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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।

MathematicsIn the proof for (\sqrt{5}), after putting (x=5n), (25n^2=5y^2) is obtained. What is the next correct simplification?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsIn the proof for (\sqrt{3}), after getting (b^2=3m^2), what conclusion about (b) is correct?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsIf (r) is prime and (\sqrt{r}=\frac{p}{q}) is assumed in lowest form, which equation is obtained after squaring?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsWhich structure remains common in the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsIf a student writes only (\sqrt{5}\approx2.236) to prove rationality or irrationality, why is this argument incomplete?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsIn the proof for (\sqrt{3}), after putting (a=3m), into what form does (a^2=3b^2) change?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsWhich option is the most serious error in the proof of irrationality of (\sqrt{2})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsIf (p) and (q) are coprime, what does obtaining (5\mid p) and (5\mid q) in the proof for (\sqrt{5}) indicate?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsIn the proof for (\sqrt{3}), the conclusion (3\mid a) from (3\mid a^2) is based on which principle?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsIn the proof for (\sqrt{2}), after getting (q^2=2k^2), which conclusion helps complete the proof?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsIf (\sqrt{5}) is assumed rational and written as (\sqrt{5}=\frac{x}{y}), which algebraic step correctly leads to (x^2=5y^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsWhile proving the irrationality of (\sqrt{3}), what weakness occurs if (a) and (b) in (\sqrt{3}=\frac{a}{b}) are not taken coprime?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsAfter assuming (\sqrt{2}=\frac{p}{q}) in lowest form and getting (p^2=2q^2), why is it correct to write (p=2k)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsWhat main exam lesson is learned from the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Expert MathematicsWhich statement is not correct in the proof for (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Expert MathematicsIf (\sqrt{3}) were rational, what inconsistency would finally appear in the proof?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Expert MathematicsIn the proof for (\sqrt{2}), after getting (q^2=2r^2), why is (q) even?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Expert MathematicsWhich option is unnecessary in the proof of irrationality of (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Expert MathematicsIn the proof for (\sqrt{3}), after (p^2=3q^2) shows (p) divisible by (3), what is the correct path to reach (q)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Expert MathematicsWhich part of the proof of irrationality of (\sqrt{2}) shows proof by contradiction?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Expert