Consider data storage for university students. Each student data, StuData which is in a file of size of less than $64$ MB$.$ A data block stores the full file data for a student of StuData$\_$idN, where N $=1$ to $2000.$

a$)$ How the files of each student will be distributed at a Hadoop Cluster? How much student data can be stored in one cluster? Assume that each rack has two DataNodes for processing each of $256$ GB memory. Assume that cluster consists of $480$ racks.

b$)$ What is the total memory capacity of the cluster in PB and DataNodes in each rack?

c$)$ Show the distributed blocks for students with ID $=384$ and $4100.$ Assume default replication in the DataNodes $=12.$

d$)$ What shall be the changes when a StuData file size $<=512$ MB$?$