If \( \lim _{x \rightarrow c^{-}}\{\ln x\} \) and \( \lim _{x \rightarrow c^{+}}\{\ln x\} \) exi...

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If \( \lim _{x \rightarrow c^{-}}\{\ln x\} \) and \( \lim _{x \rightarrow c^{+}}\{\ln x\} \) exists finitely but they are not equal (where \( \{\cdot\} \) denotes fractional part function), then
(a) \( c \) can take only rational values
(b) \( c \) can take only irrational values
(c) \( c \) can take infinite values in which only one is irrational
(d) \( c \) can take infinite values in which only one is rational
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