The sum of the rational terms in the expansion of (2+35)10, is

Let Tr+1 be (r+1)th term in the expansion of(2+35)10. ThenTr+1=10Cr(2)10−r(35)r=10Cr×25−r/2×3r/5Here, 0≤r≤10For Tr+1 to be rationalr2and r5must be integers. ⇒ r must be a multiple of 10 and 0≤r≤10⇒ r=0, 10Thus, T1and T11 are rational terms. Now,T1+T11=10C0× 25× 30+ 10C10× 20× 32= 25+ 9=41