Step 1: Context.
The Constitution came into force on 26 January 1950, replacing the Federal Court of India (1937–1950) with the Supreme Court.
Step 2: Exact establishment date.
The Supreme Court of India held its first sitting and formally came into being on 28 January 1950 (initially in the Chamber of Princes, Parliament House).
Step 3: Eliminate nearby dates.
26 Jan is Republic Day/Constitution enforcement; 29–30 Jan have no bearing on establishment.
Step 4: Conclude.
\[
\boxed{\text{28th January, 1950 (Option B).}}
\]