Step 1: Understanding the Concept:
Indian astronomy uses several types of 'days', each defined by a different astronomical cycle. Comparing their durations helps in understanding the hierarchical structure of cosmic time.
Step 2: Defining the Measures:
1. Nakshatra-dinam (Sidereal Day - C): The time taken for the Earth to rotate $360^\circ$ relative to fixed stars. It is approximately 23 hours, 56 minutes. This is the shortest "day" in this set.
2. Savana-dinam (Civil Day - A): The time from one sunrise to the next. Due to the Sun's motion, the Earth must rotate about $361^\circ$ to see the Sun again. It is exactly 24 hours (or 60 Ghatikas).
3. Paitra-dinam (Lunar Month - B): As discussed earlier, one day for the ancestors equals one human lunar month (approx. 29.5 days).
4. Divya-dinam (Divine Day - E): One day for the Devas equals one human solar year (approx. 365.25 days).
5. Brahma-dinam (Kalpa - D): One day for Brahma equals 4,320,000,000 human years. This is the largest unit.
Step 3: Arranging in Increasing Order:
C (Nakshatra) $<$ A (Savana) $<$ B (Paitra) $<$ E (Divya) $<$ D (Brahma).
Sequence: C, A, B, E, D.
Step 4: Final Answer:
The correct increasing order is C, A, B, E, D.