Question

Number of rational terms in expansion of (4^1/5 + 7^1/10)⁴⁵ = .......

(a) 40 

(b) 5 

(c) 41 

(d) 8

Answer 1

Correct option: (c) 41

Explanation:

T_r+1  = ⁴⁵c_r [4^(1/5)]^45–r [7^(1/10)]^r 

= ⁴⁵c_r 4^[9–(r/5)] ∙ 7^(r/10) 

i.e. r is multiple of 5 and 10

i.e. r is multiple of 10 and 0 ≤ r ≤ 45

∴  r = 0, 10, 20, 30 or 40

∴   Rational terms = 5

∴  Irrational terms = 46 – 5 = 41