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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{2}), when both (p) and (q) turn out even, which initial statement is proved false?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsHow does (5) not being a perfect square help in understanding the irrationality of (\sqrt{5})?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 MathematicsWhich option shows the correct order for proving the irrationality of (\sqrt{3})?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 MathematicsIf someone writes (q^2=4k^2) after putting (p=2k) in (p^2=2q^2), where is the mistake?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsWhich statement correctly generalizes the proof of irrationality of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsIn the irrationality proof of (\sqrt{5}), what idea is hidden in moving from (5\mid x^2) to (x=5m)?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 MathematicsIf no contradiction appears while proving (\sqrt{3}) irrational by assuming it rational, which condition is probably missing?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 opening sentence is most complete for proving the irrationality of (\sqrt{2})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsIn the proofs of (\sqrt{3}) and (\sqrt{5}), which prime factors appear respectively instead of (2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsIf the square of an integer (n) is even, then (n) is even. How many times is this fact used in the proof for (\sqrt{2})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsWhich statement correctly uses the primality of (5) in the proof for (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsIn the proof for (\sqrt{3}), if someone writes (a=3b) directly from (3\mid a^2), what is the mistake?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsWhich statement shows that the proof of irrationality of (\sqrt{2}) is not based on decimals?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsIf assuming (\sqrt{5}) rational gives (x^2=5y^2), after writing (x=5n), toward which conclusion does the proof move?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 MathematicsIn the proof for (\sqrt{2}), when both (p) and (q) are proved even, which statement about (\frac{p}{q}) is correct?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert