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Class 12 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

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 MathematicsIf (a*b=a+b+kab) and (k\neq0), which element will not have an inverse?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (\mathbb{R}), (a*b=a+b+k). What is the identity element of this operation?Class 12Relations and FunctionsBinary operationsHard MathematicsOn (\mathbb{R}), (a*b=ka+b). For which (k) will the operation be associative?Class 12Relations and FunctionsBinary operationsHard MathematicsOn \(A=\mathbb{R}\setminus\left{-\frac{1}{\lambda}\right}\), \(a*b=a+b+\lambda ab\), where \(\lambda\neq0\). What is the inverse of (a)?Class 12Relations and FunctionsBinary operationsHard MathematicsOn real numbers, (a*b=a+b+\lambda ab). When will the inverse of (a) be undefined?Class 12Relations and FunctionsBinary operationsHard MathematicsOn real numbers, (a*b=a+b+\lambda ab). What is the identity element of this operation?Class 12Relations and FunctionsBinary operationsHard MathematicsOn real numbers, (a*b=a+b+\lambda ab). Which statement is correct, where (\lambda) is a fixed real number?Class 12Relations and FunctionsBinary operationsHard MathematicsOn real numbers, (a*b=a+b+k). What will be the inverse of (a) under this operation?Class 12Relations and FunctionsBinary operationsHard MathematicsOn real numbers, (a*b=ka+kb). For which (k) will this operation be associative?Class 12Relations and FunctionsBinary operationsHard MathematicsOn real numbers, \(a*b=a+b+k ab\) is defined. If the inverse of (2) is \(-\frac{1}{2}\), what is the value of (k)?Class 12Relations and FunctionsBinary operationsHard MathematicsIf (a*b=a+kb) and (2*3=3*2) must hold for unequal values like (2,3), what is (k)?Class 12Relations and FunctionsBinary operationsMedium MathematicsIf (f:\mathbb{R}\to\mathbb{R}), (f(x)=ax+b), when will (f) be onto?Class 12Relations and FunctionsOnto functionExpert MathematicsIf (f:\mathbb{R}\to[a,\infty)), (f(x)=x^2-6x+11) is onto, what should be the value of (a)?Class 12Relations and FunctionsOnto functionExpert MathematicsIf (f:\mathbb{R}\to\mathbb{R}), (f(x)=kx+3), when will (f) be onto?Class 12Relations and FunctionsOnto functionMedium MathematicsIf (f:[a,\infty)\to\mathbb{R}) and (f(x)=x^2), which condition on (a) is necessary and sufficient for (f) to be one-one?Class 12Relations and FunctionsOne-one functionExpert MathematicsFor the linear fractional function (f(x)=\frac{ax+b}{cx+d}), if (ad-bc\neq0) and (cx+d\neq0), what is correct about (f)?Class 12Relations and FunctionsOne-one functionExpert MathematicsIf (f:\mathbb{R}\to\mathbb{R}) and (f(x)=(k+1)x+4), when will (f) be one-one?Class 12Relations and FunctionsOne-one functionExpert