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

Divisibility

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

MathematicsWhile proving the irrationality of \(\sqrt{3}\) by contradiction, suppose \(\sqrt{3}=\frac{p}{q}\) is in lowest terms. What conclusion about \(p\) follows from \(p^2=3q^2\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Hard MathematicsIn the proof by contradiction that \(\sqrt{3}\) is irrational, if \(p\) and \(q\) are coprime and \(p^2=3q^2\), which conclusion follows immediately?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Hard MathematicsIn the proof of (\sqrt{3}), if (p) is not divisible by (3), why does (p^2=3q^2) create conflict?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Hard MathematicsIf n² is divisible by 3 for an integer n, which statement about n must be true?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Hard MathematicsIn the proof that \(\sqrt{3}\) is irrational (using \(\sqrt{3}=\frac{p}{q}\) and coprime integers), what is the correct “middle objective” after squaring?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Medium MathematicsIn the proof that \(\sqrt{3}\) is irrational, which statement gives both the correct reason and the correct conclusion?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Medium MathematicsIn the proof of (\sqrt{3}), if (p) is not divisible by (3), what conflict occurs with (p^2=3q^2)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Medium MathematicsIf \(\sqrt{3}\) is assumed to be \(\frac{p}{q}\) in lowest terms, what conclusion follows from \(p^2=3q^2\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Medium MathematicsA student believes that the statement “If the square of an integer is divisible by 3, then the integer is also divisible by 3” is false. Which statement correctly removes this misconception?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Medium 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 3Medium 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 3Medium 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 3Medium MathematicsAman assumes that ext{\(\sqrt{3}=\frac{p}{q}\)}, where ext{\(p\)} and ext{\(q\)} are coprime. On squaring, he gets ext{\(p^2=3q^2\)}. Aman says, “ ext{\(3\mid p^2\)} does not necessarily imply ext{\(3\mid p\)}.” What is the correct evaluation of Aman’s statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Easy MathematicsIf (r^2=3s^2), what is true about (r^2)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Easy MathematicsA student says that if \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are integers and \(q\ne0\), then \(p^2=3q^2\) proves only that \(p\) is divisible by 3. What is the correct next conclusion in this argument?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Easy MathematicsWhich statement is the key conclusion in the proof by contradiction that \(\sqrt{3}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Easy MathematicsIf (p^2) is divisible by (3) what is the correct conclusion about (p)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Easy MathematicsWhy is the equation a² = 3b² important in the proof of √3?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Easy MathematicsFrom (b^2=3k^2), what conclusion follows about (b)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Easy MathematicsFrom (a^2=3b^2), which conclusion is obtained about (a^2)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Easy