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Cartesian Product

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={2,4,6}), which is not an element of (A\times B)?Class 11Relations and FunctionsCartesian product of setsLevel 23Expert MathematicsIf A={x:x²=4} and B={y:y²−5y+6=0}, how many elements are in A×B?Class 11Relations and FunctionsCartesian product of setsLevel 23Medium MathematicsIf (A\neq \varnothing), (B\neq \varnothing) and (A\times B=B\times A), which conclusion is correct?Class 11Relations and FunctionsCartesian product of setsLevel 23Expert MathematicsIf n(A × B) = 72 and n(A) = 8, what is n(B)?Class 11Relations and FunctionsCartesian product of setsLevel 23Easy MathematicsIf \(A=\{1,2,3\}\), \(B=\{1,2,3\}\), and \(C=\{1,2\}\), how many ordered triples \((a,b,c)\) in \(A\times B\times C\) satisfy \(a+b=2c+1\)?Class 11Relations and FunctionsCartesian product of setsLevel 22Expert MathematicsIf \(A=\{1,2,3,4\}\), \(B=\{1,2,3,4,5\}\), and \(R=\{(a,b): b-a\in\{0,2\}\}\), where \(a\in A\) and \(b\in B\), what is the value of \(|R|\)?Class 11Relations and FunctionsRelationsLevel 22Expert MathematicsIf A={1,2,3,4,5,6} and B={1,2,3,4,5,6}, how many ordered pairs (a,b) in A×B satisfy a+b=9 or ab=12?Class 11Relations and FunctionsCartesian product of setsLevel 22Hard MathematicsIf \(A=\{1,2,3,4,5\}\) and \(B=\{1,2,3,4,5\}\), how many ordered pairs \((a,b)\) in \(A\times B\) satisfy that \(a+b\) is even and \(ab\) is divisible by \(3\)?Class 11Relations and FunctionsCartesian product of setsLevel 22Expert MathematicsIf (A={1,2,3,4,5}), (B={1,2,3,4,5}), and (R={(a,b):a+b=6}), how many pairs are in (R\circ R)?Class 11Relations and FunctionsCartesian product of setsLevel 22Expert MathematicsIf \(A=\{0,1,2,3,4\}\), \(B=\{0,1,2,3,4\}\), and \(R=\{(a,b)\in A\times B: a^2\equiv b\pmod{5}\}\), what is the value of \(|R|\)?Class 11Relations and FunctionsRelationsLevel 22Expert MathematicsIf (A={1,2,3,4}), (B={1,2,3,4}), and (R=A\times B), what is the minimum number of pairs to remove from (R) so that no pair ((a,a)) remains?Class 11Relations and FunctionsCartesian product of setsLevel 22Expert MathematicsIf A = {1, 2, 3, 4}, B = {1, 2, 3, 4, 5, 6}, and R = {(a, b) ∈ A × B : b = 2a or b = 3a}, what is the value of |R|?Class 11Relations and FunctionsRelationsLevel 22Expert MathematicsIf A={1,2,3,4,5,6} and B={1,2,3,4,5,6}, how many ordered pairs (a,b) in A×B satisfy a+b=ab?Class 11Relations and FunctionsCartesian product of setsLevel 22Hard MathematicsIf \(A=\{1,2,3,4,5\}\), \(B=\{1,2,3,4,5\}\), and \(R=\{(a,b):a+b\le6\}\), how many ordered pairs in \(R\) have an even first component \(a\)?Class 11Relations and FunctionsRelationsLevel 22Expert MathematicsIf \(A=\{1,2,3\}\) and \(B=\{1,2,3,4,5,6\}\), how many ordered pairs \((a,b)\) in \(A\times B\) satisfy that \(b\) is a multiple of \(a\) and \(b\ne a\)?Class 11Relations and FunctionsCartesian product of setsLevel 22Expert MathematicsIf A={1,2,3,4,5}, B={1,2,3,4,5}, and R={(a,b): a+b=7}, which of the following ordered pairs must belong to R⁻¹?Class 11Relations and FunctionsRelationsLevel 22Expert MathematicsIf A = {1, 2, 3, 4}, B = {1, 2, 3, 4, 5}, and R = {(a, b) : a² < b}, how many ordered pairs are in R, that is, what is |R|?Class 11Relations and FunctionsRelationsLevel 22Expert MathematicsIf A={1,2,3,4}, B={1,2,3,4}, and U=A×B, how many ordered pairs (a,b) in U satisfy a<b or a+b=5?Class 11Relations and FunctionsCartesian product of setsLevel 22Expert MathematicsIf A={1,2,3,4,5}, B={1,2,3,4,5}, and T={(a,b): |a−b|≤2}, what is |T|?Class 11Relations and FunctionsCartesian product of setsLevel 22Hard MathematicsIf \(A=\{1,2,3,4\}\), \(B=\{1,2,3\}\), and \(C=\{0,1\}\), how many ordered triples \((a,b,c)\) in \(A\times B\times C\) satisfy \(a=b+c\)?Class 11Relations and FunctionsCartesian product of setsLevel 22Expert