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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।

MathematicsIf (f:\mathbb{R}\to\mathbb{R}) and (f(x)=x+\sin x), what is the suitable statement about (f)?Class 12Relations and FunctionsOne-one functionHard MathematicsIf (f:(-\infty,1]\to\mathbb{R}) and (f(x)=x^2-2x), what is the correct statement about (f)?Class 12Relations and FunctionsOne-one functionHard MathematicsIf (f:\mathbb{R}-{0}\to\mathbb{R}) and (f(x)=\frac{1}{x}), is (f) one-one?Class 12Relations and FunctionsOne-one functionHard MathematicsIf (f:\mathbb{R}\to(0,\infty)) and (f(x)=2^x), what is the correct statement about (f)?Class 12Relations and FunctionsOne-one functionHard MathematicsIf (f:\mathbb{R}\to\mathbb{R}) and (f(x)=2x^3+1), what is the nature of (f)?Class 12Relations and FunctionsOne-one functionHard MathematicsIf (f:\mathbb{R}\setminus{1}\to\mathbb{R}\setminus{2}) is defined by (f(x)=\frac{2x+3}{x-1}), what is (f^{-1}(x))?Class 12Relations and FunctionsFunctionsHard MathematicsIf (R) is transitive and contains ((x,x)) and ((x,y)), which conclusion is correct?Class 12Relations and FunctionsTransitive relationHard MathematicsIf (R={(1,2),(2,4),(4,8),(1,4),(2,8),(1,8)}), what is the correct conclusion for (R)?Class 12Relations and FunctionsTransitive relationHard MathematicsIf (R={(a,b):a,b\in\mathbb{R}\text{ and }a-b>2}), is (R) transitive?Class 12Relations and FunctionsTransitive relationHard MathematicsIf (R={(1,2),(2,5),(5,3),(1,5),(2,3)}), which pair is immediately required to make it transitive?Class 12Relations and FunctionsTransitive relationHard MathematicsIf for a relation (R), (R\circ R\subseteq R), what is the correct conclusion about (R)?Class 12Relations and FunctionsTransitive relationHard MathematicsIf (R={(1,4),(4,2),(2,2),(1,2),(4,4)}), what is the correct statement about (R)?Class 12Relations and FunctionsTransitive relationHard MathematicsWhat is the most common difficult mistake while checking a transitive relation?Class 12Relations and FunctionsTransitive relationHard MathematicsWhat is the safest method to prove transitivity in hard relation questions?Class 12Relations and FunctionsTransitive relationHard MathematicsIf (R={(1,2),(2,3),(1,3),(3,2)}), what is the correct reason that (R) is not transitive?Class 12Relations and FunctionsTransitive relationHard MathematicsIf (R={(a,b):a,b\in\mathbb{R}\text{ and }a\le b+2}), is (R) transitive?Class 12Relations and FunctionsTransitive relationHard MathematicsIf (R) is transitive, which statement is correct about (R^{-1})?Class 12Relations and FunctionsTransitive relationHard MathematicsIf (R={(1,2)}) and (S={(2,3)}), both are transitive individually. What about (R\cup S)?Class 12Relations and FunctionsTransitive relationHard MathematicsIf (R={(1,2),(2,3),(3,1)}), which group must start getting added to form the full transitive closure?Class 12Relations and FunctionsTransitive relationHard MathematicsOn (A={1,2,3}), (R={(1,1),(1,2),(2,2),(2,1),(2,3),(1,3)}). Is (R) transitive?Class 12Relations and FunctionsTransitive relationHard