Step 1: Understanding Hindutva
- Hindutva refers to the idea of defining Indian culture in terms of Hindu values and identity.
- It was developed as a political and cultural ideology in the early 20th century.
Step 2: Role of V. D. Savarkar
- Vinayak Damodar Savarkar, popularly known as Veer Savarkar, was the key figure who popularized Hindutva.
- In his 1923 pamphlet titled "Hindutva: Who is a Hindu?", he outlined the principles of Hindutva.
- Savarkar argued that Hindutva was the basis of Indian nationalism, emphasizing cultural unity and heritage.
Step 3: Analyzing the options
- (A) Shyama Prasad Mukherjee: Founder of Bharatiya Jan Sangh, but not the one who originally popularized Hindutva.
- (B) V. D. Savarkar: Correct, he conceptualized and popularized Hindutva.
- (C) Deen Dayal Upadhyaya: Known for "Integral Humanism," but not Hindutva as nationalism.
- (D) None of them: Incorrect, since (B) is correct.
Step 4: Conclusion
Thus, Hindutva as the basis of Indian Nationalism was popularized by V. D. Savarkar.
\[
\boxed{\text{Correct Answer: (B) V. D. Savarkar}}
\]