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Divisibility

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

MathematicsIf A = {x ∈ ℤ : x is divisible by 3 and x² < 30}, how many elements does A have?Class 10SetsThe Empty Set, Finite and Infinite Sets, Equal SetsLevel 6Medium MathematicsFor the set A = {x ∈ ℕ : x divides 0}, which statement is correct?Class 10SetsThe Empty Set, Finite and Infinite Sets, Equal SetsLevel 3Medium MathematicsIf M = {x : x ∈ N and x is not divisible by 2}, what type of set is M?Class 10SetsThe Empty Set, Finite and Infinite Sets, Equal SetsLevel 4Easy MathematicsIf L = {x : x ∈ N, x ≤ 20, and x is not divisible by 3}, what type of set is L?Class 10SetsThe Empty Set, Finite and Infinite Sets, Equal SetsLevel 4Easy MathematicsIf Z = {x : x ∈ ℕ, x is divisible by both 2 and 3, and x < 20}, what type of set is Z?Class 10SetsThe Empty Set, Finite and Infinite Sets, Equal SetsLevel 4Medium MathematicsWhat type of set is Y = {x : x ∈ ℕ and x is divisible by both 2 and 3}?Class 10SetsThe Empty Set, Finite and Infinite Sets, Equal SetsLevel 4Easy MathematicsWhat type of set is V = {x : x is a positive integer divisible by 7}?Class 10SetsThe Empty Set, Finite and Infinite Sets, Equal SetsLevel 6Easy MathematicsIf A = {3, 6, 9, 12} and B = {x : x ∈ N, x ≤ 12 and 3 divides x}, which statement is correct?Class 10SetsThe Empty Set, Finite and Infinite Sets, Equal SetsLevel 5Easy MathematicsHow many elements are in A = {x : x ∈ N, x is divisible by 5 and x < 40}?Class 10SetsThe Empty Set, Finite and Infinite Sets, Equal SetsLevel 4Easy 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 MathematicsIf (p^2=3q^2) in the proof for (\sqrt{3}), what is the simple reason that (p^2) is divisible by (3)?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 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 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 MathematicsWhat type of set is A = {x : x ∈ ℕ and x is divisible by 11}?Class 10SetsThe Empty Set, Finite and Infinite Sets, Equal SetsLevel 10Easy MathematicsIn the proof for (\sqrt{3}), after putting (a=3k), what becomes clear from (b^2=3k^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Expert MathematicsIf (a^2=3b^2) is obtained in proving (\sqrt{3}) irrational, why is it correct to say (a^2) is a multiple of (3)?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}), after getting (b^2=3m^2), what conclusion about (b) is correct?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