Step 1: Key fact.
On 15 August 1947, India became independent and Jawaharlal Nehru assumed office as the first Prime Minister.
Step 2: Eliminate alternatives.
Dr. Rajendra Prasad became the first President (1950), Vallabhbhai Patel served as Deputy PM/Home Minister, and Mohammad Ali Jinnah became Pakistan’s first Governor-General.
Step 3: Conclusion.
Therefore, the correct answer is (B) Jawaharlal Nehru.