Concept:
Banaras Hindu University (BHU) is one of the oldest and largest central universities in India.
It was established to promote higher education and Indian culture.
Step 1: Identify the founder of BHU.
Banaras Hindu University was founded by:
\[
\text{Pandit Madan Mohan Malaviya}
\]
with support from many national leaders and social reformers.
Step 2: Identify the establishment year.
BHU was established in:
\[
1916
\]
through the:
\[
\text{BHU Act, 1915}
\]
Step 3: Know the location of BHU.
The university is located in:
\[
\text{Varanasi, Uttar Pradesh}
\]
It is one of Asia's largest residential universities.
Step 4: Eliminate incorrect options.
• 1910 -- Incorrect
• 1916 -- Correct
• 1921 -- Incorrect
• 1931 -- Incorrect
Step 5: Conclusion.
Therefore, the correct answer is:
\[
\boxed{1916}
\]