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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}), both (a) and (b) are found divisible by (5). What type of result is this?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsIn the proof for (\sqrt{5}), if someone writes (a=25k) from (5\mid a^2), what is the mistake?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsWhich statement starts the proof of irrationality of (\sqrt{5}) most clearly?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsIn the proof for (\sqrt{5}), what is the correct intermediate conclusion needed to write (a=5k) from (a^2=5b^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsIn the proof for (\sqrt{5}), while writing (5\mid b) from (5\mid b^2), what must be added?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsIn the proof for (\sqrt{5}), putting (a=5k) gives (25k^2=5b^2). What will (b^2) be?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsWhich idea is common in the proofs of (\sqrt{3}) and (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsIf assuming (\sqrt{5}) rational gives (a^2=5b^2), which statement about (a^2) is correct?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 MathematicsWhich option gives the correct basis for divisibility of (b) in the proof for (\sqrt{5})?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 MathematicsAfter assuming (\sqrt{5}) rational and getting (a^2=5b^2), how does a common factor appear in (a) and (b)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsIn the proof for (\sqrt{5}), after showing (a) is divisible by (5) from (a^2=5b^2), which conclusion would be immediately wrong?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 MathematicsIn the proof for (\sqrt{5}), after (5\mid a) is proved from (a^2=5b^2), (a=5t) is written. What does this indicate?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 MathematicsWhich option gives an incorrect conclusion about (x) from (x^2=5y^2) in the proof for (\sqrt{5})?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 MathematicsWhich option gives the correct final sentence for proving the irrationality of (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsIn the proof for (\sqrt{5}), which condition is necessary while taking (5\mid y) from (5\mid y^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert