Mark the correct alternative in the following :

The number of irrational terms in the expansion of is

A. 40

B. 5

C. 41

D. None of these

Given:

Total number of terms in expansion =n+1

=45+1

=46

irrational terms = total terms – rational terms

For rational terms; the power of each term should be integer.

Therefore, k must be divisible by 5 and (45-k) by 10.

i.e. the terms having power as multiples of 5.

i.e. 0,5,10,15,20,25,30,35,40 & 45

for k= 5,15,25,35 & 45;

(45-k) do not give an integral power, so these powers have to be rejected.

Now, we have k= 0,10,20,30 & 40 which give us rational terms.

Hence, irrational terms = 46-5 = 41