What will be the day of the week on 1st January, 2010?

2000 years have 2 odd days.

$$\begin{gathered} \mathrm{Year} 2001 2002 2003 2004 2005 2006 2007 2008 2009 \\ \mathrm{Odd} \mathrm{days} 1 1 1 2 1 1 1 2 1 \end{gathered}$$

= 11 odd days = 4 odd days

1st January, 2010 has1odd day. Total number of odd days

$=(2+4+ 1)=7=0.$

$\therefore$1st January, 2010 will be Sunday