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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+b+ab+2). Does this operation have an identity element?Class 12Relations and FunctionsBinary operationsLevel 28Expert MathematicsOn (\mathbb{R}), (a*b=a+b+1). What is the inverse of (a) under this operation?Class 12Relations and FunctionsBinary operationsLevel 28Expert MathematicsOn (\mathbb{R}), (a*b=a+b-ab). Is this operation commutative?Class 12Relations and FunctionsBinary operationsLevel 30Hard MathematicsOn (\mathbb{R}), (a*b=a+b+3ab). Which element has no inverse?Class 12Relations and FunctionsBinary operationsLevel 30Hard MathematicsOn (\mathbb{R}), (a*b=a+b+ab). Which statement about (a=-1) is correct?Class 12Relations and FunctionsBinary operationsLevel 30Hard MathematicsOn (\mathbb{R}), (a*b=a^2+b^2) is defined. Which property does this operation satisfy?Class 12Relations and FunctionsBinary operationsLevel 30Hard MathematicsOn real numbers, (a*b=a+2b). Which property does this operation not satisfy?Class 12Relations and FunctionsBinary operationsLevel 29Hard MathematicsOn real numbers, (a*b=a+b+\lambda ab). When will the inverse of (a) be undefined?Class 12Relations and FunctionsBinary operationsLevel 29Hard MathematicsOn real numbers, (a*b=a+b+\lambda ab). What is the identity element of this operation?Class 12Relations and FunctionsBinary operationsLevel 29Hard MathematicsOn real numbers, (a*b=a+b+\lambda ab). Which statement is correct, where (\lambda) is a fixed real number?Class 12Relations and FunctionsBinary operationsLevel 29Hard 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 operationsLevel 29Hard MathematicsOn real numbers, (a*b=a^2+b^2). It is a binary operation, but which property generally fails?Class 12Relations and FunctionsBinary operationsLevel 29Hard MathematicsOn real numbers, (a*b=a+b+k). What will be the inverse of (a) under this operation?Class 12Relations and FunctionsBinary operationsLevel 29Hard MathematicsOn real numbers, (a*b=2a+2b). In which property does this operation fail?Class 12Relations and FunctionsBinary operationsLevel 29Hard MathematicsOn real numbers, (a*b=ab+a+b+1). Does this operation have an identity element?Class 12Relations and FunctionsBinary operationsLevel 29Hard MathematicsOn real numbers, (a*b=a+b+ab+1). Which simple form is connected to this operation?Class 12Relations and FunctionsBinary operationsLevel 29Hard MathematicsOn (A=\mathbb{R}\setminus{-1}), (a*b=a+b+ab). What is the inverse of (a) under this operation?Class 12Relations and FunctionsBinary operationsLevel 29Hard MathematicsOn (\mathbb{R}\setminus{0}), (a*b=\frac{ab}{a+b}), where (a+b\neq0). Why is it not a binary operation on the whole set?Class 12Relations and FunctionsBinary operationsLevel 29Hard MathematicsOn real numbers, (a*b=a+b-ab). Which statement is correct?Class 12Relations and FunctionsBinary operationsLevel 29Hard MathematicsOn real numbers, (a*b=a+b+ab). Which statement is correct?Class 12Relations and FunctionsBinary operationsLevel 29Hard