The number of irrational terms in the expansion of 51/6+21/8100is

Tr+1, the (r+1)th the expansion of 51/6+21/8100 is given by                            Tr+1=100Cr51/6100−r21/8rAs 5 and 2 are relatively prime, Tr+1 will be rational if 100-r6and r8 are both integers. i.e. if 100-r is a multiple of 6 and r is multiple of 8. As 0≤r≤100, multiples of 8 upto 100 and corresponding value of 100-r are          r=0,8,16,24,…,88,96100−r=100,92,84,76,…,12,4Out of these values for 100-r, multiples of 6 are 84, 60, 36, 12∴  there are just four rational terms in the expansion of 51/6+21/8100.⇒  number of irrational terms is 101-4=97