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Equivalence Class

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

MathematicsOn (A={1,2,3,4,5,6}), (aRb) holds when (a) and (b) have the same remainders modulo (2) and modulo (5). Which is the equivalence class of (3)?Class 12Relations and FunctionsEquivalence relationLevel 17Hard MathematicsOn (A={1,2,3,4,5,6,7,8}), (aRb) holds when (\min(a,5)=\min(b,5)). Which is the equivalence class of (7)?Class 12Relations and FunctionsEquivalence relationLevel 17Hard MathematicsOn real numbers, (aRb) holds when (a^2+2a=b^2+2b). Which is the equivalence class of (-4)?Class 12Relations and FunctionsEquivalence relationLevel 17Hard MathematicsOn integers, (aRb) holds when (a^2\equiv b^2 \pmod{9}). Which integer must belong to the equivalence class of (4)?Class 12Relations and FunctionsEquivalence relationLevel 17Hard MathematicsIf (R) is an equivalence relation and ([a]\subseteq B\subseteq A), but (B) is not an equivalence class. Which reason is possible?Class 12Relations and FunctionsEquivalence relationLevel 16Hard MathematicsOn integers, (aRb) holds when (a\equiv b \pmod{3}), and (aSb) holds when (a\equiv b \pmod{5}). In (R\cap S), which is the equivalence class of (7)?Class 12Relations and FunctionsEquivalence relationLevel 16Hard MathematicsOn (A={1,2,3,4,5,6,7,8}), (aRb) holds when (a) and (b) have the same status of being a multiple of (2) and the same status of being a multiple of (4). Which is the equivalence class of (6)?Class 12Relations and FunctionsEquivalence relationLevel 16Hard MathematicsIf (R) is an equivalence relation on (A) and ([a]) has exactly (4) elements, how many ordered pairs of (R) come from inside ([a])?Class 12Relations and FunctionsEquivalence relationLevel 16Hard MathematicsOn the set of all subsets of (S={1,2,3,4}), (A R B) holds when (|A\cap{1,2}|=|B\cap{1,2}|). What is the size of the equivalence class of ({1,3})?Class 12Relations and FunctionsEquivalence relationLevel 16Hard MathematicsOn (A={1,2,3,4,5,6,7,8}), (aRb) holds when (a^2\equiv b^2 \pmod{5}). Which is the equivalence class of (2)?Class 12Relations and FunctionsEquivalence relationLevel 16Hard MathematicsOn non-zero real numbers, (aRb) holds when (\frac{a}{b}) is a positive rational number. Which element is in the class of (-2\sqrt{5})?Class 12Relations and FunctionsEquivalence relationLevel 16Hard MathematicsOn real numbers, (aRb) holds when (a-b\in\mathbb{Q}). Which element belongs to the class of (\sqrt{2}+\sqrt{3})?Class 12Relations and FunctionsEquivalence relationLevel 16Hard MathematicsFor points in the plane, (P R Q) holds when (P) and (Q) have the same distance from the origin. Which point belongs to the equivalence class of ((3,4))?Class 12Relations and FunctionsEquivalence relationLevel 16Hard MathematicsOn (A={1,2,3,4,5,6}), (aRb) holds when (\max(a,4)=\max(b,4)). Which is the equivalence class of (2)?Class 12Relations and FunctionsEquivalence relationLevel 16Hard MathematicsOn (A=\mathbb{R}), (aRb) holds when (\lfloor a\rfloor=\lfloor b\rfloor). Which is the equivalence class of (-1.2)?Class 12Relations and FunctionsEquivalence relationLevel 16Hard MathematicsOn (A={1,2,3,4,5,6,7,8,9,10}), for the relation (\gcd(a,10)=\gcd(b,10)), which is the equivalence class of (8)?Class 12Relations and FunctionsEquivalence relationLevel 16Hard MathematicsOn (A={1,2,3,4,5,6}), (aRb) holds when (a) and (b) have the same remainder modulo (2) and also the same remainder modulo (3). Which is the equivalence class of (5)?Class 12Relations and FunctionsEquivalence relationLevel 16Hard MathematicsOn (A={1,2,3,4,5,6,7,8,9}), (aRb) holds when (a) and (b) have the same number of prime factors counted with repetition. Which is the equivalence class of (6)?Class 12Relations and FunctionsEquivalence relationLevel 16Hard MathematicsFor the relation (\sin a=\sin b) on real numbers, which is the correct form of the class of (0)?Class 12Relations and FunctionsEquivalence relationLevel 16Hard MathematicsOn (A={1,2,3,4,5,6,7,8}), (aRb) holds when (\gcd(a,8)=\gcd(b,8)). Which is the equivalence class of (6)?Class 12Relations and FunctionsEquivalence relationLevel 16Hard