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Commutativity

Class 12 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsOn (\mathbb{R}), (a*b=a^2+b). In which property does this operation fail?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn real numbers, (a*b=a+b+ab) is defined. Why is (a*b=b*a) true?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn real numbers, (a*b=2a+3b) is defined. Is this operation commutative?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn real numbers, (a*b=a^2+b^2) is defined. Choose the correct conclusion about this operation.Class 12Relations and FunctionsBinary operationsExpert MathematicsOn the set (A={1,2,3}), (a*b=a) is defined. Which property is satisfied by this operation?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn natural numbers, (a*b=a^b) is defined. Which statement about commutativity of this operation is correct?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn real numbers, (a*b=a+2b). Which property does this operation not satisfy?Class 12Relations and FunctionsBinary operationsHard MathematicsOn real numbers, (a*b=a+b+\lambda ab). Which statement is correct, where (\lambda) is a fixed real number?Class 12Relations and FunctionsBinary operationsHard MathematicsOn real numbers, (a*b=|a|b). Why is this operation not commutative?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (\mathbb{Q}\setminus{0}), (a*b=\frac{a}{b}). What kind of operation is it?Class 12Relations and FunctionsBinary operationsHard MathematicsOn real numbers, (a*b=a-b). Choose the correct statement about this operation.Class 12Relations and FunctionsBinary operationsHard MathematicsOn natural numbers, (a*b=a^b). Which property does this operation not satisfy?Class 12Relations and FunctionsBinary operationsHard MathematicsOn real numbers, (a*b=a^2+b) is defined. Is this operation commutative?Class 12Relations and FunctionsBinary operationsMedium MathematicsIf (a*b=a+3b), which statement about (2*4) and (4*2) is correct?Class 12Relations and FunctionsBinary operationsMedium MathematicsOn real numbers, (a*b=\frac{a+b}{2}). Is this operation commutative?Class 12Relations and FunctionsBinary operationsMedium MathematicsOn integers, (a*b=a+2b). Is this operation commutative?Class 12Relations and FunctionsBinary operationsMedium MathematicsOn real numbers, (a*b=a-b). Is this operation commutative?Class 12Relations and FunctionsBinary operationsMedium MathematicsThe operation (a\ast b=a) is given on a set (A). What is the nature of this operation?Class 12Relations and FunctionsBinary operationsEasy MathematicsThe operation (a\ast b=a-b) is given on integers. Is it commutative?Class 12Relations and FunctionsBinary operationsEasy MathematicsOn the set (A={1,2}), (a*b=a) is defined. Is it commutative?Class 12Relations and FunctionsBinary operationsEasy