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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{R}), (a*b=a+b+4). What is the inverse of (6)?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (\mathbb{R}), the operation (a*b=a+b+4) is defined. What is its identity element?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (\mathbb{Z}), the operation (a*b=a+b+ab) is defined. Choose the correct statement.Class 12Relations and FunctionsBinary operationsHard MathematicsIf (A) has (n) elements, how many commutative binary operations can be defined on (A)?Class 12Relations and FunctionsBinary operationsExpert MathematicsIf (A) has (n) elements, how many binary operations can be defined on (A)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (A={0,1,2,3,4}), (a*b) is the remainder of (a+b) modulo (5). What is the inverse of (4)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (A={0,1,2,3,4}), (a*b) is the remainder when (a+b) is divided by (5). What is (3*4)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=a+b+mab). If the inverse of (2) is (-1), what is the value of (m)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=a+b+\lambda ab). For which (\lambda) will the element (2) have no inverse?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=a+b+\lambda). For which (\lambda) will the identity element be (5)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (A=\mathbb{R}\setminus{\frac{1}{2}}), (a*b=a+b-2ab). What is the inverse of (a)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=a+b-2ab). Which element has no inverse?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (A={1,2,4,5}), (a*b) is the remainder when (ab) is divided by (6). Which statement is correct?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (A={0,1,2}), (a*b) is the remainder when (ab) is divided by (3). Which element has no inverse?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (A={1,2,3,6}), (a*b=\operatorname{lcm}(a,b)). What is the identity element?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (A={1,2,3,6}), (a*b=\gcd(a,b)). What is the identity element?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{N}), (a*b=\gcd(a,b)). Does the identity element lie in (\mathbb{N})?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{N}), (a*b=\operatorname{lcm}(a,b)). What is the identity element?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=|a-b|). Is there an identity element?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=|a-b|). Which statement is correct?Class 12Relations and FunctionsBinary operationsExpert