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Binary Operations

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

MathematicsOn (A={0,1,2}), define (a*b) as the remainder when (a+b) is divided by (3). What is the identity element?Class 12Relations and FunctionsBinary operationsMedium MathematicsOn real numbers, (a*b=a+2b) is defined. When will this operation be commutative?Class 12Relations and FunctionsBinary operationsMedium MathematicsOn real numbers, (a*b=a^2+b^2) is defined. Is this operation commutative?Class 12Relations and FunctionsBinary operationsMedium MathematicsOn positive real numbers, (a*b=\frac{ab}{2}) is defined. What is the identity element of this operation?Class 12Relations and FunctionsBinary operationsMedium MathematicsOn real numbers, (a*b=a-b) is defined. Which property does this operation have?Class 12Relations and FunctionsBinary operationsMedium MathematicsOn integers, (a*b=a+b+1) is defined. Choose the correct statement about this operation.Class 12Relations and FunctionsBinary operationsMedium MathematicsOn real numbers, (a*b=a+b-2) is defined. What is the inverse of (3) under this operation?Class 12Relations and FunctionsBinary operationsMedium MathematicsOn real numbers, (a*b=a+b+ab) is defined. What is the identity element of this operation?Class 12Relations and FunctionsBinary operationsMedium MathematicsOn the set (A={1,2,3,4,5}), the operation (a*b=\max(a,b)) is defined. Which element is the identity element?Class 12Relations and FunctionsBinary operationsMedium MathematicsOn the set (A={1,2,3,4}), the operation (a*b=\min(a,b)) is defined. What is the identity element of this operation?Class 12Relations and FunctionsBinary operationsMedium MathematicsIf (a*b=2a+b), which statement about ((1*2)*3) and (1*(2*3)) is correct?Class 12Relations and FunctionsBinary operationsMedium MathematicsOn (A={1,2,4,8}), (a*b=\operatorname{lcm}(a,b)). What is the identity element?Class 12Relations and FunctionsBinary operationsMedium MathematicsOn (A={1,2,4,8}), (a*b=\gcd(a,b)). What is the identity element?Class 12Relations and FunctionsBinary operationsMedium MathematicsFor (a*b=a+b-ab) on real numbers, which element does not have an inverse?Class 12Relations and FunctionsBinary operationsMedium MathematicsFor (a*b=a+b+ab) on real numbers, which element does not have an inverse?Class 12Relations and FunctionsBinary operationsMedium MathematicsOn integers, (a*b=ab). Does (2) have an inverse in integers?Class 12Relations and FunctionsBinary operationsMedium MathematicsOn positive real numbers, (a*b=ab). What is the inverse of (5)?Class 12Relations and FunctionsBinary operationsMedium MathematicsOn positive real numbers, (a*b=ab). What is the identity element of this operation?Class 12Relations and FunctionsBinary operationsMedium MathematicsOn real numbers, (a*b=a+b-ab). What is the inverse of (3)?Class 12Relations and FunctionsBinary operationsMedium MathematicsOn real numbers, (a*b=a+b+ab). What is the inverse of (3)?Class 12Relations and FunctionsBinary operationsMedium