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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+\alpha ab). If the inverses of (2) and (3) are (-1) and (-\frac{3}{2}) respectively, what is (\alpha)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=pa+qb). Which condition is necessary and sufficient for associativity?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=pa+qb). What condition is needed for this operation to be commutative?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=a+\mu b). Which values of (\mu) make this operation associative?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=a+\mu b). The operation will be commutative only for what value of (\mu)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=a+b+\lambda). For which (\lambda) will the identity be (5)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{Z}), (a*b=a+b+3). What is the inverse of (4) under this operation?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=a-b). Which of the following statements is correct?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=a+b) and (a\circ b=ab). Which operation distributes over the other?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=a+b+ab) and (a\circ b=a+b). Under what condition does (*) distribute over (\circ)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn ({0,1}), (a*b=ab). Which statement is correct for this operation?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn ({0,1}), (a*b=a+b-ab). This operation behaves like which common logical operation?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=a+b-ab). What is the correct reason this operation is associative?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=a+b-ab). Which statement is correct?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{Z}), (a*b=a+b+ab). Why does this operation not form a group on the whole set?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}\setminus{1}), (a*b=a+b-ab). What is the inverse of (a)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}\setminus{1}), (a*b=a+b-ab). What is the identity element?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=a+b-ab). Which element motivates restricting the operation to (\mathbb{R}\setminus{1})?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=a+b+1). Which element acts as the identity that allows every real number to have an inverse?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{Q}\setminus{0}), (a*b=\frac{ab}{2}). What is the inverse of (5)?Class 12Relations and FunctionsBinary operationsExpert