No.of records = 30000, Block Size = 1024 bytes, record size = 100 bytes, search key = 9 bytes, block pointer size 6 bytes
index blocking factor : $\left \lfloor (block size/(key size+pointer) \right \rfloor$= 1024/15 =68
table blocking factor : $\left \lfloor (block size/(record size) \right \rfloor $= 10
A) for dense index we will have one entry in index table for each record so no of block entries = $\left \lceil 30000/68 \right \rceil $ = 442(1st level)
2nd level no of block entries = $\left \lceil 442/68 \right \rceil $ = 7
3rd level no of block entries = $\left \lceil 7/68 \right \rceil $ = 1
3 level.
B) for spars index, number of entries in index file is equal to number of data blocks = 30000/table block factor =30000/10 =3000
1st level no of block entries = $\left \lceil 3000/68 \right \rceil $ = 45
2nd level no of block entries = $\left \lceil 45/68 \right \rceil $ = 1
2 level