Question $4$

A $B-$tree index has the height of $4($including the root$),$ stored on disk using Alternative $(2)$ for data entries. The number of data entry pages is $1,000$ and the number of data record pages is $100,000,$ and the number of data records is $10M.$ Suppose that the search key value $k=5$ matches $10\%$ of data records in the file. What is the I$/$O cost $($in page$)$ of retrieving the records matching the search key $k=5$ using the index under the following two cases:

The index is clustered.

The index is unclustered.