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Binary Operation

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

MathematicsOn real numbers, (a*b=a+2b). Which property does this operation not satisfy?Class 12Relations and FunctionsBinary operationsHard MathematicsOn positive real numbers, (a*b=\sqrt{ab}) is defined. Does this operation have an identity element?Class 12Relations and FunctionsBinary operationsHard MathematicsOn \(A=\mathbb{R}\setminus\left{-\frac{1}{\lambda}\right}\), \(a*b=a+b+\lambda ab\), where \(\lambda\neq0\). What is the inverse of (a)?Class 12Relations and FunctionsBinary operationsHard MathematicsOn real numbers, (a*b=a+b+\lambda ab). When will the inverse of (a) be undefined?Class 12Relations and FunctionsBinary operationsHard MathematicsOn real numbers, (a*b=a+b+\lambda ab). What is the identity element of this operation?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-ab). Which element has no inverse under this operation if the set is the whole (\mathbb{R})?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (A=\mathbb{R}\setminus{1}), (a*b=a+b-ab). Why is this operation closed in (A)?Class 12Relations and FunctionsBinary operationsHard MathematicsOn integers, (a*b=a+b-2). What is the inverse of (5)?Class 12Relations and FunctionsBinary operationsHard MathematicsOn integers, (a*b=a+b-2). Which is the identity element?Class 12Relations and FunctionsBinary operationsHard MathematicsOn natural numbers, (a*b=a+b-2). When does this operation fail to be closed on natural numbers?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (A={1,-1}), (a*b=ab). What kind of operation is it?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (A={1,-1}), usual multiplication is taken as the operation. What is the inverse of (-1)?Class 12Relations and FunctionsBinary operationsHard MathematicsOn real numbers, (a*b=|a|b). Why is this operation not commutative?Class 12Relations and FunctionsBinary operationsHard MathematicsOn real numbers, (a*b=|a-b|). In which property does this operation fail?Class 12Relations and FunctionsBinary operationsHard MathematicsOn real numbers, (a*b=a^2+b^2). It is a binary operation, but which property generally fails?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (A=\mathbb{R}\setminus{0}), (a*b=\frac{ab}{2}). Which statement is correct?Class 12Relations and FunctionsBinary operationsHard MathematicsOn real numbers, (a*b=a+b+k). What will be the inverse of (a) under this operation?Class 12Relations and FunctionsBinary operationsHard MathematicsOn real numbers, (a*b=ka+kb). For which (k) will this operation be associative?Class 12Relations and FunctionsBinary operationsHard MathematicsOn real numbers, (a*b=2a+2b). In which property does this operation fail?Class 12Relations and FunctionsBinary operationsHard