Q$\mathrm{.}2$ Set. $($A$)$ You have been asked to design an $$Open File System$$ which is derived from HDFS architecture with following variances $$ chunk size of $100$ MB$,$ block size of $1$ MB$.$ A file of size $1$ TB needs to be stored on this file system Marks:$1*5+2=7$

a$.$ How many chunks will be required to store the file?

b$.$ How many blocks will be required to store the file?

c$.$ How many chunk servers will be needed if each server hosts $1000$ blocks?

d$.$ How many chunk servers will be needed if each server hosts $100$ GB of file?

e$.$ How many chunk servers will be needed if the replication factor is $6$ and the capacity of the chunk server is $200$ GB$?$

f$.$ Using Amdahl$$s law, what is the maximum speed up that can be achieved with $14$ processors with a program for which $27\%$ of code can be executed in parallel?