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Number Systems

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

MathematicsRima says, “\(\sqrt{2}\) is irrational because its decimal expansion is infinite.” What is the main flaw in her reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsWhich prime-divisibility property is crucial in a proof by contradiction that \(\sqrt{3}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsIf a student stops after proving only that a is divisible by 3 in the proof of √3, what is the main error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsSuppose \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. Which conclusion follows from this assumption and produces a contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsA student says that the decimal expansion of \(\sqrt{2}\) never terminates, so it is irrational. Which of the following arguments rigorously proves this conclusion?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsSuppose \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. Which conclusion is needed to establish the contradiction in the proof of irrationality?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard 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 3Level 18Hard MathematicsIf a proof writes \(\sqrt{2}=\frac{m}{n}\) but does not state lowest form, what is the biggest weakness?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard 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 3Level 18Hard MathematicsWhat is the correct difference between the roles of (b\neq0) and (\gcd(a,b)=1) in the proof of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsWhat is the correct difference between the roles of (n\neq0) and (\gcd(m,n)=1) in the proof of (\sqrt{2})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsIf a and b are coprime and both are proved divisible by 3, what is the correct contradiction about gcd(a,b)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsIf (m,n) are coprime and both are proved even, what is the correct contradiction about (\gcd(m,n))?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsWhich idea about exponents of prime factors deeply explains the irrationality of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsWhich idea about exponents of prime factors deeply explains the irrationality of (\sqrt{2})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsIn a proof that \(\sqrt{3}\) is irrational, if \(\frac{p}{q}\) is assumed to be in lowest terms and \(p^2=3q^2\) is obtained, which conclusion establishes the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsIf \(\sqrt{3}=p/q \), where \(p \) and \(q \) are coprime positive integers, which conclusion is required to establish the contradiction?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 in lowest terms and \(p^2=3q^2\) is obtained, which conclusion is necessary to reach the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsWhile proving the irrationality of \(\sqrt{3}\) by contradiction, Riya shows that in the fraction \(a/b\) written in lowest terms, both \(a\) and \(b\) are divisible by 3. Why is this conclusion impossible?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsIn the proof by contradiction that \(\sqrt{3}\) is irrational, if \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime positive integers, which conclusion necessarily follows from \(3q^2=p^2\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard