Calculation for finding the day of the week

To find out the day of the week on a particular date, we can use the concept of the Zeller's Congruence formula. The formula is as follows:


\[ h = \left(q + \left\lfloor \frac{13(m+1)}{5} \right\rfloor + K + \left\lfloor \frac{K}{4} \right\rfloor + \left\lfloor \frac{J}{4} \right\rfloor - 2J \right) \mod 7 \]

Where:
- h is the day of the week (0 = Saturday, 1 = Sunday, 2 = Monday, ..., 6 = Friday)
- q is the day of the month
- m is the month (3 = March, 4 = April, ..., 12 = December). January and February are counted as months 13 and 14 of the previous year.
- K is the year of the century (year \mod 100)
- J is the zero-based century (actually ⌊ year/100 ⌋) (For example, 1984 has J = 19)

Calculation for 31st October 1984:

Given that Indira Gandhi died on 31st October 1984, let's calculate the day of the week using the Zeller's Congruence formula.

- q = 31
- m = 13 (since October is counted as the 13th month of the previous year)
- K = 84
- J = 19

Substituting the values into the formula:
\[ h = \left(31 + \left\lfloor \frac{13(13+1)}{5} \right\rfloor + 84 + \left\lfloor \frac{84}{4} \right\rfloor + \left\lfloor \frac{19}{4} \right\rfloor - 2(19) \right) \mod 7 \]

Simplifying the formula:
\[ h = \left(31 + \left\lfloor \frac{169}{5} \right\rfloor + 84 + 21 + 4 - 38 \right) \mod 7 \]
\[ h = \left(31 + 33 + 84 + 21 + 4 - 38 \right) \mod 7 \]
\[ h = 135 \mod 7 \]
\[ h = 1 \]

Therefore, the day of the week for 31st October 1984 is Sunday (option A).