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Relations And Functions

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

MathematicsA relation \(R=\{(a,b):a,b\in A\text{ and }a+b=6\}\) is defined on the set \(A=\{1,2,3,4,5\}\). How many ordered pairs does \(R\) contain?Class 11Relations and FunctionsRelationsLevel 26Hard MathematicsOn the set \(A=\{1,2,3,4,5,6\}\), the relation \(R=\{(a,b):\gcd(a,b)=1\}\) is defined. Choose the correct statement.Class 11Relations and FunctionsRelationsLevel 26Hard MathematicsIf A has n elements, what is the number of symmetric relations on A?Class 11Relations and FunctionsRelationsLevel 26Hard MathematicsIf \(R=\{(x,y)\in\mathbb{R}^2:x-y>0\}\), what is the nature of \(R\)?Class 11Relations and FunctionsRelationsLevel 26Hard MathematicsIf A = {1, 2, 3} and B = {2, 3, 4}, how many relations from A to B contain exactly 2 ordered pairs?Class 11Relations and FunctionsRelationsLevel 26Medium MathematicsWhich properties are required for a relation R on a set A to be an equivalence relation?Class 11Relations and FunctionsRelationsLevel 25Medium 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 \(A=\{1,2,3,4,5\}\), let \(R=\{(a,b)\in A\times A:a+b\le 6\}\). Choose the correct statement.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 MathematicsWhich is the identity relation I_A on A = {1,2,3}?Class 11Relations and FunctionsRelations that are reflexive and symmetricLevel 25Medium 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 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 \(A=\{1,2,3,4,5,6\}\), 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 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 the relation \(R=\{(a,b):|a-b|=2\}\) defined on the set \(A=\{1,2,3,4,5\}\), which of the following properties is true?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 MathematicsWhy is the relation \(R=\{(a,b):a<b\}\) defined on \(A=\{1,2,3,4\}\) not reflexive?Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsOn A = Z, define aRb when a − b is divisible by 3. What type of relation is this?Class 11Relations and FunctionsRelationsLevel 25Hard MathematicsSet A has 3 elements. How many symmetric relations are there on A?Class 11Relations and FunctionsCounting symmetric relationsLevel 25Hard MathematicsSet A has 4 elements. How many reflexive relations are there on A?Class 11Relations and FunctionsRelationsLevel 25Hard