Meher finds this old newspaper at home. Using its date, on which day of the week was Children's Day (14 November) that year?

From 5 September to 14 November is $25+31+14=70$ days (25 left in September, 31 in October), and $70=10\times 7$. So 14 November is the same weekday as the newspaper: Sunday. (Monday takes September as 31 days.)