Hi.

 

2¹⁹⁹⁰=(1+1)¹⁹⁹⁰

 

=>1990C0+1990C1+1990C2+.......+1990C1989 + 1990C1990

 

=>1 + 1990C1 + 1990C2........1990C1989 + 1

 

Now except for the first and last terms all terms are divisible by 1990

 

{all will have 1990! in the numerator which is obviously divisible by 1990}

 

=> so when you divide 2 by 1990 the remainder is 2