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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 real numbers, (a*b=a+b-2ab) is defined. What is the identity element of this operation?Class 12Relations and FunctionsBinary operationsExpert MathematicsFor (a*b=a+b-ab) on real numbers, which is a useful rewritten form?Class 12Relations and FunctionsBinary operationsMedium MathematicsIf (a*b=a+b+ab) and (a*0=a) for every (a), what property of (0) is shown?Class 12Relations and FunctionsBinary operationsMedium MathematicsIf (g\circ f:A\to C) is onto, which of the following conclusions is always true?Class 12Relations and FunctionsOnto functionMedium MathematicsIf (f:A\to B) is one-one and (S\subseteq A), which statement is correct about the restricted function (f|_S:S\to B)?Class 12Relations and FunctionsOne-one functionExpert MathematicsWhat is the correct conclusion for (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^3+x\cos^2 x)?Class 12Relations and FunctionsOne-one functionExpert MathematicsIf (g\circ f) is one-one, which statement about (g) is correct?Class 12Relations and FunctionsOne-one functionHard MathematicsWhich statement is correct for a one-one function?Class 12Relations and FunctionsOne-one functionMedium MathematicsIf (f:\mathbb{R}\to\mathbb{R}), (f(x)=c), where (c) is a fixed real number, when will (f) be one-one?Class 12Relations and FunctionsFunctionsExpert MathematicsIf (f:\mathbb{R}\to\mathbb{R}) and (f(x)=5), which statement about (f) is correct?Class 12Relations and FunctionsFunctionsHard MathematicsIf (f:\mathbb{R}\to\mathbb{R}) and (f(x)=x^2), why is (f) not one-one?Class 12Relations and FunctionsFunctionsHard MathematicsOn the set of all students, (xRy) if and only if (x) and (y) have the same date of birth. Why is this an equivalence relation?Class 12Relations and FunctionsEquivalence relationExpert MathematicsOn real numbers, (aRb) if and only if (a-b) is rational. Choose the correct statement about the equivalence classes of this relation.Class 12Relations and FunctionsEquivalence relationExpert MathematicsWhich statement correctly describes the connection between an equivalence relation and a partition?Class 12Relations and FunctionsEquivalence relationMedium MathematicsWhich option is a correct example of a transitive relation?Class 12Relations and FunctionsTransitive relationMedium MathematicsA relation (R) is transitive on a set. If ((a,b) \in R) and no pair of the form ((b,c)) is in (R), is any new ((a,c)) pair forced only from ((a,b))?Class 12Relations and FunctionsTransitive relationEasy MathematicsOn a set (A), (R={(a,b):a\ne b}). Choose the correct statement about (R).Class 12Relations and FunctionsSymmetric relationExpert MathematicsIf (R) is symmetric and has no diagonal pair, which statement is correct?Class 12Relations and FunctionsSymmetric relationExpert MathematicsWhen will the relation (R={(a,b):d(a,b)=2}) be symmetric, where (d) is a distance function?Class 12Relations and FunctionsSymmetric relationHard MathematicsOn (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1)}). Which missing pair does not break symmetry?Class 12Relations and FunctionsSymmetric relationMedium