01 is the correct ans...
Below i have given a try to come up with the same using binomial expansion...
7 ^ (2008) = 7 ^(4*251) = (7^4)^(251) = (2401)^(251) ....
2401 ^ 251 = (2400 + 1)^251
= Summation [ 251(C)X * (2400^X) * (1^(251 - X)) ]
(X = 0 to 251)
As it is obvious from the above term that when X >= 1 , each term will be a multiple of 100 as it will contain 2400 as a factor.. the only term which won't have 2400 as a factor is the first term when X = 0 and the value of term will be 1...
Therefore, 7 ^ (2008) = K * 100 + 1.... where K is a natural no...