Question

The product of last 2 digits of \((1919)^{1919}\) is

(1) 56

(2) 63

(3) 45

(4) 54

Answer 1

Correct option is: (2) 63  

\((1920-1)^{1919}={ }^{1919} \mathrm{C}_{0}(1920)^{1919}-{ }^{1919} \mathrm{C}_{1}(1920)^{1918}+\ldots .\ldots { }^{1919} \mathrm{C}_{1918}(1920)^{1}-{ }^{1919} \mathrm{C}_{1919}{ }^{1}\)

Last two digits \({ }^{1919} \mathrm{C}_{1918}(1920)-1\)  

= 3684479