The greatest term in the expansion of 51+1520is :

We have Tr+1=20Cr5(5)r=20Cr1(5)r−1Suppose (r + 1)th term is the greatest term. ThenTr+1Tr>1 and Tr+1Tr+2>1⇒20−rr+115>1 and r+219−r5>1⇒20−r>5r+5 and r5+25>19−r⇒19−25<(5+1)r<20−5⇒14(19−25)(5−1)