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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।

MathematicsIn the proof of (\sqrt{3}), if a student directly writes from (p^2=3q^2) that (q) is divisible by (3), what is the correct comment?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsIn the proof of (\sqrt{2}), if a student writes directly from (m^2=2n^2) that (n) is even, what is the correct comment?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsOn what basis does the final conclusion in irrationality of (\sqrt{3}) come?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsOn what basis does the final conclusion in irrationality of (√2) come?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsWhich option gives the correct reasoning from (p²) to (p) in the proof of (√3)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsIf \(\sqrt{3}\) is assumed to be \(\frac{p}{q}\) in lowest terms, where \(p\) and \(q\) are coprime integers, what follows from \(p^2=3q^2\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsIn a proof by contradiction, Arjun assumes that \(\sqrt{2}=\frac{m}{n}\), where \(m\) and \(n\) are coprime. He obtains \(m^2=2n^2\) and says, “\(m\) is even, so \(\sqrt{2}\) is irrational.” What is missing from his argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsIn the proof of (\sqrt{2}), which condition is necessary along with assuming (\sqrt{2}=\frac{m}{n})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsA student says, “3 is not a perfect square, so \(\sqrt{3}\) is irrational.” Which step is needed to complete this argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsIn a proof that √3 is irrational, suppose √3 = p/q, where p and q are coprime. Squaring gives p² = 3q², and on writing p = 3k, we get q² = 3k². Which conclusion is needed to complete the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsWhich option shows the correct logical chain in the proof of (√3)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsWhich option shows the correct logical chain in the proof of (√2)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsIn the proof of (\sqrt{3}), (p^2=3q^2) gives (p=3k) and then (q^2=3k^2). What will be the final conclusion?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsWhich of the following numbers has an irrational positive square root?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsWhich statement is a wrong conclusion in the proof of \(\sqrt{3}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsA student assumes that \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime positive integers. If \(p^2=3q^2\) is obtained, what is the correct next conclusion in the proof?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsIn the proof of (\sqrt{3}), after getting (q^2=3k^2), what is the next conclusion toward final contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsWhile proving the irrationality of \(\sqrt{3}\) by contradiction, if assuming \(\sqrt{3}=\frac{p}{q}\) in lowest terms gives \(p^2=3q^2\), which conclusion creates the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsIn the proof of (\sqrt{3}), why can we write (p=3k) from (p^2=3q^2)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsIn contradiction method, which initial assumption is taken for (\sqrt{2})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium