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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-ab). What is the solution of (2*x=3)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}^{+}), (a*b=\frac{a+b}{2}). Which statement is correct?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (S={1,2,3,4,6,12}), (a*b=\operatorname{lcm}(a,b)). What is the identity element of this operation?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (S={1,2,3,4,6,12}), (a*b=\gcd(a,b)). What is the identity element of this operation?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{Z}), (a*b=a+b+ab). Which of the following elements is not its own inverse?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{Z}), (a*b=a+b+ab). Which element is its own inverse?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=a+b-ab). If (a*b=0), what is the correct value of (b)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=a+b+ab). If (a*b=0), what is the correct value of (b) in terms of (a)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=a+b+ab). Which form is most useful for explaining closure on (\mathbb{R}\setminus{-1})?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=a^2+b). In which property does this operation fail?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}\setminus{-2}), (a*b=a+b+\frac{ab}{2}). What is the inverse of (4)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn \(\mathbb{R}\setminus{-2}\), \(a*b=a+b+\frac{ab}{2}\). What is the identity element of this operation?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=a+b+ab). What is the solution of (x*2=8)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=a+b-1). What is the inverse of (8)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=a+b-1). What is the identity element of this operation?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=a+b-1). What is the value of ((2*3)*4)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}), (a*b=a+b-1). Which statement about ((2*3)*4) and (2*(3*4)) is correct?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}^{+}), (a*b=\frac{ab}{a+b}). Which property does this operation satisfy?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}^{+}), (a*b=\sqrt{ab}). What is the correct conclusion about this operation?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (\mathbb{R}\setminus{0}), (a*b=\frac{a}{b}). Which statement is correct?Class 12Relations and FunctionsBinary operationsExpert