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Coprime

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

MathematicsWhich statement is correct about the decimal expansion of (\frac{23}{2^2\times5^3})?Class 10Real NumbersDecimal expansion of rational numbersLevel 19Medium MathematicsIn the proof for (\sqrt{3}), after getting (3\mid p) and then (3\mid q), which statement would be false?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 MathematicsWhich property of rational numbers is used in the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsIn the proof for (\sqrt{5}), both (a) and (b) being divisible by (5) breaks which initial condition?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 MathematicsWhile proving (\sqrt{5}) irrational, both (a) and (b) turn out divisible by (5). What is its effect on (\gcd(a,b))?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 MathematicsIf (\sqrt{5}) is assumed rational as (\sqrt{5}=\frac{a}{b}), which condition about (a) and (b) is essential for the proof?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsIf assuming (\sqrt{3}=\frac{p}{q}) gives (p^2=3q^2), what is the main purpose of showing divisibility by (3) for both (p) and (q) in the proof?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsIn the proof for (\sqrt{5}), if both (x) and (y) are divisible by (5), which statement would be false?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 MathematicsIf (a) and (b) are coprime but the proof gives (a=3m) and (b=3n), what conclusion follows?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsIn the proof for (\sqrt{2}), if both (p) and (q) are even, by which number can the fraction be further reduced?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsWhich option directly conflicts with (p) and (q) being coprime in the proof for (\sqrt{2})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsIn the proof for (\sqrt{5}), if both (x) and (y) turn out divisible by (5), what can be said about (\gcd(x,y))?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsWhich option states the correct final contradiction in the proof for (\sqrt{3})?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 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 MathematicsIf (p) and (q) are coprime, why can (p=5m) and (q=5n) not hold together?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Expert