The general term in the expansion of (91/4 + 81/6)1000 is
The above term will be rational if exponent of 3 and 2 are integers
It means 1000 - r/2 and r/2 must be integers.
The possible set of values of r is {0, 2, 4, ............, 1000}
Hence, number of rational terms is 501.