Question

The greatest term in expansion of (3+5x)¹⁵ is ____ where x = 1/5

(a) ¹⁵C₃ (3¹³) 

(b) ¹⁵C₄ (3¹²) 

(c) ¹⁵C₄ (3¹⁰) 

(d) ¹⁵C₄ (3¹¹)

Answer 1

Correct option: (d) ¹⁵C₄ (3¹¹)

Explanation:

given (3 + 5x)¹⁵ and x = (1/5)

k  = [{(n + 1)y} / {x + y}]

= [{(15 + 1){5 × (1/5)}} / {3 + {5 × (1/5)}}]

= (16 / 4)

= 4

∴  Greatest term is 4^th & 5^th term.

and T₅ = ¹⁵C₄ (3)^15–4 ∙ [5 × (1/5)]⁴ 

= ¹⁵C₄ (3¹¹)