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Number Theory

Class 12 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsOn positive integers, (aRb) if and only if (a) and (b) have the same power of (2), that is, (a=2^k m) and (b=2^k n), where (m,n) are odd. What forms the equivalence class of (12)?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn (A={1,2,3,4,5,6}), (aRb) if and only if (\operatorname{lcm}(a,6)=\operatorname{lcm}(b,6)). Which is the equivalence class of (4)?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn (A={1,2,3,4,5,6,7}), (aRb) if and only if (a^2\equiv b^2 \pmod{7}). Which is the equivalence class of (3)?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn (A={1,2,3,4,5,6}), (aRb) if and only if the greatest common divisor of (a) and (6) equals the greatest common divisor of (b) and (6). Which is the equivalence class of (5)?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn natural numbers, (aRb) if (a) and (b) are coprime. Is (R) transitive?Class 12Relations and FunctionsTransitive relationHard MathematicsOn (A={1,2,3,4,6}), (R={(a,b):\gcd(a,b)=2}). Choose the correct statement about (R).Class 12Relations and FunctionsSymmetric relationExpert MathematicsOn (A={1,2,3,4}), what type is the relation (R={(a,b):\gcd(a,b)=1})?Class 12Relations and FunctionsSymmetric relationMedium MathematicsIf (A={1,2,3,4,5,6}) and ((a,b)\in R) only when (a) and (b) have a common prime factor, is (R) reflexive?Class 12Relations and FunctionsReflexive relationExpert MathematicsOn (A={1,2,3,4,5}), (R={(a,b):a) and (b) have a common factor greater than (1)(}). Is (R) reflexive?Class 12Relations and FunctionsReflexive relationExpert MathematicsOn (A={1,2,3,4}), relation (R) is defined by ((a,b)\in R) if (a) and (b) have a common prime factor. Is (R) reflexive?Class 12Relations and FunctionsReflexive relationExpert