Skip to content

Update

Muft Shiksha™ एक 100% Free Education Portal है 🇮🇳, जिसका उद्देश्य Class 9–12 के हर विद्यार्थी तक High-Quality Education को पूरी तरह मुफ्त पहुँचाना है। 🇮🇳 हम मानते हैं कि अच्छी शिक्षा किसी student की आर्थिक स्थिति पर निर्भर नहीं होनी चाहिए। 🇮🇳 हर विद्यार्थी को वही Quality Study Material, MCQs, Quizzes, Exam Preparation, Concept-Based Learning और Bilingual Support मिलना चाहिए, जो आमतौर पर महंगी Coaching या Premium Platforms में मिलता है। Muft Shiksha™ 🇮🇳 इसी सोच के साथ बनाया गया है

RELATED QUESTIONS

Number Systems

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

MathematicsIf (x,y) are coprime and both are proved even, what is the correct contradiction about (\gcd(x,y))?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsWhat is the deeper prime-factor reason in the proof of (\sqrt{3})?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsWhich idea about the exponents of prime factors explains the irrationality of √2?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsWhich statement is sufficient to reject the rational assumption for √3?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIn the standard proof, assume that \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime. Which number-theoretic fact is needed to obtain a contradiction from \(p^2=3q^2\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIf assuming \(\sqrt{3}=\frac{p}{q}\) in lowest terms leads to \(p^2=3q^2\), which conclusion proves a contradiction in this assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsSuppose \(\sqrt{3}=\frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers. On squaring, we get \(a^2=3b^2\). Which conclusion is justified at this stage?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIf \(\sqrt{3}=\frac{p}{q}\) is assumed in lowest terms and \(p^2=3q^2\) is obtained, what is the valid basis for concluding that \(3\mid p\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsWhile assuming (\sqrt{3}) rational, which form is most suitable for proof?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsA student claims that \(3\sqrt{2}\) is rational because 3 is a rational number. What is the correct evaluation of this claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIn the proof of √3, what kind of step is it to write directly that v is divisible by 3 from u² = 3v²?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIf \(\sqrt{3}=\frac{p}{q}\) is assumed with \(p\) and \(q\) coprime, and the proof shows that both \(p\) and \(q\) are divisible by 3, what does this establish?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsWhat is the correct argument involving the prime number 3 in the proof of √3?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIf \(\sqrt{3}=p/q\) is assumed with \(p\) and \(q\) coprime, which condition contradicts this assumption in the proof of irrationality?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIf (u^2=3v^2) and (u=3t), what is the combined conclusion about (u) and (v)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsSuppose \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers. Which conclusion produces the contradiction in the proof that \(\sqrt{3}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsWhy does the proof of (\sqrt{3}) become weak without writing (\gcd(u,v)=1)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsSuppose \(\sqrt{3}=\frac{p}{q}\) is written in lowest terms. If \(3\mid p^2\), which of the following conclusion is valid?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIn a proof by contradiction, assume that \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime. If \(3\mid p^2\) is obtained, which conclusion must follow next?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard MathematicsIf \(p\) and \(q\) are coprime integers and \(p^2=3q^2\), which conclusion necessarily follows?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 17Hard