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

MathematicsIf (\sqrt{2}) is assumed rational and finally both (p,q) turn out even, which conclusion is logical?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsIf (p) and (q) are coprime, why is it impossible to get both (p=2m) and (q=2n)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsIn the proof for (\sqrt{2}), (p^2=2q^2) shows (p^2) is even. If (p) is assumed odd, what problem occurs?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsIf (n) is an odd integer, then (n^2) is odd. This fact is especially useful in which proof?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsWhich option gives the correct basis for proving (q) even in the proof for (\sqrt{2})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsWhich conclusion should be written at the very end of the proof of irrationality of (\sqrt{2})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsIf someone says (\sqrt{2}) is irrational because (2) is not a perfect square, what correction is appropriate at expert level?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsIn the proof for (\sqrt{2}), why is (q) called even after getting (q^2=2k^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsWhile writing the proof for (\sqrt{2}), if someone assumes (\sqrt{2}=\frac{p}{q}) but does not mention lowest form, what problem occurs?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsWhich statement correctly moves from (p^2) to (p) in the proof for (\sqrt{2})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsIf both (p) and (q) are proved even in the proof for (\sqrt{2}), by what can (\frac{p}{q}) be reduced?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsIn the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5}), what changes while the proof method remains the same?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsWhich statement would leave the proof of (\sqrt{2}) incomplete?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsIf (\sqrt{8}) is considered instead of (\sqrt{2}), what is the best short reason that (\sqrt{8}) is irrational?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsWhich statement directly conflicts with the coprimality of (p) and (q) in the proof for (\sqrt{2})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsIn the proof for (\sqrt{2}), if someone writes (q^2=4k^2) after putting (p=2k), what is the correct correction?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsIf (\sqrt{2}=\frac{p}{q}) is assumed in lowest form and (p^2=2q^2) is obtained, which sequence is most logical to reach the contradiction?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsIn the proof for (\sqrt{2}), if both (p) and (q) are even, what does writing (p=2m) and (q=2n) show?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsAt which point is coprimality used decisively in the proof for (\sqrt{2})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsWhich option correctly explains the parity idea in the proof for (\sqrt{2})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert