Step 1: Understanding the Concept:
This is a recall question on dates. The safest way is to place each paper in time and pick the oldest one.
Step 2: Place the papers in time.
Udant Martand started in 1826 in Calcutta. Saraswati, the literary monthly, started in 1900. Hindustan, the daily, was started in 1936. Navbharat Times arrived in the 1940s.
Step 3: Pick the oldest.
The earliest date is 1826, which belongs to Udant Martand. The other three come about a century or more later.
Step 4: Link with a known day.
Hindi Journalism Day falls on 30 May, which is the date on which Udant Martand first came out. This supports the answer.
Step 5: Why the others cannot be first.
Saraswati is remembered as a literary magazine that shaped modern Hindi prose, but it came when Hindi printing was already established. Hindustan and Navbharat Times are big daily papers of the modern age, and they grew with later press houses. Being famous today is not the same as being first, so the oldest date decides.
Step 6: Conclude.
The first Hindi newspaper is Udant Martand, which is option (4).
Final Answer:
Udant Martand is the first Hindi newspaper, option (4).
\[ \boxed{\text{4}} \]