Match the function in Column-I with its behaviour at \( \mathrm{x}=0 \) in column-II, where [.] denotes greatest integer function \& \( \operatorname{sgn}(\mathrm{x}) \) denotes signum function.
\( \mathrm{P} \)
Column-I
(A) \( f(\mathrm{x})=[\mathrm{x}][1+\mathrm{x}] \)
Column-II
W
(B) \( f(\mathrm{x})=[-\mathrm{x}][1+\mathrm{x}] \)
(P) LHL exist at \( \mathrm{x}=0 \)
(Q) RHL exist at \( x=0 \)
(C) \( f(\mathrm{x})=(\operatorname{sgn}(\mathrm{x}))[2-\mathrm{x}][1+|\mathrm{x}|] \)
(R) Continuous at \( x=0 \)
(D) \( f(\mathrm{x})=[\cos \mathrm{x}] \)
(S) \( \lim _{x \rightarrow 0} f(\mathrm{x}) \) exists but function is
discontinuous at \( x=0 \)
(T) \( \lim _{x \rightarrow 0} f(x) \) does not exist
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