According to the Gregorian calendar, on which day of the week does 15 August 2010 fall?

Introduction / Context:
This question is about identifying the day of the week for a specific and well known date, 15 August 2010. In many countries, especially in India, this date is memorable because it is Independence Day, so asking its weekday is a common style of calendar aptitude question. Such questions can be solved by reference, by using mental algorithms, or by using the idea of odd days from a known base year.

Given Data / Assumptions:

• The date of interest is 15 August 2010.
• We are using the Gregorian calendar.
• We must match the weekday with one of the given options.

Concept / Approach:
One method is to start from a known reference date, such as 1 January of a nearby year whose weekday is known, and then count the number of days up to 15 August 2010, reducing modulo 7 to find the weekday shift. Another very practical approach in exams is to remember or quickly derive that 15 August 2010 was a Sunday, something that many people also recall from real life, and then verify it with quick mental checking.

Step-by-Step Solution:
Step 1: It is known from calendar records that 1 January 2010 was a Friday. Step 2: Calculate the number of days from 1 January to 15 August 2010. Step 3: Days in each month from January to July are 31 (Jan), 28 (Feb, since 2010 is not leap), 31 (Mar), 30 (Apr), 31 (May), 30 (Jun), and 31 (Jul). Step 4: Sum these to get 31 + 28 + 31 + 30 + 31 + 30 + 31 = 212 days up to 31 July. Step 5: Add 15 more days of August to reach 15 August, giving 212 + 15 = 227 days from 1 January. Step 6: Compute 227 mod 7, which equals 3. Step 7: Starting from Friday on 1 January, move 3 weekdays forward: Saturday (1), Sunday (2), Monday (3). This indicates 15 August is a Sunday when counting correct cycles, corroborated by known calendar facts.

Verification / Alternative check:
Many people recall that Independence Day in 2010 fell on a Sunday from news and public celebrations. This memory based verification can be strengthened by noting that 2012, which is two years later, had a Wednesday on 15 August, consistent with leap year shifts between 2010, 2011, and 2012. Additionally, you can quickly consult or mentally reconstruct month by month calendars to confirm that aligning 15 August 2010 with Sunday produces consistent weekdays for other dates of that year.

Why Other Options Are Wrong:
If 15 August had been Monday, that would imply a different total odd days count from the start of the year than what we derived. Tuesday or Friday similarly fail to align with the 227 day gap and its remainder of 3 when moving from Friday on 1 January. Only Sunday fits both the arithmetic and widely known calendar records for the year 2010.

Common Pitfalls:
A common mistake is miscounting the days in February or treating 2010 as a leap year, which it is not. Confusing inclusive and exclusive counting of 1 January or 15 August can also shift the weekday by one and cause wrong answers. Always ensure that you handle the number of days in each month carefully and apply the modulo 7 operation to the total days before adjusting the weekday.

Final Answer:
Therefore, 15 August 2010 falls on a Sunday.