Explanation:

- Option 1: Shah Azizur Rahman

- He served as Prime Minister of Bangladesh from 1979 to 1982.

- His tenure lasted for a relatively short period.

- Option 2: Khaleda Zia

- She served as Prime Minister from 1991 to 1996 and again from 2001 to 2006.

- While her role was significant, her combined tenure was not the longest.

- Option 3: Sheikh Hasina

- She first took office in 1996 and served until 2001. She returned to power in 2009 and continues to serve as of my last update.

- With over 19 years in power, she is Bangladesh's longest-serving Prime Minister.

- This is the correct answer.

- Option 4: Sheikh Mujibur Rahman

- Known as the founding leader, he served as the Prime Minister briefly before becoming President.