Let \(f: R \rightarrow R\) be defined as \(f(x)=\left[\begin{array}{ll}{\left[e^{x}\right],} \,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,x<0 \\ a e^{x}+[x-1], \,\,\,\,\,\,\,\,\,0 \leq x<1 \\ b+[\sin (\pi x)], \,\,\,\,\,\,\,\,\,\,\,\,1 \leq x<2 \\ {\left[e^{-x}\right]-c,} \,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,x \geq 2\end{array}\right.\) where a,b,c \(\in R\) and \([t]\) denotes greatest integer less than or equal to \(t.\) Then, which of the following statements is true \(?\)

1. A There exists \(a,b,c\) \(\in R\) such that \(f\) is continuous of \(R\).
2. B If \(f\) is discontinuous at exactly one point, then \(a+b+c=1\)
3. C If \(f\) is discontinuous at exactly one point, then \(a+b+c \neq 1\)
4. D \(f\) is discontinuous at atleast two points, for any values of \(a , b\) and \(c\).