2=3q^2\), which statement correctly justifies the conclusion \(3\mid p\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Expert MathematicsA student says that if \(\sqrt{3}=\frac{p}{q}\), then \(p^2=3q^2\) only implies that \(p\) is divisible by 3; nothing can be concluded about \(q\). What is the student's error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Expert MathematicsIf the contradiction proof of \(\sqrt{2}\) succeeds, what is the final logical conclusion?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Expert MathematicsIn the contradiction proof that \(\sqrt{3}\) is irrational, assume \(\sqrt{3}=\frac{p}{q}\), where \(\gcd(p,q)=1\). This gives \(p^2=3q^2\). Which principle is correctly applied from \(3\mid p^2\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Expert MathematicsWhich statement is correct about the decimal expansion of \(\sqrt{3}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Expert MathematicsA student claims that the diagonal of a square of side 1 unit is a rational number. Which argument correctly disproves this claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Expert MathematicsWhich assumption is made at the beginning to prove the irrationality of \(\sqrt{3}\) by contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Expert MathematicsIn a proof by contradiction for the irrationality of \(\sqrt{3}\), a student obtains \(p^2=3q^2\). Given that \(p\) is divisible by 3, which next step correctly advances the proof?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Hard MathematicsRima says, “If \(\sqrt{12}\) were rational, then \(\sqrt{3}=\frac{\sqrt{12}}{2}\) would also be rational, which contradicts the irrationality of \(\sqrt{3}\).” What is Rima’s conclusion?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Hard