The correct option is C 501
The general term in the expansion of (91/4+81/6)1000 is
Tr+1=1000Cr(914)1000−r(816)r
=1000Cr31000−r2212
The above term will be rational if exponent of 3 and 2 are integers.
It means 1000−r2 and r2 must be integers
The possible set of values of r is {0,2,4,....,1000}
Hence, number of rational terms is 501.