Question

Cache tag directory entry contains modified/dirty-bit if the cache is

Answer 1

option (b)

In write-back cache only modified blocks are written back into main memory; not modified blocks are directly overwritten. It saves memory access time. To keep track of modified blocks one bit is stored in cache tag directory entry for each block: which is known as modified/dirty bit.
In write through cache main memory content is immediate updated a long with cache updation. So no need to keep track of modified block. Hence no any modified/dirty bit needed in cache directory entry.