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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}, let R = {(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}. Which pair or pairs must be added to make R an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 26Hard MathematicsIf (f:\mathbb{R}\to\mathbb{R}), (f(x)=|x-2|+|x+2|), choose the correct option for (f).Class 12Relations and FunctionsOne-one functionLevel 22Hard MathematicsOn (A=\mathbb{R}), (xRy) if (x-y\geq 0). Why is this not an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 18Hard MathematicsOn (A={1,2,3,4,5}), relation (R) contains all diagonal pairs, ((1,2),(2,1),(2,5),(5,2)). Which minimum pairs must be added to make it an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 17Hard MathematicsOn (A={1,2,3,4,5}), relation (R) contains all diagonal pairs and ((1,2),(2,1),(2,4),(4,2)). Which minimum pairs must be added to make it an equivalence relation?Class 12Relations and FunctionsEquivalence relationLevel 16Hard MathematicsIf a relation always has ((b,a)\in R) whenever ((a,b)\in R), which property is this?Class 12Relations and FunctionsEquivalence relationLevel 17Medium MathematicsIf (R) is an equivalence relation and ((4,7)\in R), why must ((7,4)\in R)?Class 12Relations and FunctionsEquivalence relationLevel 16Easy MathematicsIf (R=R^{-1}), what can be said about (R)?Class 12Relations and FunctionsSymmetric relationLevel 11Hard MathematicsIf (R) is an equivalence relation on a set and (aRb), which statement is necessary?Class 12Relations and FunctionsTypes of relationsLevel 4Expert MathematicsWhich relation on A={1,2,3} is transitive but not symmetric?Class 12Relations and FunctionsTypes of relationsLevel 4Expert MathematicsLet A={1,2,3,4,5} and define aRb if and only if a+b is odd. Which statement correctly describes this relation?Class 12Relations and FunctionsTypes of relationsLevel 4Expert MathematicsLet R be an equivalence relation on A and let [a] and [b] denote equivalence classes. If aRb, which statement must be true?Class 12Relations and FunctionsTypes of relationsLevel 6Hard MathematicsIf (R) is an equivalence relation on a set and (aRb), which statement is necessarily true?Class 12Relations and FunctionsTypes of relationsLevel 6Hard MathematicsOn (A={1,2,3}), (R) is to be an equivalence relation and ((1,2)\in R). Which pair must necessarily be in (R)?Class 12Relations and FunctionsTypes of relationsLevel 5Hard MathematicsIf (R) is an equivalence relation and (aRb), by which property do we get (bRa)?Class 12Relations and FunctionsTypes of relationsLevel 6Medium MathematicsA relation (R) contains both ((a,b)) and ((b,a)), where (a\ne b). Which property is not guaranteed by this information alone?Class 12Relations and FunctionsTypes of relationsLevel 4Medium MathematicsWhich single pair should be added to R={(1,1),(2,2),(3,3),(1,2)} so that it becomes an equivalence relation on A={1,2,3}?Class 12Relations and FunctionsTypes of relationsLevel 4Easy MathematicsWhat is the smallest change needed to make R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)} an equivalence relation on A={1,2,3}?Class 12Relations and FunctionsIntroduction to RelationsLevel 2Hard MathematicsOn (A={1,2,3,4,6,12}), (R={(a,b):a) divides (b)(}). Which statement about ((3,12)) and ((12,3)) is correct?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Hard MathematicsIf (R) is an equivalence relation and ((4,7)\in R), which pair must definitely be in (R)?Class 12Relations and FunctionsIntroduction to RelationsLevel 1Medium