Question

Number of rational terms in expansion of (41/5 + 71/10)45 = .......

(a) 40

(b) 5

(c) 41

(d) 8

Answer 1

Correct option: (c) 41

Explanation:

Tr+1 = 45cr [4(1/5)]45–r [7(1/10)]r

= 45cr 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