The correct option is B 20C727
Let (r+1)th term be the greatest term in the expansion of (1+1√3)20.
So, Tr+1Tr=20−r+1r(1√3)≥1
⇒20−r+1≥√3r
⇒21≥r(√3+1).
⇒r≤21√3+1
⇒r≤7.686
So, the greatest term occurs when r=7.
Hence, the greatest term in √3(1+1√3)20 is
T8=√3 20C7(1√3)7= 20C727