Question

The number of irrational terms in the expansion of `(2^(1//5) + 3^(1//10))^(55)` is
A. 47
B. 56
C. 50
D. 48

Answer 1

Correct Answer - 3
`T_(r+1) =.^(55)C_(r) .(2)^((55-r)/(5)) .(3)^((r)/(10))`
(i) `(2)^((55-r)/(5)) in Z if r=0, 5,10,15, 20,.....,55`
(ii) `(3)^((55-r)/(5)) in Z if r=0, 10,20,30,40,50`
`therefore` finally r= 0, 10,20,30,40,50 so that term will become integer
`therefore` no. of radtional terms=6
`therefore` no.of irrational terms = (56) - 6= 50