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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।

MathematicsOn positive real numbers, (a*b=a^{\log b}), where (\log) has base (10). When is this operation commutative?Class 12Relations and FunctionsBinary operationsExpert MathematicsWhat is the correct conclusion for (f:(0,\infty)\to(0,\infty)), (f(x)=\ln x)?Class 12Relations and FunctionsOnto functionExpert MathematicsIf (f:(0,\infty)\to\mathbb{R}), (f(x)=\ln x), which statement about (f) is correct?Class 12Relations and FunctionsOnto functionExpert MathematicsIf (f:\mathbb{R}\to(0,\infty)) and (f(x)=2^x), what preimage of (y>0) proves that (f) is onto?Class 12Relations and FunctionsOnto functionHard MathematicsIf (f:\mathbb{R}\to(0,\infty)) and (f(x)=e^x), choose the correct statement.Class 12Relations and FunctionsOnto functionHard MathematicsFor (f:(0,\infty)\to(0,\infty)), (f(x)=\ln x), which conclusion is correct?Class 12Relations and FunctionsOnto functionHard MathematicsIf (f:(0,\infty)\to\mathbb{R}), (f(x)=\ln x), which statement is correct?Class 12Relations and FunctionsOnto functionHard MathematicsIf (f:(0,\infty)\to \mathbb{R}), (f(x)=\ln x), what type is (f)?Class 12Relations and FunctionsOnto functionHard MathematicsIf (f:\mathbb{R}\setminus{0}\to\mathbb{R}), (f(x)=\ln(x^2)), why is (f) not one-one?Class 12Relations and FunctionsOne-one functionExpert MathematicsWhat is correct about the one-one nature of (f:(0,\infty)\to\mathbb{R}), (f(x)=\ln(x^2))?Class 12Relations and FunctionsOne-one functionExpert MathematicsIf (f:(0,\infty)\to\mathbb{R}), (f(x)=\ln x), choose the correct answer for (f).Class 12Relations and FunctionsOne-one functionHard MathematicsWhich statement is correct for (f:(0,\infty)\to\mathbb{R}), (f(x)=\ln x)?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{R}\to(0,\infty)) is given by (f(x)=e^{2x+1}), what is (f^{-1}(x))?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:(0,\infty)\to\mathbb{R}) is defined by (f(x)=\ln x), what is (f^{-1}(x))?Class 12Relations and FunctionsFunctionsHard MathematicsOn positive real numbers, (aRb) if and only if (\frac{\ln a}{\ln b}) is defined and rational. Why is this not an equivalence relation?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn all positive real numbers, (aRb) if and only if (\log a-\log b\in Z). Which is the equivalence class of (1)?Class 12Relations and FunctionsEquivalence relationExpert