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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{Z}), (a*b=a+b+1). What is the inverse of (5)?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (\mathbb{R}^+), (a*b=\frac{a}{b}). What is the correct statement?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (\mathbb{R}^+), (a*b=ab). What is its identity element?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (\mathbb{R}), (a*b=a+b+c). What will be the inverse of an element (p)?Class 12Relations and FunctionsBinary operationsHard MathematicsIf (a*b=a+b+kab) on (\mathbb{R}), for which values of (k) is the operation associative?Class 12Relations and FunctionsBinary operationsHard MathematicsIf (a*b=ka+b) on (\mathbb{R}) is commutative, what is the value of (k)?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (\mathbb{R}), (a*b=a^2+b^2). Choose the correct property.Class 12Relations and FunctionsBinary operationsHard MathematicsOn (\mathbb{Z}), (a*b=\frac{a+b}{2}) is defined. Why is it not a binary operation?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (\mathbb{Z}), (a*b=a-b). Which statement is correct?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (A={1,2,3,6}), (a*b=\operatorname{lcm}(a,b)). What will be the identity element?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (A={1,2,3,6}), (a*b=\gcd(a,b)). What is the identity element of this operation?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (A={2,4,6,8}), (a*b=\min(a,b)). Which is the identity element?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (A={2,4,6,8}), (a*b=\max(a,b)). What is its identity element?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (\mathbb{Q}-{0}), (a*b=\frac{ab}{5}). What is the inverse of (10)?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (\mathbb{Q}-{0}), (a*b=\frac{ab}{5}). Which is the identity element?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (\mathbb{R}), (a*b=a+b+ab). Which number does not have an inverse?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (A=\mathbb{R}-{-1}), (a*b=a+b+ab). What is the inverse of (2)?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (A=\mathbb{R}-{-1}), (a*b=a+b+ab). What is the identity element?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (\mathbb{R}), (a*b=a+b-ab). What is the inverse of (4)?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (\mathbb{R}), (a*b=a+b-ab). Which is its identity element?Class 12Relations and FunctionsBinary operationsHard