(31∕4+51∕8)60 By using Binomial expansion, (r+1) th term, Tr+1=60Cr(31∕4)r(51∕8)60−r =60Cr3r∕45
60−r
8
For this term to be a rational number, r should be a multiple of 4 and (60−r) should be a multiple of 8 . Let A be a set when r is the multiple of 4 . A={4,8,12,...,56,60} n(A)=15 Let B be a set of r, when (60−r) is the multiple of 8 . B={4,12,20,28,36,44,52,60} n(B)=8 Now, n(A∩B)=8 So, there are only 8 terms out of 61 terms which will be rational numbers. 53 terms will be irrational. So, n=53
and n−1=52 which is divisible only by 26 among the given options.