(A) For 2≤x<3, [x]=2, not 3. False.
(B) Correct definition. True.
(C) RHD at x=2: h→0+limh[2+h]−[2]=h2−2=0, defined. False.
(D) LHD at x=2: h→0+lim−h[2−h]−2=−h1−2→∞, not zero. False.
(E) Since LHD does not exist finitely, f is not differentiable at x=2. True.
So (B) and (E) only.