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Nonzero Real Numbers

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{0}), (a*b=\frac{ab}{2}). Which statement is correct?Class 12Relations and FunctionsBinary operationsHard MathematicsIn the operation (a\ast b=2ab), (\frac{1}{2}) is the identity. What is the inverse of (4)?Class 12Relations and FunctionsBinary operationsEasy MathematicsThe operation (a\ast b=2ab) is given on non-zero real numbers. What is the identity element?Class 12Relations and FunctionsBinary operationsEasy MathematicsOn the set of non-zero real numbers, (a\ast b=\frac{a}{b}) is given. Is it a binary operation?Class 12Relations and FunctionsBinary operationsEasy MathematicsIf (f:\mathbb{R}\setminus{0}\to\mathbb{R}\setminus{0}), (f(x)=\frac{1}{x}), choose the correct statement.Class 12Relations and FunctionsOnto functionEasy MathematicsOn all non-zero real numbers, (aRb) if and only if (\frac{a}{b}\in Q). What type of relation is this?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn the set of non-zero real numbers, (aRb) if and only if (\frac{a}{b}>0). On what basis is this an equivalence relation?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn non-zero real numbers, (aRb) holds when (\frac{a}{b}) is a positive rational number. Which element is in the class of (-2\sqrt{5})?Class 12Relations and FunctionsEquivalence relationHard MathematicsOn non-zero real numbers, (aRb) holds when (\frac{1}{a}) and (\frac{1}{b}) have the same sign. What type of relation is it?Class 12Relations and FunctionsEquivalence relationMedium MathematicsOn non-zero real numbers, (aRb) holds when (\frac{a}{b}>0). What type of relation is it?Class 12Relations and FunctionsEquivalence relationMedium