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Class 11 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsWhich properties are required for a relation R on a set A to be an equivalence relation?Class 11Relations and FunctionsRelationsLevel 25Medium MathematicsIf (R) is an equivalence relation and ((a,b)\in R), which statement is always true?Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsHow many equivalence classes are formed by the relation R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(3,4),(4,3)} defined on the set A={1,2,3,4}?Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsWhy is the relation \(R=\{(a,b)\in A\times A:a+b\ge 5\}\), defined on \(A=\{1,2,3,4\}\), not reflexive?Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsOn the set \(A=\{1,2,3,4\}\), let \(R=\{(a,b)\in A\times A:a-b>0\}\). Which statement about this relation is correct?Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsWhat is R = {(a,b): a² = b²} on A = {-2,-1,1,2}?Class 11Relations and FunctionsRelations that are reflexive and symmetricLevel 25Hard MathematicsFor (R={(a,b):a^2=b^2}) on (A={1,2,3,4}), choose the correct statement.Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsWhich is the identity relation I_A on A = {1,2,3}?Class 11Relations and FunctionsRelations that are reflexive and symmetricLevel 25Medium MathematicsWhich is the smallest reflexive relation on the set \(A=\{1,2,3\}\)?Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsIf the relation \(R\) is transitive and \((1,4)\in R\) and \((4,6)\in R\), which of the following ordered pairs must belong to \(R\)?Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsIf (R) is antisymmetric and ((3,7)\in R), which pair cannot be in (R)?Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsIf \(R\) is a symmetric relation and \((2,5)\in R\), which of the following pairs must definitely belong to \(R\)?Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsOn the set \(A=\{1,2,3,4,6,12\}\), a relation \(R\) is defined by \(aRb\) if and only if \(a\mid b\). How many first elements are related to \(12\)?Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsOn the set \(A=\{1,2,3,4,5,6\}\), consider the relation \(R=\{(a,b):\gcd(a,b)=1\}\). Which of the following properties is true for this relation?Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsOn the set of real numbers \(\mathbb R\), a relation \(R\) is defined by \(xRy\iff x-y\in\mathbb Q\). Choose the correct classification of this relation.Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsIf \(A=\{1,2,3,4\}\), how many ordered pairs are there in the relation \(R=\{(a,b):a+2b=6\}\) defined on \(A\)?Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsFor R = {(a,b): |a − b| ≤ 1} on A = {1,2,3,4}, which statement is correct?Class 11Relations and FunctionsRelations that are reflexive and symmetricLevel 25Hard MathematicsFor (R={(a,b):a+b \text{ is even}}) on (A={1,2,3,4}), choose the correct option.Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsOn the set \(A=\{1,2,3,4\}\), what is the nature of the relation \(R=\{(a,b)\in A\times A : a+b\text{ is odd}\}\)?Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsFor the empty relation (R=\varnothing) on a non-empty set (A), which statement is correct?Class 11Relations and FunctionsRelationsLevel 25Hard