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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=ab+a+b+1). Does this operation have an identity element?Class 12Relations and FunctionsBinary operationsHard MathematicsOn real numbers, (a*b=a+b+ab+1). Which simple form is connected to this operation?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (A={1,2,3,4}), (a*b) is the remainder when (ab) is divided by (5). What is the inverse of (3)?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (A={1,2,3,4}), (a*b) is the remainder when (ab) is divided by (5). Which is the identity element?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (A={1,2,3,4}), (a*b) is the remainder when (ab) is divided by (5), and remainder (0) is not replaced by (5). Is this a binary operation on (A)?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (A={0,1,2}), (a*b) is the remainder when (a+b) is divided by (3). What is the inverse of (2)?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (A={0,1,2}), (a*b) is defined as the remainder when (a+b) is divided by (3). What is the identity element?Class 12Relations and FunctionsBinary operationsHard MathematicsOn integers, (a*b=a+b-1). Which is the inverse of (a)?Class 12Relations and FunctionsBinary operationsHard MathematicsOn integers, (a*b=a+b-1). Which will be the identity element?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 (A=\mathbb{Q}\setminus{0}), (a*b=\frac{a}{b}). Is it a binary operation?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (A=\mathbb{R}\setminus{0}), (a*b=ab). Which statement is correct for this operation?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 (A=\mathbb{R}\setminus{-1}), (a*b=a+b+ab). What is the inverse of (a) under this operation?Class 12Relations and FunctionsBinary operationsHard 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 operationsHard MathematicsOn real numbers, (a*b=a+b-ab). Which statement is correct?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 statement is correct?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+b+ab). Which statement is correct?Class 12Relations and FunctionsBinary operationsHard