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Contradiction

Class 10 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsIn the proof for (\sqrt{2}), if both (p) and (q) are proved even, which final conclusion is appropriate?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Expert MathematicsWhich statement creates the actual contradiction in the proof for (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Expert MathematicsIf (\sqrt{2}) were rational, why would its form (\frac{p}{q}) finally be rejected?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsWhich option clearly shows that assuming (\sqrt{5}) rational is wrong?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsWhich option gives the correct contradictory result after assuming (\sqrt{2}) rational?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsIn the proof for (\sqrt{5}), if both (a) and (b) turn out divisible by (5), what conclusion is correct?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsWhich option correctly states the contradiction in the proof of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsIn the proof for (\sqrt{5}), if (a=5k), what is proved about (b)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsWhy is the assumption (\sqrt{3}=\frac{m}{n}) finally proved wrong when (m,n) are taken coprime?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsIn the proof that (\sqrt{2}) is irrational, what conclusion is obtained after putting (p=2k)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsIn the proof of (\sqrt{3}), (p^2=3q^2) gives (p=3k) and then (q=3r). Why does this make the original assumption false?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Hard MathematicsIf (\sqrt{5}=\frac{p}{q}) is assumed in lowest form and (p=5k) is obtained in the proof, what is the next important aim?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Hard MathematicsIn the proof of (\sqrt{2}), when both (a) and (b) are proved even, which conclusion is most appropriate?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Medium MathematicsIf in the proof of (\sqrt{2}=\frac{p}{q}), both (p) and (q) get common factor (2), which initial statement becomes false?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Medium MathematicsWhat is the importance of getting (q^2=2k^2) in the proof of (\sqrt{2})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Medium MathematicsIn the proof of (\sqrt{3}), if both (p) and (q) are found divisible by (3), what does this contradict?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Medium MathematicsWhich option explains why the rational assumption for (\sqrt{3}) breaks?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Medium MathematicsIf the rational assumption for (\sqrt{3}) is proved false, what is the correct final conclusion?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Medium MathematicsAfter assuming (\sqrt{2}) rational, (\sqrt{2}=\frac{p}{q}) is written. If finally both (p) and (q) are even, what is the correct conclusion?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Medium MathematicsWhich option is common in the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Medium