Who was the first woman to serve as the Prime Minister of India?

Introduction / Context:
Political history questions often focus on firsts, especially when they relate to the participation of women in high office. In India, one of the most significant milestones was the appointment of the first woman Prime Minister. This question tests knowledge of Indian political history by asking for her name.

Given Data / Assumptions:
- The office in question is the Prime Minister of India.
- The focus is on identifying the first woman who held this office.
- The options list four prominent female figures: Sarojini Naidu, Sonia Gandhi, Indira Gandhi, and Rani Lakshmi Bai.
- Only one of them served as Prime Minister.

Concept / Approach:
Indira Gandhi, daughter of India's first Prime Minister Jawaharlal Nehru, became the third Prime Minister of India and the first woman to hold that office. She served multiple terms and played a major role in shaping Indian politics. The other women listed were significant leaders and freedom fighters but did not serve as Prime Minister of India. Therefore, identifying the correct answer requires recalling this key historical fact.

Step-by-Step Solution:
Step 1: Recall the list of Indian Prime Ministers and identify which of them were women. Step 2: Recognise that Indira Gandhi served as Prime Minister for several years, starting in the 1960s. Step 3: Consider Sarojini Naidu, who was a noted poet and freedom fighter and served as the Governor of Uttar Pradesh, but not as Prime Minister. Step 4: Note that Sonia Gandhi has been a powerful political leader and headed the Indian National Congress for many years but has not assumed the office of Prime Minister. Step 5: Understand that Rani Lakshmi Bai was a nineteenth century queen and warrior who resisted British rule but lived before the modern Prime Ministerial system. Step 6: Conclude that Indira Gandhi is the only candidate among the options who actually served as Prime Minister of India.

Verification / Alternative check:
Any standard list of Indian Prime Ministers shows Jawaharlal Nehru, followed by Lal Bahadur Shastri, and then Indira Gandhi as the third Prime Minister. She is also clearly identified as the first woman to hold that position. School textbooks and competitive exam guides frequently highlight this milestone, so cross checking with such lists reinforces that Indira Gandhi is correct.

Why Other Options Are Wrong:
Sarojini Naidu: A great freedom fighter and poet who became a state governor, but she never served as Prime Minister.
Sonia Gandhi: A leading political figure and former Congress president, but she did not assume the Prime Minister's office.
Rani Lakshmi Bai: A historic queen of Jhansi and symbol of resistance during the revolt of 1857, but the role of Prime Minister did not even exist in colonial India during her lifetime.

Common Pitfalls:
Some students may confuse party leadership with the office of Prime Minister and mistakenly choose Sonia Gandhi. Others may be influenced by the fame of Sarojini Naidu or Rani Lakshmi Bai without focusing on the specific constitutional post described. Carefully reading the question and recalling the official list of Prime Ministers is the best way to avoid such errors.

Final Answer:
Therefore, the first woman to serve as the Prime Minister of India was Indira Gandhi.