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Ordered Pairs

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

MathematicsIf (A={1,2,3,4,5}) and (R={(a,b):a+2b=7}), how many ordered pairs are in (R)?Class 11Relations and FunctionsRelationsLevel 25Expert MathematicsIf \(A=\{1,2,3\}\) and \(R=\{(1,1),(2,2),(3,3),(1,2),(2,3)\}\), which single ordered pair must be added to make \(R\) transitive?Class 11Relations and FunctionsRelationsLevel 25Expert MathematicsIf an equivalence relation \(R\) defined on the set \(A=\{1,2,3,4\}\) has equivalence classes \(\{1,4\}\) and \(\{2,3\}\), how many ordered pairs does \(R\) contain?Class 11Relations and FunctionsRelationsLevel 25Expert MathematicsA relation R is defined on the set A = {1, 2, 3, 4} by R = {(a, b) : a + b = 6}, where a, b ∈ A. How many ordered pairs does R contain?Class 11Relations and FunctionsRelationsLevel 25Expert MathematicsIf \(R=\{(1,2),(2,3),(1,3)\}\) and \(S=\{(2,1),(3,2),(3,1)\}\), what is \(S\) in relation to \(R\)?Class 11Relations and FunctionsRelationsLevel 25Expert MathematicsIf (A={1,2,3,4}) and (R={(1,1),(2,2),(3,3),(4,4),(1,3),(3,1)}), which statement about (R) is correct?Class 11Relations and FunctionsRelationsLevel 25Expert MathematicsOn the set (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}) is given. Which property fails for (R)?Class 11Relations and FunctionsRelationsLevel 25Expert MathematicsIf \(A=\{1,2,3,4\}\), \(B=\{3,4,5,6\}\), and \(R=\{(a,b)\in A\times B: b=a+2\}\), how many ordered pairs does \(R\) contain?Class 11Relations and FunctionsRelationsLevel 27Hard MathematicsIf (R={(1,2),(2,4),(3,1)}), what is (R^{-1})?Class 11Relations and FunctionsRelationsLevel 27Hard MathematicsHow many ordered pairs are in the equivalence relation induced by the partition \(P=\{\{1,4\},\{2,3,5\}\}\) of the set \(\{1,2,3,4,5\}\)?Class 11Relations and FunctionsRelationsLevel 27Hard MathematicsThe set A is partitioned into P = {{1,2}, {3,4,5}, {6}}. How many ordered pairs are in the equivalence relation induced by this partition?Class 11Relations and FunctionsRelationsLevel 27Hard MathematicsOn A = {0, 1, 2, 3, 4}, let R = {(a, b) : a + b ≡ 0 (mod 5)}. How many ordered pairs are in R?Class 11Relations and FunctionsRelationsLevel 27Medium 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 \(A=\{1,2,3,4,6,12\}\), a relation \(R\) is defined by \(aRb\) if and only if \(a\mid b\). Which of the following ordered pairs does not belong to \(R\)?Class 11Relations and FunctionsRelationsLevel 26Hard MathematicsOn the set \(A=\{1,2,3,4\}\), let \(R=\{(a,b):a\leq b\}\). When the first element is \(4\), which set contains all the second elements related to it?Class 11Relations and FunctionsRelationsLevel 25Hard 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 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 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