Concept:
Chronological arrangement means arranging events or institutions according to their time of establishment from earliest to latest.
Step 1: Identify the earliest museum.
Indian Museum, Kolkata is one of the oldest museums in India.
So, the first is:
\[
B = \text{Indian Museum, Kolkata}
\]
Step 2: Place National Museum, New Delhi.
National Museum, New Delhi was established after Indian Museum.
So, the second is:
\[
A = \text{National Museum, New Delhi}
\]
Step 3: Place National Handicraft Museum.
National Handicraft Museum came later and is related to crafts and traditional art.
So, the third is:
\[
D = \text{National Handicraft Museum, New Delhi}
\]
Step 4: Place Visvesvaraya Museum.
Visvesvaraya Industrial and Technological Museum is a later science and technology museum.
So, the fourth is:
\[
C = \text{Visvesvaraya Industrial and Technological Museum}
\]
Step 5: Place Pradhanmantri Sangrahalaya.
Pradhanmantri Sangrahalaya is the most recent among the given museums.
So, the last is:
\[
E = \text{Pradhanmantri Sangrahalaya}
\]
Thus, the correct order is:
\[
B \rightarrow A \rightarrow D \rightarrow C \rightarrow E
\]
Hence, the correct answer is:
\[
\boxed{\text{(B) B, A, D, C, E}}
\]