11^2003 gives remainder 1.

Cyclicity of 7 is 4n+1
7^4n gives last digit 1.Therefore 7^(4*501) gives last digt 1.

Cyclicity of 3 is 4n+1.
3^(4*501+1) gives remainder 3.

The final remainder (1*1*3)=3.(According to remainder theorem)...........You can get this theorem from any kind of good CAT Quantitative Book..........
Happy Solving..........................

Thank you
Dipanjan.............