Concept:
India has several important financial institutions that support banking, industry, rural development, and stock markets.
Step 1: Identify the establishment year of Bombay Stock Exchange.
Bombay Stock Exchange (BSE) was established in:
\[
1875
\]
Thus:
\[
A \rightarrow III
\]
Step 2: Identify the establishment year of NABARD.
NABARD was established in:
\[
1982
\]
Thus:
\[
B \rightarrow II
\]
Step 3: Identify the establishment year of IDBI.
Industrial Development Bank of India (IDBI) was established in:
\[
1964
\]
Thus:
\[
C \rightarrow IV
\]
Step 4: Identify the establishment year of SIDBI.
Small Industries Development Bank of India (SIDBI) was established in:
\[
1990
\]
Thus:
\[
D \rightarrow I
\]
Step 5: Write the complete matching.
The correct matching becomes:
\[
A-III,\; B-II,\; C-IV,\; D-I
\]
Step 6: Conclusion.
Hence, the correct answer is:
\[
\boxed{A\text{-}III,\; B\text{-}II,\; C\text{-}IV,\; D\text{-}I}
\]