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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 positive real numbers, (a*b=ab) is defined. Choose the correct option about (a*b=b*a) and ((a*b)*c=a*(b*c)).Class 12Relations and FunctionsBinary operationsExpert MathematicsOn real numbers, (a*b=a+b+1) is defined. What will be the inverse of (a) in this operation?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 natural numbers, (a*b=a-b) is defined. Why is it not a binary operation?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn integers, (a*b=a+b+2ab) is defined. Is this a binary operation on integers?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn real numbers, (a*b=a+b-3) is defined. Which statement is correct?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn real numbers, (a*b=a+b-ab) is defined. What is the inverse of (3) with respect to 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 the set (A={1,2,3,4,5}), (a*b=\min(a,b)) is defined. What will be the identity element of this operation?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn the set (A={1,2,3,4,5}), (a*b=\max(a,b)) is defined. What is the identity element of this operation?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn real numbers, (a*b=a+b+ab) is defined. Which element does not have an inverse?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn non-zero real numbers, (a*b=\frac{ab}{2}) is defined. What will be the inverse of (5)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn non-zero real numbers, (a*b=\frac{ab}{2}) is defined. What is the identity element for this operation?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn real numbers, (a*b=a+b-2ab) is defined. What is the identity element of this operation?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn real numbers, (a*b=a+b+kab) is defined. If the product of (2) and (3) is (11), what is the value of (k)?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 the set (A={0,1,2,3}), (a*b) is defined as the remainder obtained when (a+b) is divided by (4). What is the inverse of (3)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn positive real numbers, (a*b=\sqrt{ab}) is defined. Choose the correct statement about associativity of this operation.Class 12Relations and FunctionsBinary operationsExpert MathematicsOn the set of integers, (a*b=a+b-1) is defined. What is the inverse of (7) with respect to this operation?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn the set of real numbers, the operation (a*b=a+b+ab) is defined. If (a\neq -1), what will be the inverse of (2)?Class 12Relations and FunctionsBinary operationsExpert