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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।

MathematicsIf (A={1,2,3}) and (B={4,5,6,7}), how many relations from (A) to (B) contain exactly (3) ordered pairs?Class 11Relations and FunctionsRelationsLevel 27Hard MathematicsOn the set \(A=\{0,1,2,3,4,5,6,7,8\}\), a relation \(R\) is defined by \(aRb\) if and only if \(a\equiv b\pmod{3}\). Which of the following is the equivalence class \([7]\)?Class 11Relations and FunctionsRelationsLevel 27Hard MathematicsOn (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}). Why is (R) not an equivalence relation?Class 11Relations and FunctionsRelationsLevel 26Hard MathematicsIf a relation (R) is reflexive and antisymmetric, is it always transitive?Class 11Relations and FunctionsRelationsLevel 26Hard MathematicsIf (R) is an equivalence relation on a set (A), which property below is not required and is wrongly added as compulsory?Class 11Relations and FunctionsRelationsLevel 26Hard MathematicsOn (A={1,2,3,4}), (R={(a,b):a\neq b}). Choose the correct statement.Class 11Relations and FunctionsRelationsLevel 26Hard MathematicsIf (A={1,2,3,4,5}) and (R={(a,b):a+b\equiv0\pmod{2}}), how many ordered pairs are in (R)?Class 11Relations and FunctionsRelationsLevel 26Hard MathematicsIf (A={1,2,3,4}) and (R={(a,b):ab \text{ is even}}), which statement is correct for (R)?Class 11Relations and FunctionsRelationsLevel 26Hard 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 (A=\mathbb{R}), (aRb) if and only if (a-b\geq0). Which relation is this?Class 11Relations and FunctionsRelationsLevel 26Hard MathematicsA relation R on the set of real numbers is defined by aRb if and only if |a| = |b|. What type of relation is R?Class 11Relations and FunctionsRelationsLevel 26Hard MathematicsOn (A={1,2,3,4}), (R={(a,b):\operatorname{lcm}(a,b)=4}). Which pair belongs to (R)?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 antisymmetric relations on (A)?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 (A) has (n) elements, what is the formula for the number of reflexive relations on (A)?Class 11Relations and FunctionsRelationsLevel 26Hard MathematicsIf (A) has (n) elements, what is the correct formula for the total number of relations on (A)?Class 11Relations and FunctionsRelationsLevel 26Hard MathematicsOn the set \(A=\{2,3,4,6,8,12\}\), relation \(R\) is defined by \(aRb\) if and only if \(a\mid b\). If \((2,6)\in R\) and \((6,12)\in R\), which of the following pairs must belong to \(R\) by transitivity?Class 11Relations and FunctionsRelationsLevel 26Hard MathematicsOn the set of integers, a relation R is defined by aRb if and only if \(a\leq b\). Which of the following properties is not true for this relation?Class 11Relations and FunctionsRelationsLevel 26Hard MathematicsOn (A={1,2,3,4}), (R={(a,b):a=b \text{ or } |a-b|=1}). Choose the correct statement.Class 11Relations and FunctionsRelationsLevel 26Hard