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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) being divisible by (5) breaks which initial condition?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsIf (3\mid p) is obtained from (p^2=3q^2), what is correct about (k) when writing (p=3k)?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 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 MathematicsWhy is it necessary to write (q\neq0) while proving the irrationality of (\sqrt{3})?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 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{3}), which shortcut from (p^2=3q^2) to (p=3k) is wrong?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsIf (r) is a prime number and (\sqrt{r}=\frac{p}{q}) is assumed in lowest form, what is the first general conclusion from (p^2=rq^2)?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 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 MathematicsIn the proof for (\sqrt{3}), if (\frac{p}{q}) is in lowest form but (p=3m) and (q=3n) are obtained, which conclusion is most precise?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 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 MathematicsIf a student writes (\sqrt{3}\approx1.732) and treats it as proof of irrationality, what is the main weakness?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{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 (p=3r) has been proved in the irrationality proof of (\sqrt{3}), which step is correct to conclude about (q)?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