It is known that in the expansion (a+b)n if n is even, then the middle terms is (n2+1)th term.
Therefore, the middle term in the expansion of (x3+9y)10 is (102+1)th term
which is, T6=T5+1=10C5(x3)10−5(9y)5=10!5!5!.x535.95.y5
=10.9.8.7.6.5!5.4.3.2.5!135.310.x5y5
=252×35.x5.y5=61236x5y5
Thus the middle term in the expansion of (x3+9y)10 is 61236x5y5