$[6$ pojints$]$ Assume a $2$way set associative write$-$back cache with many cache entries that starts empty. Following is a sequence of five memory operations:

Write Mem$[0$x$140]$;

Write Mem$[0$x$184]$; $?$

Read Mem$[0$x$142]$;

Write Mem$[0$xI$4$C$]$;

Write Mem$[0$x$170].$

With $C=16KB$ and $b-32W,$ and $32b$ address line.

a$)$ What is the hit rate when using no$-$write allocate cache?

b$)$ What is the size of the tag array?

c$)$ How to improve hit rate without increasing cache size?