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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।

MathematicsWhy is it incomplete to write (b) divisible by (3) directly from (a^2=3b^2) in the proof of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsA student says that \(\sqrt{2}+\sqrt{3}\) is irrational because the sum of two irrational numbers is always irrational. What is the correct evaluation of this statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsWhat is the basis of 3 ∣ a² ⇒ 3 ∣ a in the proof of √3?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsA student claims that if the square of an integer is divisible by 3, then the integer itself is divisible by 3. What is the correct evaluation of this claim?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, which condition on \(p\) and \(q\) is necessary?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsIf \(m=2k\) and \(n^2=2k^2\), what is the combined conclusion in the proof of \(\sqrt{2}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsRavi claims that \(7+\sqrt{2}\) is a rational number because 7 is rational. What is the error in Ravi’s reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsWhat problem occurs if (\gcd(m,n)=1) is not written in the proof of (\sqrt{2})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsWhich option gives the correct complete logical chain for the proof of \(\sqrt{3}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsWhich option gives the correct complete logical chain for the proof of \(\sqrt{2}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsIn the proof of (\sqrt{3}), if (a) is not divisible by (3), what inconsistency arises from (a^2=3b^2)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsIf \\(\sqrt{3}\\) is written as \\(a/b\\), where \\(a\\) and \\(b\\) are coprime integers, which conclusion produces the contradiction in the proof of its irrationality?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsWhich option shows a wrong shortcut in the proof of √3?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsWhich option shows an invalid shortcut in the proof of √2?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsIf (\sqrt{3}=\frac{a}{b}) with (\gcd(a,b)=1), but both (a,b) are proved divisible by (3), which contradiction is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsIn a proof that \(\sqrt{3}\) is irrational, a student assumes \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime, and obtains \(p^2=3q^2\). The student directly writes that \(q\) is divisible by 3. Which statement is needed to make the reasoning valid?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsIf b^2=3a^2 is obtained when b is in lowest form, which property is used to prove that b is divisible by 3?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsA student claims that \(\sqrt{12}\) is rational because 12 is not a perfect square. Which is the correct simplified form of \(\sqrt{12}\) that identifies the error in the claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsA student assumes that \(\sqrt{2}=\frac{m}{n}\), where \(m\) and \(n\) are coprime. Which conclusion from \(m^2=2n^2\) proves that this assumption is contradictory?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard MathematicsIf ext{\(\sqrt{3}\)} is assumed to be ext{\(p/q\)} , where ext{\(p\)} and ext{\(q\)} are coprime integers, which fact produces the contradiction in the proof?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 18Hard