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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 (A=\mathbb{R}\setminus{1}), (a*b=a+b-ab) is defined. Choose the correct statement about this operation on this set.Class 12Relations and FunctionsBinary operationsExpert MathematicsOn real numbers, (a*b=a+b+ab) is defined. If (a*b=0), how will (b) be written in terms of (a), where (a\neq -1)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn real numbers, (a*b=a+b+mab) is defined. For which (m) will the inverse of (2) be (-1)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn real numbers, (a*b=a+b+m) is defined. If the identity element is (5), what is the value of (m)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn real numbers, (a*b=2a+3b) is defined. Does this operation have an identity element?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn real numbers, (a*b=2a+3b) is defined. Is this operation commutative?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn real numbers, (a*b=a+b+ab) is defined. What is the solution of (x*2=7)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn real numbers, (a*b=a+b-4ab) is defined. Choose the correct statement about (a=\frac{1}{4}).Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (A={0,1,2}), (a*b) is the remainder when (a+b) is divided by (3). What is the value of (2*2)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn real numbers, (a*b=a+b-ab) is defined. Which element does not have an inverse?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn real numbers, (a*b=a+b+\lambda ab) is defined. If (\lambda\neq 0), which element will not have an inverse?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn real numbers, (a*b=a+b+\lambda ab) is defined. For which (\lambda) will (0) be the identity element?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (A={1,2,3,6}), (a*b=\operatorname{lcm}(a,b)) is defined. Which element is the inverse of (6), if the identity is (1)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (A={1,2,3,4,5,6}), (a*b=\gcd(a,b)) is defined. What is the correct statement about the inverse of (4), if identity is assumed to be (6)?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn real numbers, (a*b=a+b+ab) is defined. Evaluating (1*2*3) from left to right as ((1*2)*3), what is the value?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn real numbers, (a*b=a+b+ab) and (f(x)=x+1) are given. What is (f(a*b)) equal to?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn positive integers, (a*b=\gcd(a,b)) is defined. Does this operation have an identity element?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn positive integers, (a*b=\operatorname{lcm}(a,b)) is defined. What is the identity element of this operation?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn (A={0,1}), (a*b) is the remainder when (a+b) is divided by (2). Which statement is correct for this operation?Class 12Relations and FunctionsBinary operationsExpert MathematicsOn real numbers, (a*b=a+b+2) and (a\circ b=a+b-2) are defined. What is the value of (3*(4\circ 5))?Class 12Relations and FunctionsBinary operationsExpert