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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{N}), (a*b=a^b). Which statement is correct?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=a+b+ab+2). Does this operation have an identity element?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=a+b+1). What is the inverse of (a) under this operation?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn non-zero real numbers, (a*b=\frac{ab}{2}). Which is the inverse of (a)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn non-zero real numbers, (a*b=\frac{ab}{2}). What is the identity element?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (A={1,2,3,4}), (a*b=\min(a,b)). What is the identity element?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (A={1,2,3,4}), (a*b=\max(a,b)). Which is the identity element?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (A={0,1,2,3}), (a*b) is the remainder when (a+b) is divided by (4). What is the inverse of (2)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn positive real numbers, (a*b=\sqrt{ab}). Choose the correct conclusion about this operation.Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{Z}), (a*b=a+b-3). What is the inverse of (a) under this operation?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{Z}), (a*b=a+b-3) is defined. Which statement is correct?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (A=\mathbb{R}\setminus{-1}), (a*b=a+b+ab). What is the inverse of (a)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn the set (A=\mathbb{R}\setminus{-1}), the operation (a*b=a+b+ab) is defined. What is the identity element?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (A={1,2,4,8}), (a*b=\operatorname{lcm}(a,b)). Which statement is correct?Class 12Relations and FunctionsBinary operationsHard MathematicsIn (a*b=a+b+\lambda ab) on (\mathbb{R}), (\lambda=2). What is the inverse of (4)?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (\mathbb{R}), (a*b=a+b+\lambda ab). Under which condition will the inverse of (a) exist?Class 12Relations and FunctionsBinary operationsHard MathematicsIf (a*b=a+b+\lambda ab) and (\lambda\neq0), what is the identity element?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (\mathbb{R}), (a*b=a+b-3). What is the simplified form of (a*(b*c))?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (\mathbb{R}), (a*b=a+b-3). What is the value of ((2*5)*7)?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (\mathbb{R}), (a*b=a+b-3). What is the inverse of (8)?Class 12Relations and FunctionsBinary operationsHard