Explanation:

- Let's first find the total number of days between 15 July 2002 (Monday) and 16 October 2005.

- From 15 July 2002 to 15 July 2005 = 3 years. 2004 is a leap year. Total days: (2×365) + 366 = 1096 days.

- From 15 July 2005 to 16 October 2005:

- 15 July to 15 August: 31 days

- 15 August to 15 September: 31 days

- 15 September to 15 October: 30 days

- 15 October to 16 October: 1 day

- Total: 31+31+30+1 = 93 days.

- Total days in between = 1096 + 93 = 1189 days.

- Find the remainder on dividing 1189 by 7: 1189 ÷ 7 = 169 weeks and 6 days.

- Add 6 days to Monday: Monday ? Tuesday (1), Wednesday (2), Thursday (3), Friday (4), Saturday (5), Sunday (6).

- So, 16 October 2005 will be Sunday.

Option:1, Sunday is correct.