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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।

MathematicsWhat is the main reason for assuming (\sqrt{3}=\frac{p}{q}) in lowest form?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsA student claims that if \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers, then \(p^2=3q^2\) proves only that \(p\) is divisible by 3. What is the correct improvement to the argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Medium MathematicsWhich option gives the correct final argument in the proof of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsA student has to prove that \(1+\sqrt{3}\) is irrational. Which of the following arguments is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIn the proof of (\sqrt{3}), if after taking (p=3k) we get (q^2=3k^2), which conclusion does it lead to?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIn the proof of √2, if after taking a = 2r we get b² = 2r², what does it prove next?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsWhich option is the correct final statement for both (\sqrt{2}) and (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsA student assumes that \(\sqrt{2}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. After obtaining \(p^2=2q^2\), which conclusion creates a contradiction in this assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsA student assumes that \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. After obtaining \(p^2=3q^2\), which conclusion is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsWhich option gives the correct rational form used in the proof of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsWhich option gives the correct rational form used in the proof of (\sqrt{2})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsA student claims that if the square of an integer is divisible by 2, then the integer itself is divisible by 2. How is this statement useful in proving the irrationality of \(\sqrt{2}\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIf assuming \(\sqrt{3}=p/q\), where \(p\) and \(q\) are coprime, leads to \(p^2=3q^2\), which conclusion creates the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsWhy is \(\frac{p}{q}\) taken in lowest terms while proving the irrationality of \(\sqrt{2}\) by contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIf (a) and (b) are coprime, which situation is not possible?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsWhich option gives the correct conclusion and reason for the proof of √3?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsA student writes: If \(\sqrt{3}=\frac{a}{b}\), where \(a\) and \(b\) are coprime, then \(a^2=3b^2\). The student concludes that 3 divides \(b\). What is the error in this conclusion?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIn the proof of (\sqrt{3}), which assumption is finally rejected?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsIn the proof of √2, what is finally proved false?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium MathematicsA student claims that \(\sqrt{3}=\frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers. Which correct conclusion follows from this claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 16Medium