Binomial Theorem Part 1

(31/4+51/8)60
By using Binomial expansion, (r+1) th term,
Tt+1=‌60Cr(31/4)t(51/8)60−t=‌60Cr3t/45‌

60−t

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.