If in the expansion of a13+b196561 ; where a,b are distinct prime numbers, the number of  irrational terms is N, then the value of N100 is

Given expansion is a13+b196561Tr+1=6561Cra136561−r(b)r9=6561Cr(a)(6561−r)3(b)r9∵In⁡(x+a)n expansion ,Tr+1=nCrxran−r Since, Tr+1 will be integral if r9 and 6561−r3 both are integers ⇒r=0,9,18,……,6561∴ Number of values of r=65619+1=730 So, number of irrational terms =6562−730=5832⇒N100=5832100=58.32Therefore, the correct answer is 58.32