Concept:
Shri Aurobindo Ghosh (also known as Sri Aurobindo) was a great Indian philosopher, nationalist, poet, yogi, and spiritual teacher. He played an important role in India's freedom movement and later became widely known for his contributions to spiritual philosophy and Integral Yoga.
He emphasized the evolution of human consciousness and the integration of spiritual practice with daily life.
Step 1: Identify the birth year of Shri Aurobindo Ghosh.
Sri Aurobindo was born on:
\[
15 \text{ August } 1872
\]
Thus, his birth year is:
\[
\boxed{1872}
\]
Step 2: Analyze the given options.
Option (A): 1872
This is the correct birth year of Shri Aurobindo Ghosh.
Option (B): 1850
Incorrect. This year does not correspond to Sri Aurobindo's birth.
Option (C): 1862
Incorrect. Sri Aurobindo was born later than this year.
Option (D): 1882
Incorrect. This is ten years after his actual birth year.
Step 3: Identify the correct option.
Since Shri Aurobindo Ghosh was born in 1872, the correct answer is:
\[
\boxed{1872}
\]