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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 (\mathbb{Q}\setminus{0}), (a*b=\frac{ab}{2}). What is the identity element of this operation?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=a^2+b^2). Which property does this operation satisfy?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn ({1,2,3,4,5}), (a*b=\min(a,b)). What is the identity element of this operation?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{N}), (a*b=\min(a,b)). What is the correct conclusion about the identity element?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{N}), (a*b=\max(a,b)). Which statement about this operation is correct?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{Z}), (a*b=a+b-2). What is the inverse of (7) under this operation?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=a+b+kab). Which value of (k) makes this operation associative?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn positive real numbers, (a*b=a^{\log b}), where (\log) has base (10). When is this operation commutative?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}\setminus{-1}), for (a*b=a+b+ab), what is the inverse of (a)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn the set (\mathbb{R}\setminus{-1}), the operation (a*b=a+b+ab) is defined. What is the identity element for this operation?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn the set (A=\mathbb{R}\setminus{-1}), the operation (a*b=a+b+ab) is defined. If (x) is the inverse of (5), what is the value of (x*2)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn real numbers, (a*b=a+b+ab) is defined. If ((x*1)=5), what is the value of (x)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn real numbers, (a*b=a+b+ab) is defined. If (a*b=a), what is the value of (b), where (a\neq -1)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn real numbers, (a*b=a+b+ab) is defined. Why is (a*b=b*a) true?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn positive real numbers, (a*b=\frac{a}{b}) is defined. Which property is not satisfied by this operation?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (A={0,1,2,3,4}), (a*b) is the remainder when (ab) is divided by (5). Which element does not have an inverse?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (A={0,1,2,3,4}), (a*b) is the remainder when (ab) is divided by (5). What is the inverse of (2)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn real numbers, (a*b=a+b+ab) is defined. Which is the most suitable reason for this operation being associative?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn real numbers, (a*b=a+b+ab) is defined. What is the simplified form of (a*(b*c))?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (A=\mathbb{R}\setminus{-1}), (a*b=a+b+ab) is defined. Which statement about this operation is correct?Class 12Relations and FunctionsBinary operationsExpert