Idk why meta data is being considered as the record size. I highly doubt if that's correct.
Records = 2000.
Block size = 100B
Size of an index record = 10B
1st level index $= 2000/10 = 200$ $blocks.$
2nd level index $= 200/10 = 20$ $blocks.$
3rd level index $= 20/10 = 2$ $blocks.$
4th level index $= 2/10 = 0.2$ $blocks = 1$ $block$.
Hence, we need 4 levels of indexing.
Number of accesses would be $4+1=5$